Seminars this semester

Jan 29	Wed	K.S.Williams (Carleton, Ottawa)
16:00		Continued fractions and Eisenstein's problem
Feb 19	Wed	M.M.Dodson (York)
16:00		Covers, $s$-lengths and order
Feb 26	Wed	Peter Kropholler (QMW)
16:00		Bounded cohomology
Mar 4	Wed	David Jordan (Sheffield)
16:00		Iterations of automorphisms and representations of rings
Mar 18	Wed	John Greenlees (Sheffield)
16:00		Groups and spheres
May 6	Wed	P.Gruber (Vienna)
16:00		Modern and classical aspects of the geometry of numbers
May 20	Wed	E.Kappos (Sheffield)
16:00		Dynamical systems approach to nonlinear control theory
Jun 24	Wed	T.Lau (Alberta)
16:00		Invariant subalgebras and subgroups of locally compact groups
Oct 14	Wed	A.Sudbery (York)
16:00		Quantum groups
Oct 28	Wed	Victor Bryant (Sheffield)
16:00		Two interesting matroid problems
Nov 11	Wed	Richard Pinch (Cambridge)
16:00		Pseudoprimes and Carmichael numbers
Nov 25	Wed	C.A.McGibbon (Wayne State)
16:00		Algebraic limits and infinite dimensional spaces
Dec 2	Wed	Martin Holland (Sheffield)
16:00		Differential operators, curve singularities and finite dimensional algebras
Jan 20	Wed	K.A.Brown (Glasgow)
16:00		What is a quantum group?
Feb 3	Wed	B.D.Mestel (Exeter)
16:00		An application of dynamical systems theory to adaptive control
Feb 17	Wed	A.J.Granville (Georgia)
16:00		Primality testing and Carmichael numbers
Feb 24	Wed	David Benson (Oxford)
16:00		Primality testing and Carmichael numbers
Mar 10	Wed	M.Brodmann (Z)
16:00		Bounds for the cohomology of projective varieties
Mar 16	Tue	V.Lyubashenko (York)
16:00		Algebra of functions on a quantum group at a root of unity
May 19	Wed	Peter Dixon (Sheffield)
16:00		Varieties of Banach algebras
May 26	Wed	M.Herrmann (K)
16:00		On the blowing-up of powers of ideals
May 26	Wed	N.V.Trung (Hanoi)
16:00		Criteria for Gorenstein Rees algebras
Oct 20	Wed	C.J.H.MacDiarmid (Oxford)
16:00		Age-dependent branching processes; recent improved estimates
Oct 27	Wed	D.Burns (KCL)
16:00		Adams operations, cannabalistic classes and integral representations
Nov 17	Wed	Shaun Bullett (QMW)
16:00		Mating quadratic maps with the modular group
Dec 1	Wed	Bruce Westbury (Nottingham)
16:00		State sum model invariants of 3-manifolds
Feb 2	Wed	David Mond (Warwick)
16:00		The geometry of free divisors
Feb 9	Wed	Ronnie Brown (Bangor)
16:00		Holonomy, foliations and groupoids
Feb 16	Wed	Jeremy Rickard (Bristol)
16:00		What could be simpler than the trivial module?
Mar 9	Wed	M.P.Brodmann (Z)
16:00		Blowing-ups and their visualisation by computer
Mar 9	Wed	T.Albu (Bucharest and Glasgow)
16:00		Krull dimension, dual Krull dimension, and the Hopkins-Levitzki theorem
Mar 16	Wed	L.Beineke (Purdue and Oxford)
16:00		A survey of graph decompositions
May 4	Wed	D.Strauss (Hull)
16:00		The semigroup $\beta\mathbb{N}$
Jun 2	Thu	Andy Baker (Glasgow)
16:00		Vertex operators in algebraic topology
Jun 2	Thu	Neil Strickland (MIT)
16:00		Isogenies and Dyer-Lashof operations in $E_n$-theory
Oct 4	Tue	P.Polo (Pierre et Marie Curie, CNRS)
16:00		K-theory of twisted differential operators on complete homogeneous spaces
Oct 5	Wed	T.Bridgeman (Liverpool)
16:00		The marking of examination papers
Oct 19	Wed	M.V.Karasev (Moscow)
16:00		Noncommutative products of functions defined by ``membranes'' and ``strings''
Oct 26	Wed	M.Hirsch (Berkeley)
16:00		Fixed points of monotone mappings
Nov 2	Wed	P.J.Rippon (OU)
16:00		On the boundary of certain Siegel discs
Nov 9	Wed	A.King (Liverpool)
16:00		The cohomology rings of moduli spaces
Nov 23	Wed	J.Cremona (Exeter)
16:00		The arithmetic of elliptic curves
Jan 11	Wed	G.R.Robinson (Leicester)
16:00		On eigenvalues of elements of finite linear groups
Feb 22	Wed	Karen Smith (MIT)
16:00		Prime characteristic techniques in the study of algebraic varieties over the complex numbers
Mar 1	Wed	Y.Kosman-Schwarzbach (Paris)
16:00		Poisson geometry and odd Poisson brackets
Mar 8	Wed	L.Avramov (Purdue)
16:00		Hilbert series and Laurent coefficients of graded modules
Mar 9	Thu	L.Avramov (Purdue)
16:00		L.c.i. homomorphisms and vanishing of André-Quillen homology
May 10	Wed	T.Thompson (Dalhousie)
16:00		When are soap bubbles spheres? -- an excursion into other normed spaces
May 15	Mon	T.Bier (Ulm)
16:00		Existence and nonexistence of magic structures
May 17	Wed	Grant Walker (Manchester)
16:00		Modular analogues of classical symmetric functions
May 24	Wed	M.Cannell (George Green Memorial Fund)
16:00		George Green, mathematician and physicist, 1793--1840; the background to his life and work
May 31	Wed	I.Anderson (Glasgow)
16:00		Remarkable revelations concerning Kirkman's schoolgirls
Oct 4	Wed	D.Woodcock (QMW)
16:00		The partition algebra as a `deformation' of the Schur algebra
Oct 11	Wed	C.M.Wood (York)
16:00		Energy in geometry
Oct 18	Wed	R.J.Sharp (Manchester)
16:00		Zeta functions, closed geodesics and periodic orbits of dynamical systems
Oct 25	Wed	E.C.Lance (Leeds)
16:00		Compact quantum groups
Nov 1	Wed	K.M.Ball (UCL)
16:00		The reverse isoperimetric problem
Nov 8	Wed	Jeremy Gunawardena (Hewlett-Packard)
16:00		Dynamics of nonexpansive maps
Nov 15	Wed	John Greenlees (Sheffield)
16:00		Algebraic shadows of equivariant topology
Nov 29	Wed	H.Petzl (Utrecht)
16:00		Cousin complexes and flat ring extensions
Dec 6	Wed	Bill Crawley-Boevey (Leeds)
16:00		General representations of quivers
Jan 31	Wed	K.Mischaikow (Georgia Institute of Technology)
16:00		Chaotic dynamics and the Conley index
Feb 13	Tue	M.Brodmann (Z)
16:00		A survey of local cohomology and connectivity in algebraic varieties
Feb 21	Wed	E.J.Beggs (Swansea)
16:00		Soliton interactions in the principal chiral model
Feb 28	Wed	K.Erdmann (Oxford)
16:00		Representations of general linear groups and symmetric groups
Mar 4	Mon	C.Le Merdy (France-Comte)
16:00		Operator algebra structures on commutative and noncommutative $\ell^p$
Apr 24	Wed	Reg Wood (Manchester)
16:00		Differential operators and the Steenrod algebra
May 8	Wed	D.Salomon (Warwick)
16:00		Floer homology and the general Arnold conjecture
May 15	Wed	S.M.Rees (Liverpool)
16:00		Some new examples of convergence groups
May 22	Wed	T.Bier (Sheffield)
16:00		Permutations and posets
Aug 21	Wed	M.Filali (Oulu)
16:00		On the semigroup $\beta$S and some applications
Oct 9	Wed	Victor Flynn (Liverpool)
16:00		Rational points on curves
Oct 23	Wed	J.Roberts (Edinburgh)
16:00		Moduli spaces of flow graphs and 3-manifold invariants
Oct 30	Wed	David Mond (Warwick)
16:00		Families of free divisors
Nov 12	Tue	Y.V.Selivanov (Moscow)
16:00		Biprojective topological algebras
Nov 20	Wed	Ronnie Brown (Bangor)
16:00		A non-abelian tensor product of groups
Nov 27	Wed	J.C.McConnell (Leeds)
16:00		Effective calculation -- first steps in Gröbner bases
Dec 11	Wed	A.K.Austin (Sheffield)
16:00		Mathematical proof -- what shall we tell the students?
Jan 29	Wed	A.S.Dzhumadil'daev (Alma-Ata)
16:00		Lie algebroids, cohomologies and noncommutative Lie algebras
Feb 26	Wed	R.Marsh (Glasgow)
16:00		Quantum groups and canonical bases
Mar 5	Wed	Roger Webster (Sheffield)
16:00		Log-convex solutions to $f(x+1)=g(x)f(x)$ -- $;amma$-type functions
Apr 16	Wed	V.Goryunov (Liverpool)
16:00		Plane curves and Legendrian knots
Apr 23	Wed	J.F.McKee (Edinburgh)
16:00		Factoring on a desert island
May 7	Wed	F.Vivaldi (QMW)
16:00		Discrete dynamics and algebraic numbers
May 7	Wed	P.Shiu (Loughborough)
16:00		A remarkable function from Diophantine Approximations (the devil's staircase and an angel's ladder)
May 14	Wed	A.West (Leeds)
16:00		Surfaces which do not intersect their focal set
May 21	Wed	Jon Carlson (Athens)
16:00		Computers, polynomial rings and group cohomology
Jun 2	Mon	Peter May (Chicago)
16:00		Equivariant topology and nonequivariant applications
Oct 21	Wed	John Hunton (Leicester)
16:00		Quasi-periodic tilings and homotopy theory
Oct 28	Wed	A.J.Power (Edinburgh)
16:00		Higher dimensional categories
Nov 11	Wed	I.Gordon (Edinburgh)
16:00		Representations of quantum groups at roots of unity
Nov 25	Wed	Kevin Buzzard (Imperial)
16:00		Artin's conjecture on L-functions
Dec 2	Wed	Niall Mackay (Sheffield)
16:00		Yangians and Dorey's rule
Dec 9	Wed	W.W.Wheeler (Leicester)
16:00		Infinite dimensional modules for finite groups
Jan 20	Wed	Kirill Mackenzie (Sheffield)
16:00		Notions of double
Feb 3	Wed	S.Merkulov (Glasgow)
16:00		Strong homotopy and Gerstenhaber-Batalin-Vilkovoski algebras of a Kähler manifold
Feb 17	Wed	M.Weber (Dresden)
16:00		On finite elements in vector lattices
Mar 3	Wed	P.Shiu (Loughborough)
16:00		Problems on sums of two squares
Mar 10	Wed	G.A.Jones (Southampton)
16:00		Dessins d'enfant: geometric actions of Galois groups
Apr 28	Wed	J.C.Robson (Leeds)
16:00		Dedekind-like noncommutative rings
May 12	Wed	I.R.Porteous (Liverpool)
16:00		Robust features of surfaces in $\mathbb{R}^3$
May 19	Wed	Burt Totaro (Cambridge)
16:00		Singular algebraic varieties and elliptic cohomology
May 26	Wed	K.A.Brown (Glasgow)
16:00		Some current themes in representation theory
Oct 13	Wed	Michael Weiss (Aberdeen)
16:00		Homotopy theoretic analysis of spaces of smooth embeddings
Oct 20	Wed	R.Green (Lancaster)
16:00		Quantum algebras at $v=\infty$
Nov 3	Wed	Srikanth Iyengar (Sheffield)
16:00		Intersection theorems in commutative algebra
Nov 17	Wed	A.Borovik (UMIST)
16:00		Probabilistic recognition of black box groups
Nov 24	Wed	John Pym (Sheffield)
16:00		The Ellis semigroup of the action of a connected semisimple Lie group on a maximal compact subgroup
Dec 8	Wed	Ulrike Tillmann (Oxford)
16:00		Moduli spaces of Riemann surfaces and CFT
Dec 15	Wed	H.Hauer (Nottingham)
16:00		Generalised Riemann-Roch formulas
Feb 9	Wed	Susan Howson (Nottingham)
16:00		Non-Abelian Iwasawa theory and applications to elliptic curves
Feb 16	Wed	M.Brodmann (Z)
16:00		Associated primes of local cohomology modules
Feb 18	Fri	Larry Smith (G)
16:00		Coinvariants, Jacobians and Poincaré duality
Mar 1	Wed	Ronnie Brown (Bangor)
16:00		Non-abelian methods for computing modules of identities among relations for presentations of groups: crossed complexes
Mar 15	Wed	A.Henke (Kassel)
16:00		The Sierprinski gasket, representations and the symmetric group
Mar 22	Wed	Ian Grojnowski (Cambridge)
16:00		Rigid structure and the symmetric group
Apr 5	Wed	Y.Kosmann-Schwarzbach (Ecole Polytechnique)
16:00		Poisson homogeneous spaces
May 3	Wed	Moty Katzman (Sheffield)
16:00		Edge algebras which are complete intersections
May 10	Wed	Ran Levi (Aberdeen)
16:00		The spaces of equivalences between $p$-completed classifying spaces
May 22	Mon	K.Mischaikow (Georgia Institute of Technology)
16:00		Rigorous computation of low-dimensional dynamics and the combinatorial geometry of flows
Sep 27	Wed	A.Frankild (Copenhagen)
16:00		Vanishing of local homology and some applications
Oct 2	Mon	J.Br (Stuttgart)
16:00		Almost periodic sequences. binary additive problems and the circle method
Oct 11	Wed	Roger Plymen (Manchester)
16:00		The Baum-Connes conjecture and the local Langlands conjecture for GL(n): are they related?
Oct 17	Tue	P.Jorgensen (Copenhagen)
16:00		Spectra of modules
Oct 18	Wed	P.Covey-Crump (GCHQ)
16:00		Campanology and mathematics
Nov 1	Wed	H.Khudaverdyan (visiting UMIST)
16:00		Batalin-Vilkovisky formalism geometry and semidensities of odd symplectic manifolds
Nov 15	Wed	Hellen Colman (Sheffield)
16:00		LS-category of compact Hausdorff foliations
Nov 22	Wed	S.Hurder (Chicago)
16:00		Foliations: at the crossroads of geometry and topology
Nov 22	Wed	Imre Leader (Cambridge)
16:00		Set systems with few disjoint pairs
Nov 29	Wed	J.Cremona (Nottingham)
16:00		Reduction of binary forms--how to find small equations for hyperelliptic curves
Dec 6	Wed	David Jordan (Sheffield)
16:00		Rings generated by Eulerian derivatives
Dec 13	Wed	A.Wilkie (Oxford)
16:00		Tame topology and O-minimal structures
Feb 7	Wed	S.Koenig (Leicester)
16:00		Schur-Weyl duality and dominant dimension
Feb 14	Wed	Vladimir Bavula (Sheffield)
16:00		Holonomic D-modules, the Dixmier problem and the Jacobian conjecture
Feb 28	Wed	A.Volovikov (Steklov, visiting Liverpool)
16:00		Indexes of G-spaces
Mar 7	Wed	V.Nikulin (Liverpool)
16:00		A theory of Lorenzian (or hyperbolic) Kac-Moody algebras
Mar 13	Tue	Matthew Ando (Urbana)
16:00		Equivariant elliptic cohomology of spin bundles
Mar 14	Wed	Alan Camina (UEA)
16:00		Sizes of conjugacy classes - what do they tell us about the structure of finite groups?
Mar 20	Tue	W.Timmermann (Dresden)
16:00		Mathematical structures in quantum physics - some historical remarks
Mar 21	Wed	B.Zilber (Oxford)
16:00		Logic and Schanuel-type conjectures
Mar 28	Wed	S.Galbraith (Bristol)
16:00		Abelian varieties and cryptography
Apr 4	Wed	Andrew Pressley (KCL)
16:00		Representations of quantum affine algebras
May 2	Wed	Charles Thomas (Cambridge)
16:00		Geometric structures on fake projective and lens spaces
May 9	Wed	John Greenlees (Sheffield)
16:00		Old and new dualities in algebra and topology
May 16	Wed	Marian Anton (Sheffield)
16:00		Undetected general linear group cohomology
May 17	Thu	H.-B.Foxby (Copenhagen)
16:00		Properties of homomorphisms in commutative algebra
Oct 3	Wed	S.Donkin (QMW)
16:00		Some remarks on cohomology of line bundles on flag varieties
Oct 10	Wed	B.Koeck (Southampton)
16:00		Computing the homology of Koszul and Dold-Puppe complexes
Oct 17	Wed	M.Mackaay (Nottingham)
16:00		Categorical groups in differential geometry and 4-dimensional geometry
Oct 24	Wed	Ieke Moerdijk (Utrecht)
16:00		Models for the leaf spaces of a foliation
Nov 7	Wed	G.Robinson (Birmingham)
16:00		Local structure and blocks
Nov 13	Tue	M.Brodmann (Z)
16:00		Bounding sheaf cohomology by the diagonal
Nov 14	Wed	J.Keating (Bristol)
16:00		Random matrix theory and $\zeta(1/2+it)$
Nov 20	Tue	R.Hill (UCL)
16:00		The Kubota symbol on $SL_n$
Nov 26	Mon	K.Mischaikow (Georgia Institute of Technology)
16:00		Searching for holes and volumes: biomedical imaging and computational topology
Dec 5	Wed	Frank Neumann (Leicester)
16:00		Etale homotopy and moduli of stacks
Dec 12	Wed	Imma Galvez (Sheffield)
16:00		Elliptic genera and invariants of manifolds with boundary
Dec 19	Wed	Rachel Camina (Cambridge)
16:00		Linearity of pro-p-groups
Feb 12	Tue	Angus MacIntyre (University of Edinburgh)
16:00		Connections between Schanuel's Conjecture and Logic.
Feb 13	Wed	M.Gross (Warwick)
16:00		Topological mirror symmetry
Feb 19	Tue	Johannes Kellendonk (University of Cardiff)
16:00		Topological aspects of aperiodic ordered systems.
Feb 20	Wed	Alan Camina (Sheffield)
16:00		Pro-$p$-groups of finite width
Feb 26	Tue	Aidan Schofield (University of Bristol)
16:00		Noncommutative moduli spaces of vector bundles
Feb 27	Wed	Ian Stewart (Leicester)
16:00		Finite model theory, complexity theory and program schemes (The MathFIT initiative)
Mar 5	Tue	Tom Lenagan (University of Edinburgh)
16:00		Noncommutative Dehomogenisation
Mar 6	Wed	C.Cocks (GCHQ)
16:00		Recent developments in identifier-based public key cryptosystems
Mar 13	Wed	Greg Sankaran (Bath)
16:00		Nef divisors in the moduli of abelian varieties
Mar 19	Tue	Arthur Chatters (University of Bristol)
16:00		Generalised quaternions
Mar 26	Tue	John McCleary (Vassar (Cambridge))
16:00		Hochschild homology and closed geodesics
Apr 2	Tue	Kevin Houston (University of Leeds)
16:00		Images of Maps
Apr 9	Tue	Sarah Whitehouse (Sheffield)
16:00		Hopf algebras related to K-theory.
Apr 17	Wed	Mike Prest (Manchester)
16:00		Gabriel-Zariski spectra of module categories
Apr 24	Wed	Hugh Morton (Liverpool)
16:00		Algebras constructed from knot theory
May 7	Tue	Elizabeth Winstanley (Sheffield, Applied Mathematics)
16:00		1905 and all that: general relativity for algebraists
May 8	Wed	A.Veselov ( Loughborough)
16:00		Algebra and geometry of quantum Calogero-Moser problems
May 14	Tue	George Wilson (Imperial College)
16:00		Differential operators on algebraic varieties
May 15	Wed	L.O'Carroll ( Edinburgh)
16:00		Maximal Cohen-Macaulay modules over hypersurfaces: some algebra, some geometry, some history+D213
May 21	Tue	Simon Willerton (Sheffield)
16:00		Connections on gerbes
May 22	Wed	N.Yui (Queen's)
16:00		Mirror moonshine phenomena
Sep 25	Wed	Mr A Middleditch (Sheffield)	Applied Mathematics Colloquium
		Measuring ocean surface currents using HF radar
Oct 2	Wed	Prof Ronald Smith (Loughborough)	Applied Mathematics Colloquium
		The optimal compact finite-difference scheme for the diffusion equation with flow
Oct 2	Wed	T.Ward (UEA)
16:00		Commuting maps and commutative algebra
Oct 9	Wed	Dr Makis Kappos (Sheffield)	Applied Mathematics Colloquium
		Singularities, Far and Near
Oct 9	Wed	Ian Leary (Southampton)
16:00		An introduction to $L^2$ homology
Oct 16	Wed	Lars Hesselholt (MIT)
16:00		Algebraic K-theory and trace invariants
Oct 23	Wed	Dr I. Ballai (Sheffield)	Applied Mathematics Colloquium
		Coronal Seismology
Oct 23	Wed	Brooke Shipley (Purdue)
16:00		Rings up to homotopy
Oct 30	Wed	Dr D. Roscoe (Sheffield)	Applied Mathematics Colloquium
		Is dark matter the new phlogiston?
Nov 6	Wed	Dr Bill Lionheart (UMIST)	Applied Mathematics Colloquium
		Anisotropic inverse boundary value problems in electromagnetics
Nov 13	Wed	Rick Jardine (Western Ontario)
16:00		Presheaves of chain complexes
Nov 20	Wed	Dr V. Yudovich (Hull)	Applied Mathematics Colloquium
		Co-symmetry and its application in mechanics
Nov 20	Wed	A.Zalesski (UEA)
16:00		Hurwitz groups
Nov 27	Wed	Mr T. Antypas (Athens)	Applied Mathematics Colloquium
		The description of concentration time series of instantaneously released gases in the atmosphere via the proper orthogonal decomposition
Nov 27	Wed	Jan Schroer (Leeds)
16:00		On the Berenstein-Zelevinsky conjecture
Dec 4	Wed	Prof A. Hood (St. Andrews)	Applied Mathematics Colloquium
		Phase mixing: heating mechanism for coronal holes
Dec 4	Wed	Cho-Ho Chu (QMW)
16:00		Harmonic functions and random walks on groups
Dec 11	Wed	Prof Sir J. Kingman (Isaac Newton Institute)	Applied Mathematics Colloquium
		On teaching Poisson processes
Dec 11	Wed	P.Giblin (Liverpool)
16:00		Features of Surfaces
Dec 18	Wed	Frazer Jarvis (Sheffield)
16:00		The Fermat equation over real quadratic fields
Jan 9	Thu	Ieke Moerdijk (Utrecht)
16:00		Lie groupoids, gerbes and nonabelian cohomology
Feb 5	Wed	Dr Kristof Petrovay (Eotvos University, Budapest)	Applied Mathematics Colloquium
		Secondary shear instability in the solar tachocline
Feb 12	Wed	Dr Stephen Belcher (Reading, Meteorology)	Applied Mathematics Colloquium
		The role of surface waves in dynamics of the ocean mixed layer
Feb 19	Wed	Prof Ray Atkin (Sheffield)	Applied Mathematics Colloquium
		Inaugural lecture: Fluids with a future?
Feb 21	Fri	Dr Ingo Mueller-Wodarg (UCL, Atmospheric Physics Laboratory)	Applied Mathematics Colloquium
		The application of General Circulation Models to terrestrial and planetary upper atmospheres
Feb 26	Wed	Prof Vladimir Vladimirov (Hull)	Applied Mathematics Colloquium
		Virial equation in fluid dynamics
Mar 5	Wed	Dr Christos Vassilicos (Imperial College London, Aeronautics)	Applied Mathematics Colloquium
		Turbulent diffusion
Mar 19	Wed	Prof Alan Zinober (Sheffield)	Applied Mathematics Colloquium
		From the brachistochrone to the calculus of variations and modern control theory
Mar 26	Wed	Prof John Gibbon (Imperial College London)	Applied Mathematics Colloquium
		Infinite energy singularity formation in a class of solutions of the 3D Euler equations
Apr 2	Wed	Prof Farideh Honary (Lancaster)	Applied Mathematics Colloquium
		Modern Riometry: techniques and results
May 6	Tue	Prof Xia (China)	Applied Mathematics Colloquium
		Periodic orbits arising from delta-modulated feedback control
May 7	Wed	Prof Shadia Habbal (Aberystwyth, Physics)	Applied Mathematics Colloquium
		The solar wind and the hidden secrets of the Sun
May 14	Wed	Dr Eleri Pryse (Aberystwyth, Physics)	Applied Mathematics Colloquium
		Imaging near-Earth space
May 29	Thu	Dr Louise Harra (UCL, MSSL)	Applied Mathematics Colloquium
		Solar flare and Coronal Mass Ejections
Oct 1	Wed	Dr R. Balthazor (Sheffield)	Applied Mathematics Colloquium
		Modelling the Upper Atmosphere - a historical perspective
Oct 1	Wed	Charudatta Hajarnavis (University of Warwick)
16:00		A symmetry theorem for invertible ideals and its applications.
Oct 8	Wed	Dr N. Mole (Sheffield)	Applied Mathematics Colloquium
		Surface waves in random media: applications to solar physics
Oct 22	Wed	Dr Kristof Petrovay (Eotvos University, Budapest)	Applied Mathematics Colloquium
		The decay of sunspots as a nonlinear turbulent erosion process
Oct 22	Wed	Paul Turner (Heriot-Watt)
16:00		Putting the fields back into Topological Quantum Field Theory
Oct 29	Wed	Prof David Hughes (Leeds)	Applied Mathematics Colloquium
		Large- and small-scale dynamo action
Oct 29	Wed	Peter Rowlinson (Stirling)
16:00		Star complements in finite graphs
Nov 5	Wed	Dr Mervyn Freeman (British Antarctic Survey)	Applied Mathematics Colloquium
		Multi-scale Sun-Earth connections
Nov 5	Wed	Richard Thomas (Imperial)
16:00		Symmetry groups and geometrics PDEs
Nov 12	Wed	Dr John Brooke (CSAR, Manchester)	Applied Mathematics Colloquium
		Using Carrington's Legacy: analysing the spatio-temporal structure of the solar cycle from 1853 to 2003
Nov 19	Wed	Dr Alan Aylward (UCL, Physics and Astronomy)	Applied Mathematics Colloquium
		Solar variability and climate change: what CMAT model can tell us about the possible mechanisms
Nov 19	Wed	Tom Bridgeland (Edinburgh)
16:00		Moduli spaces and birational geometry
Nov 26	Wed	Dr William Wilkinson (CMIS, Brighton)	Applied Mathematics Colloquium
		The Earth's quasi-parallel bow shock: review of observations and outstanding questions
Nov 26	Wed	James McKee (Royal Holloway, University of London)
16:00		Salem numbers via interlacing
Dec 10	Wed	Prof Joe Buckley (Royal Military College of Canada, Physics)	Applied Mathematics Colloquium
		Ocean waves and microwaves
Dec 10	Wed	Peter Kropholler (Glasgow)
16:00		Classifying Spaces for Proper Group Actions
Dec 17	Wed	Dr Michael Warby (Brunel)	Applied Mathematics Colloquium
		The computational modelling of the constrained inflation of solid polymers in the context of thermoforming
Dec 17	Wed	Iain Gordon (Glasgow)
16:00		Symplectic reflection algebras.
Feb 11	Wed	Shahn Majid (Queen Mary, University of London)
16:00		Quantization of differential structures and quasiassociative geometry
Feb 18	Wed	Kohji Yanagawa (University of Osaka, Japan)
16:00		Stanley Reisner rings, Sheaves and Poincare-Verdier Duality
Mar 3	Wed	Roger Heath-Brown (Oxford)
16:00		Geometric problems in analytic number theory
Mar 10	Wed	Dr Itsuki Handoh (Sheffield)	Applied Mathematics Colloquium
		The mid-Cretaceous biogeochemical cycles and climate change
Mar 10	Wed	Colin Ingalls (Warwick)
16:00		Noncommutative Surfaces and Birational Geometry
Mar 17	Wed	Theodore Voronov (UMIST)
16:00		Higher derived brackets and homotopy algebras
Mar 24	Wed	Dr Elizabeth Lucek (ICSTM)	Applied Mathematics Colloquium
		Cluster observations of the Earth's bow shock
Mar 24	Wed	Shaun Bullett (Queen Mary, University of London)
16:00		Dynamics of Holomorphic Correspondences
Mar 31	Wed	Dr John Porrill (Sheffield, Psychology)	Applied Mathematics Colloquium
		Why neuroscience needs mathematicians?
Mar 31	Wed	Gavin Brown (University of Warwick)
16:00		Classification in algebraic geometry.
Apr 28	Wed	Dr David Tsiklauri (Salford, Computer Science and Engineering)	Applied Mathematics Colloquium
		Interaction of Alfven waves with plasma structures
Apr 28	Wed	Elizabeth Winstaley (University of Sheffield)
16:00		To Infinity and Beyond: Local and Global Geometry in General Relativity
May 5	Wed	Prof Slava Kurylev (Loughborough)	Applied Mathematics Colloquium
		Uniqueness and stability in multidimensional inverse problems
May 5	Wed	Kirill Mackenzie (University of Sheffield)
16:00		Duality for double and multiple structures
May 12	Wed	Dr David Roscoe (Sheffield)	Applied Mathematics Colloquium
		Discrete dynamical states in galactic discs: New insights, new data
May 12	Wed	Marcus du Satoy (Oxford)
16:00		Through the looking glass: groups from a number theoretic perspective
May 17	Mon	Vic Snaith (Southampton)
16:00		Stiefel-Whitney classes and symplectic local root numbers
May 19	Wed	Prof Viktor Shrira (Keele)	Applied Mathematics Colloquium
		Quasi-modes in shear flows: a working concept
May 25	Tue	Reinhold H (SAP)
16:00		Evolutions, derivations and differential forms
May 26	Wed	Tony Sudbery (University of York)
16:00		Quantum Information Theory: a confection of mathematics, physics and computer science
May 28	Fri	Linus Kramer (Darmstadt)
16:00		Buildings and Symmetric Spaces: Perspectives and Horizons
Jun 29	Tue	Stefan Bauer (Bielefeld)
16:00		Monopoles and Mergers in four Dimensions
Sep 1	Wed	Dr M. Miesch (HAO/NCAR, Boulder (USA))	Applied Mathematics Colloquium
		Behind the HYPE: A Thin-Shell Model for the Solar Tachocline
Sep 17	Fri	Dr Hien Vo (Aberystwyth)	Applied Mathematics Colloquium
		Various aspects of the plasmasphere using satellite and ground data along with a study of the self-organizing criticality in using global auroral images
Sep 29	Wed	Dr E. Benilov (Limerick)	Applied Mathematics Colloquium
		Explosive instability in linear systems with stable eigenmodes
Sep 29	Wed	Neil Dummigan (Sheffield)
16:00		Elliptic Curves and Modular Degrees
Sep 29	Wed	Neil Dummigan (Sheffield)	Pure Maths Colloquium
16:00		Elliptic Curves and Modular Degrees
		Hicks Seminar Room J11
Oct 6	Wed	Dr R. Kerr (Warwick)	Applied Mathematics Colloquium
		Structure functions as a tool for atmospheric analysis
Oct 6	Wed	Ben Green (Cambridge)	Pure Maths Colloquium
16:00		Arithmetic progressions of primes
		Hicks Seminar Room J11
	Abstract: I will discuss some aspects of the recent proof that there are arbitrarily long arithmetic progressions of primes, which is joint work with Terry Tao. I will also discuss some more recent work of ours, which gives an asymptotic for the number of 4-term APs of primes, all less than N.
Oct 13	Wed	Dr W. Chaplin (Birmingham, Physics and Astronomy)	Applied Mathematics Colloquium
		Sounding the deep solar interior: modern challenges for global Helioseismology
Oct 14	Thu	Bernhard Hanke (Munich)	Pure Maths Colloquium
14:00		Enlargeability and index theory
		Hicks Seminar Room J11
Oct 20	Wed	Dr A. Ferriz-Mas (Vigo, Spain)	Applied Mathematics Colloquium
		Fluid mechanical aspects in solar magnetism: How can magnetic fields of 100 kG be produced?
Oct 20	Wed	Burt Totaro (Cambridge)	Pure Maths Colloquium
16:00		Topological Invariants of Singular Varieties
		Hicks Seminar Room J11
	Abstract: We start with some examples of singularities that algebraic varieties can have in low dimensions. We look at resolutions of singularities, that is, mappings from a smooth manifold onto a singular space. One can try to define invariants of a singular space using known invariants of its resolution. I will describe some successful invariants of this type: intersection homology theory, the elliptic genus, and stringy Betti numbers.
Oct 27	Wed	Prof I. Moss (Newcastle)	Applied Mathematics Colloquium
		Warm inflation and the hot big bang
Oct 27	Wed	Jan Schroer (Leeds)	Pure Maths Colloquium
16:00		Universal Bases for Kac-Moody Lie Algebras
		Hicks Seminar Room J11
	Abstract: The talk aims to explain the connection between the following topics: - Canonical Bases for Kac-Moody Lie Algebras - Representation Theory of Preprojective Algebras - Varieties of Modules.
Nov 3	Wed	Prof G. Tallents (York, Physics)	Applied Mathematics Colloquium
		The opacity of hot dense plasmas: application to laboratory and solar examples
Nov 3	Wed	Roger Plymen (Manchester)	Pure Maths Colloquium
16:00		Two-by-two matrices from two points of view
		Hicks Seminar Room J11
	Abstract: This will mainly be about SL(2,C) and SL(2,R). The first point of view is that of Harish-Chandra, and leads to irreducible unitary representations, the Plancherel measure and the tempered dual. The second point of view is that of Connes and Kasparov, which leads from the reduced C*-algebra back to the representations rings R(SU(2)) and R(SO(2)). I will relate these two points of view, and describe recent results for GL(3) (joint work with Anne-Marie Aubert).
Nov 10	Wed	David Calderbank (Edinburgh)	Pure Maths Colloquium
16:00		Toric selfdual Einstein metrics
		Hicks Seminar Room J11
Nov 11	Thu	Prof S. Quegan (Sheffield)	Applied Mathematics Colloquium
		A short walk around the Carbon cycle
Nov 17	Wed	Peter Larcombe (Derby)	Pure Maths Colloquium
16:00		Some Recent Results on Catalan Numbers and Catalan-Related Sequences
		Hicks Seminar Room J11
	Abstract: In this talk I will give a brief introduction to the well known Catalan number and present research results associated with them, some of which are set in historical context. Two recently announced Catalan-related sequences which arise from elliptic integrals---namely, the so called Catalan-Larcombe-French and Fennessey-Larcombe-French---are then introduced, and their properties discussed.
Nov 18	Thu	Dr N. Mavromatos (King's College, London)	Applied Mathematics Colloquium
		CPT violation and decoherence: is there a chance of observing something?
Nov 24	Wed	Dr P. Browning (UMIST)	Applied Mathematics Colloquium
		Heating the solar corona by nanoflares
Nov 24	Wed	Michael Farber (Durham)	Pure Maths Colloquium
16:00		Topology of Robot Motion Planning
		Lecture Theatre 2, Hicks Building
	Abstract: In the talk I will show that one may predict the character of instabilities of robot's behavior knowing the cohomology algebra of its configuration space.
Nov 26	Fri	Prof P. Diamond (UCSD)	Applied Mathematics Colloquium
		Zonal flows in Laboratory plasmas
Dec 1	Wed	Imre Leader (Cambridge)	Pure Maths Colloquium
16:00		Partition Regular Equations
		Hicks Seminar Room J11
Dec 7	Tue	Alfonso Gracia--Saz (UC Berkeley)
		Duality of triple structures and beyond
	Abstract: A double vector bundle is a commutative diagram $$\xymatrix{ D \ar[r] \ar[d] & B \ar[d] \\ A \ar[r] & M }$$ where every vertex is a smooth manifold, every edge is a vector bundle, plus compatibility conditions between the two structures on $D$. $D$ can be dualized with respect to these 2 structures. These 2 dualization operations have order 2, but do not commute, and generate a group isomorphic to the symmetric group $S_3$. Mackenzie found a geometric interpretation and started the study of triple vector bundles, which is not a straightforward generalization. We will show recent work on the calculation of the group generated by the $n$ dualizations of a $n$--fold vector bundle, which turns out to be a central extension of $S_{n+1}$ by ${n\choose 2} - 1$ copies of $C_2$.
Dec 8	Wed	Dr E. Winstanley (Sheffield)	Applied Mathematics Colloquium
		What Hawking did: why all the fuss in Dublin?
Dec 8	Wed	Dave Applebaum (Sheffield)	Pure Maths Colloquium
16:00		Harmonic Analysis of Semigroups of Measures on Locally Compact Groups
		Hicks Seminar Room J11
Dec 15	Wed	Dr C. van de Bruck (Sheffield)	Applied Mathematics Colloquium
		Cosmology and Extra Dimensions
Dec 15	Wed	Victor Flynn (Liverpool)	Pure Maths Colloquium
16:00		Visualisation in Higher Genus
		Hicks Seminar Room J11
Jan 13	Thu	Larry Smith (G)
16:00		Macaulay Duals for Hilbert Ideals of Reflection Groups
		Hicks Seminar Room J11
Feb 1	Tue	Samuel W (Sheffield)	Topology Seminar
16:00		I-adic towers and Koszul complexes in algebra and topology
		Hicks Seminar Room J11
Feb 8	Tue	Samuel W (Sheffield)	Topology Seminar
14:00		I-adic towers and Koszul complexes in algebra and topology
		Hicks Seminar Room J11
Feb 9	Wed	Dr J. J. Healey (Keele)	Applied Mathematics Colloquium
		A strange instability with growth normal to a boundary layer
Feb 9	Wed	Victor Snaith (Sheffield)	Pure Maths Postgraduate Seminar
12:00		Algebraic topology at work: the non-existence of maps of Hopf invariant one
		Hicks Seminar Room J11
Feb 9	Wed	Peter Cameron (Queen Mary)	Pure Maths Colloquium
16:00		The Rado graph and the Urysohn space
		Hicks Seminar Room J11
Feb 14	Mon	Moty Katzman (Sheffield)	Algebra / Algebraic Geometry seminar
16:10		Graphs and their ideals
		Hicks Seminar Room J11
Feb 15	Tue	Samuel W (Sheffield)	Topology Seminar
14:00		I-adic towers and Koszul complexes in algebra and topology
		Hicks Seminar Room J11
Feb 16	Wed	Dr D. Roscoe (Sheffield)	Applied Mathematics Colloquium
		Reaction in classical electrodynamics
Feb 16	Wed	Sam Marsh (Sheffield)	Pure Maths Postgraduate Seminar
12:10		$F_{l}$-representations of finite abelian $p$-groups
		Hicks Seminar Room J11
	Abstract: to appear
Feb 16	Wed	Rob de Jeu (Durham)	Pure Maths Colloquium
16:00		Algebraic K-theory of number fields, regulators, zeta- functions,....
		Hicks Seminar Room J11
	Abstract: We discuss relations between the K-theory of number fields and their zeta functions, both classically and (more conjecturally) p- adically. Apart from talking about the theoretical description of those regulators we also touch upon aspects on how to compute them in practice.
Feb 21	Mon	Victor Snaith (Sheffield)	Algebra / Algebraic Geometry seminar
16:10		Stickelberger series Part IV
		Hicks Seminar Room J11
Feb 22	Tue	Samuel W (Sheffield)	Topology Seminar
14:00		I-adic towers and Koszul complexes in algebra and topology
		Hicks Seminar Room J11
Feb 23	Wed	Dave Barnes (Sheffield)	Pure Maths Postgraduate Seminar
12:10		Rational homotopy of spheres
		Hicks Seminar Room J11
Feb 28	Mon	Victor Snaith (Sheffield)	Algebra / Algebraic Geometry seminar
16:10		Stickelberger V
		Hicks Seminar Room J11
	Abstract: This is the last in the Stickelberger series. In this one, finally the BIG CONJECTURE will be revealed and a sketch proof of the evidence for it will be given.
Mar 1	Tue	Neil Strickland (Sheffield)	Topology Seminar
14:00		Morava K-theory I
		Hicks Seminar Room J11
	Abstract: I will give a series of three or four lectures introducing Morava K-theory and Morava E-theory.
Mar 2	Wed	Dr J. Kaplunov (Manchester)	Applied Mathematics Colloquium
		Explicit asymptotic models for surface elastic and electroelastic waves
Mar 2	Wed	Nong Sasom (Sheffield)	Pure Maths Postgraduate Seminar
12:10		Leonard triples and the quintization of U(sl2)
		Hicks Seminar Room J11
Mar 2	Wed	Andrei Lazarev (Bristol)	Pure Maths Colloquium
16:00		p-divisible groups associated to generalized cohomology theories of Eilenberg-Mac Lane spaces
		Hicks Seminar Room J11
	Abstract: It is well-known that a generalized cohomology theory applied to the infinite dimensional complex projective space $CP^\infty$ often gives rise to a one-dimensional group law. This fact has innumerable applications in stable homotopy theory. One particularly important class of a one dimensional formal group is associated with $K(n)^* CP^\infty)$ where $K(n)$ is the nth Morava K-theory. This is an essentially unique example of a one-dimensional formal group of height $n$ over a field. It turns out that if one replaces $CP^n=K(Z,2)$ with $K(Z,l) $, the integral Eilenberg-Mac Lane space with $\pi_l=Z$ then the corresponding object is a formal group of finite height (a.k.a. smooth p-divisible group). This is essentially a 25 year old result of Ravenel-Wilson although they did not phrase it in this way. Letting l vary we obtain a collection of p-divisible groups which possesses a remarkable symmetry. Particularly, any p- divisible group enters in this collection together with its Serre dual (an analogue of the notion of principal polarization for abelian schemes). This and related results are obtained by studying the Dieudonne modules associated to the corresponding p- divisible groups. This is a joint work of myself with Victor Buchstaber.
Mar 7	Mon	Holger Brenner (Sheffield)	Algebra / Algebraic Geometry seminar
16:10		The Frobenius homomorphism - what it annihilates and how fast
		Hicks Seminar Room J11
	Abstract: Let C denote a smooth projective curve over a field of positive characteristic p. We consider a cohomology class $c \in H^1 (C,S)$ for a vector bundle S over C and ask whether c is annihilated by some power of the absolute Frobenius on C -- and if so, which power annihilates it. This question is related to the computation of the Frobenius closure of an ideal in the coordinate ring over C.
Mar 9	Wed	Dr C. Mandrini (IAFE, Argentina)	Applied Mathematics Colloquium
		Magnetic Helicity: linking solar to interplanetary phenomena
Mar 9	Wed	Mike Holcombe (Sheffield, Computer Science)	Pure Maths Colloquium
16:00		Algebraic techniques for Software Testing
		Hicks Seminar Room J11
	Abstract: Software testing is the most expensive and difficult part of the software production process. IBM, for example estimate that testing and reviewing activities account for at least 50% of any project, in safety critical projects it can reach 90%. The sales of software in the UK in 2001 was
Mar 14	Mon	Manuel Blickle (Essen)	Algebra / Algebraic Geometry seminar
16:10		Local cohomology multiplicities via etale cohomology
		Hicks Seminar Room J11
	Abstract: I will show how certain local cohomology invariants (introduced by Lyubeznik) can be completely described in terms of etale cohomology. This generalizes earlier known results, which gave a topological description of these invariants for isolated complex singularities, in two different directions. For once our techniques apply to a significantly larger class of singularities (in particular all complete intersections are inluded) and secondly (and more importantly) our results are valid in positive characteristic also. I will use this result as an excuse to explain a recent Riemann--Hilbert--type correspondence due to Emerton-- Kisin which is the tool that allows us to also treat the positive characteristic case.
Mar 15	Tue	Neil Strickland (Sheffield)	Topology Seminar
14:00		Morava K-theory III
		Hicks Seminar Room J11
	Abstract: I will discuss the Morava K-theory of various spaces, such as classifying spaces of finite groups.
Mar 16	Wed	Mary-Jane Strong (Sheffield)	Pure Maths Postgraduate Seminar
12:10		An introduction to Hopf algebras
		Hicks Seminar Room J11
Mar 16	Wed	Nick Shepherd-Barron (Cambridge)	Pure Maths Colloquium
16:00		Geometry of tangent bundles and effective Mordell over function fields.
		Hicks Seminar Room J11
Apr 12	Tue	Al Weiss (University of Alberta)
14:00		tba
		Hicks Seminar Room J11
Apr 13	Wed	Dr J. Winkler (Sheffield, Computer Science)	Applied Mathematics Colloquium
		A comparison of condition numbers of the full rank least squares problem
Apr 13	Wed	Ian Young (Sheffield)	Pure Maths Postgraduate Seminar
12:10		Alice, Bob and elliptic curves
		Hicks Seminar Room J11
Apr 13	Wed	Bernhard Koeck (Southampton)	Pure Maths Colloquium
16:00		The Chevalley-Weil formula in positive characteristic.
		Hicks Seminar Room J11
	Abstract: Let G be a finite group acting on an algebraic curve X. This action induces an action on various Riemann-Roch spaces such as the vector space of global holomorphic differentials on X. We determine these (modular) representations in local terms, thereby generalizing the classical Chevalley-Weil formula from characteristic 0 to the so-called weakly ramified case, an important case of wild ramification.
Apr 18	Mon	Andrew Stacey (Sheffield)	Topology Seminar
14:00		The Differential Topology of Loop Spaces I
		Hicks Seminar Room J11
	Abstract: The aim of these seminars is to provide a gentle but detailed introduction to the study of loop spaces as manifolds. This is a topic which has a long history, dating back at least to the days of Morse, and which has recently received renewed interest due to its strong links with string theory. We shall end this mini-series with an overview of my work on the Dirac operator on loop spaces. This finale will dictate the itinery of the tour: 1. What is an infinite dimensional manifold and how do we know that the loop space is one? 2. What does it look like, what can we do with it, and what do we want to do with it? 3. What's the big deal about Dirac operators in infinite dimensions? It is intended that anyone with basic differential topology should be able to follow these seminars.
Apr 20	Wed	Dr Gunnar Hornig (St. Andrews)	Applied Mathematics Colloquium
		Three-dimesional magnetic reconnection
Apr 20	Wed	Phil Martin (Sheffield)	Pure Maths Postgraduate Seminar
12:10		tba
		Hicks Seminar Room J11
Apr 20	Wed	Ivan Tomasic (Lyon)	Pure Maths Colloquium
16:00		Weil conjectures--with a difference
		Hicks Seminar Room J11
	Abstract: While the classical Weil conjectures are concerned with counting points on varieties over finite fields, we consider the problem of counting points on \emph {difference} varieties over algebraic closures of finite fields with powers of Frobenius. This context is suitable e.g. for uniform treatment of Ree and Suzuki families of finite simple groups.
Apr 26	Tue	Andrew Stacey (Sheffield)	Topology Seminar
15:00		The Differential Topology of Loop Spaces II
		Hicks Seminar Room J11
Apr 27	Wed	Prof. Carlo Barenghi (Newcastle)	Applied Mathematics Colloquium
		The Taylor-Couette problem: an old flow with new twists
Apr 27	Wed	Vicky Hinchcliffe (Sheffield)	Pure Maths Postgraduate Seminar
12:10		Gelfand-Kirillov dimension
		Hicks Seminar Room J11
Apr 27	Wed	Nick Bingham (Sheffield, Probability and Statistics)	Pure Maths Colloquium
16:00		Mercerian theorems
		Hicks Seminar Room J11
May 3	Tue	Andrew Stacey (Sheffield)	Topology Seminar
15:00		The Differential Topology of Loop Spaces III
		Hicks Seminar Room J11
May 4	Wed	Dr Erwin Verwichte (Warwick)	Applied Mathematics Colloquium
		Transverse waves in the solar corona
May 4	Wed	Alan Lauder (Oxford)	Pure Maths Colloquium
16:00		Title: Effective methods in rigid cohomology
		Hicks Seminar Room J11
	Abstract: Given a system of polynomial equations over a finite field, one may associate with it a finite dimensional vector space, known as the ``rigid cohomology'' of the system. This construction is very useful; for example, it allows one to prove good bounds on the number of solutions to the system over the finite field (Weil conjectures). The construction was first proposed in the 1960s; however, showing that the vector spaces it associated with systems were finite dimensional turned out to be very difficult. (This was not done until the mid 1990s, independently by Berthelot and Christol-Mebkhout.) In my talk I will discuss an ``effectivity problem'' related to the finiteness of the rigid cohomology of a system of equations.
May 10	Tue	Dr Anthony Field (Culham Laboratory)	Applied Mathematics Colloquium
		How to make 100 million a day, 100 million degrees C - the temperature at which plasma burns
May 10	Tue	Sarah Whitehouse (Sheffield)	Topology Seminar
15:10		Stable and unstable K-theory operations
		Hicks Seminar Room J11
May 11	Wed	Joe Chuang (Bristol)	Pure Maths Colloquium
16:00		Representation theory with rhombus tilings
		Hicks Seminar Room J11
	Abstract: I'll discuss some joint work with Will Turner on certain algebras associated to tilings of the plane by rhombi. These `rhombal algebras' defined by Michael Peach were inspired by the representation theory of symmetric groups in positive characteristic. There is a close connection between the combinatorics of the tilings and the homological properties of the algebras. For example certain basic mutations of tilings correspond to equivalences of derived categories of modules.
May 17	Tue	Mike Mandell (Cambridge)	Topology Seminar
15:10		A Localization Sequence for the Algebraic K-Theory of Topological K-Theory
		Hicks Seminar Room J11
	Abstract: In many ways the algebraic K-theory of ring spectra behaves like the algebraic K-theory of traditional rings. One limitation is the lack of a general formulation of a devissage theorem. Recent work (joint with Andrew Blumberg) establishes one very special case of the devissage theorem. This case is sufficient to construct the localization sequence conjectured by Rognes relating the algebraic K-theory of (complex) K-theory, connective K- theory, and the integers.
May 18	Wed	Dr Sergey Nazarenko (Warwick)	Applied Mathematics Colloquium
		Turbulence of sea waves
May 19	Thu	David Elworthy (Warwick)
14:00		Stochastic Flows and Universal Connections
		K14
	Abstract: There are various places where the geometrical notion of a connection appears in stochastic analysis. In this expository talk I shall describe some of these, and show how they are related; first describing what they are and are useful for: in fact the more general notion of a non- linear semi- connection will be needed. For probabilists I'll indicate how they might (perhaps...) be useful for such problems as - trying to estimate the behaviour of an oil slick (on the surface of a curved planet, acted on by random forces) given the behaviour of one of its particles. For geometers/ topologists the constructions involved relate to the classifying spaces for gauge groups of subbundles of tangent bundles. This talk is mainly taken from joint work with Yves LeJan and Xue-Mei Li, see http://xuemei.org/bib.html.
May 24	Tue	Ieke Moerdijk (Sheffield)	Topology Seminar
15:00		What do classifying spaces classify?
		Hicks Seminar Room J11
May 25	Wed	Dr Nils Andersson (Southampton)	Applied Mathematics Colloquium
		Gravitational-wave asteroseismology - probing the extremes of physics
May 25	Wed	Luis Hernandez-Hernandez (Sheffield)	Pure Maths Postgraduate Seminar
12:10		Fixed point degrees of equivariant maps of spheres
		Hicks Seminar Room J11
May 25	Wed	Srikanth Iyengar (Nebraska)	Pure Maths Colloquium
16:00		Levels in triangulated categories and perfect complexes over commutative rings
		Hicks Seminar Room J11
May 31	Tue	Neil Strickland (Sheffield)	Topology Seminar
15:10		The Rezk logarithm I
		Hicks Seminar Room J11
	Abstract: The Rezk logarithm is a natural map $(E^0X)^\times\rightarrow E^0X$ defined for all spaces $X$ and suitable generalised cohomology theories $E$. In many cases it is close to being an isomorphism. There is a simple definition using a functor constructed by Bousfield and Kuhn, but the thing that makes it usable is a theorem of Rezk relating it to the theory of power operations, and in particular the Hecke operators studied by Ando. This seminar will be the first of a series covering some of this material.
Jun 7	Tue	Neil Strickland (Sheffield)	Topology Seminar
15:10		The Rezk logarithm II
		Hicks Seminar Room J11
	Abstract: I will talk about generalized Moore spectra, K(n)-localisation, and the Bousfield-Kuhn functor, all of which are ingredients in the definition of the Rezk logarithm.
Jun 17	Fri	Hellen Colman (Wilbur Wright College, Chicago, USA)	Pure Maths Colloquium
16:00		Lusternik-Schnirelmann category for orbifolds
		Hicks Seminar Room J11
	Abstract: We define and study a Lusternik-Schnirelmann theory for orbifolds. The orbifold category provides a new invariant of the homotopy type of the orbifold that gives a numerical measure of the complexity of the orbifold $X$. In particular, the orbifold category gives a lower bound on the number of critical points of any orbifold smooth function $f\colon X\rightarrow R$. We use equivariant methods to find upper and lower bounds on the orbifold category in terms of the orbifold resolution of the singular set. We obtain a generalization of the classical cohomological lower bound for orbifold category using the orbifold cohomology theory constructed by Chen-Ruan.
Jul 5	Tue	Neil Strickland (Sheffield)	Topology Seminar
15:10		The Rezk Logarithm II'
		Hicks Seminar Room J11
	Abstract: I will talk about generalized Moore spectra, K(n)-localisation, and the Bousfield-Kuhn functor, all of which are ingredients in the definition of the Rezk logarithm. This will essentially be a repeat of the seminar I gave a few weeks ago when many people were away.
Sep 20	Tue	Yoshi Maeda (Keio University, Japan)	Pure Maths Colloquium
16:00		Deformation quantizations and gerbes
		Lecture Theatre 6
Sep 28	Wed	Dr Stephen Davies (Leiden)	Applied Mathematics Colloquium
		Constraining Gauss-Bonnet Dark Energy
Sep 28	Wed	Peter Symonds (Manchester)	Pure Maths Colloquium
16:10		Group actions on polynomial rings
		Hicks Seminar Room J11
	Abstract: We consider a polynomial ring $k[x_1,...,x_n]$ over a finite field $k$ and suppose that some finite group $G$ acts on it by linear substitutions. We want to understand the ring as a $kG$-module. We present a structure theorem that describes this in a finite way. It has several notable corollaries, such as the fact that only finitely many indecomposable modules occur as summands (up to isomorphism) and the fact that we can write down an a priori bound on the degrees of the generators of the invariant subring.
Oct 3	Mon	Tom Bridgeland (Sheffield)
14:00		Mirror symmetry I
		Hicks Seminar Room J11
Oct 4	Tue	Johann Sigurdsson (Sheffield)	Topology Seminar
14:00		Duality in parametrized homotopy theory
		Hicks Seminar Room J11
	Abstract: I will describe formal structure enjoyed by the parametrized stable homotopy categories and how one can encode it into a single bicategory. I will then discuss duality theory from that perspective and show how it gives simple conceptual proofs of generalizations of various known duality phenomena such as Atiyah duality and the Wirthmuller and Adams equivalences. The talk should be accessible to everyone.
Oct 5	Wed	Dr Steven Tobias (Leeds)	Applied Mathematics Colloquium
		The role of spectra in dynamo theory - does mean-field modelling make any sense?
Oct 5	Wed	Graham Everest (East Anglia)	Pure Maths Colloquium
16:00		Bilinear Recurrence Sequences
		Hicks Seminar Room J11
Oct 7	Fri	Yukinobu Toda (Tokyo)
14:00		Deformations and Fourier-Mukai transform
		Hicks Seminar Room J11
Oct 10	Mon	Tom Bridgeland (Sheffield)
14:00		Mirror symmetry II
		Hicks Seminar Room J11
Oct 11	Tue	Johann Sigurdsson (Sheffield)	Topology Seminar
14:00		Duality in parametrized homotopy theory
		Hicks Seminar Room J11
Oct 12	Wed	Rapha (Leeds)	Pure Maths Colloquium
16:00		Dunkl operators and Hecke algebras
		Hicks Seminar Room J11
	Abstract: The first parts of my talk will be very elementary. I will introduce a deformation of the ordinary derivation of real functions of one variable. I will discuss the corresponding operator on polynomials (for which values of the deformation parameter are there non constant polynomials killed by the operator ?) and on analytic functions (spectrum of the operator, eigenfunctions as Bessel functions). Then, I will switch to the dimension $n$ case, where one has a commuting family of operators deforming the $d/dx_i$ (the Dunkl operators). I will focus on the action on polynomial functions of $n$ variables and explain how this is controlled by an algebra deforming the algebra of polynomial differential operators (a doubly degenerate double affine Hecke algbra). This leads to the study of representations of this algebra. I will describe how the representation theory of this algebra is studied, in analogy with the representation theory of the Lie algebra $gl_n(\mathbb{C})$. This last part brings a lot of exciting mathematics: Knizhnik-Zamolodchikov equations, braid groups, Hecke algebras to analyze representations as systems of differential equations. quantum general linear group, Fock spaces to describe precisely the representation theory Hilbert scheme of points on $\mathbb{C}^2$ as the geometric object connected to the representation theory.
Oct 13	Thu	Victor Snaith (Sheffield)	Snaith seminar
12:10		Overview of the Beilinson conjectures.
		Hicks Seminar Room J11
Oct 14	Fri	Victor Snaith (Sheffield)	Pure Maths Postgraduate Seminar
11:10		Monomial Representations
		Hicks Seminar Room J11
Oct 14	Fri	Moty Katzman (Sheffield)
14:00		Ideals of minors of matrices with indeterminate entries
Oct 17	Mon	Tom Bridgeland (Sheffield)
14:00		Mirror symmetry III
		Hicks Seminar Room J11
Oct 18	Tue	Simon Willerton (Sheffield)	Topology Seminar
14:00		The derived category of sheaves on a complex manifold from a representation theory perspective
		Hicks Seminar Room J11
	Abstract: I will try to explain how the derived category of sheaves on a complex manifold (which I will remind you of) looks a lot like the representation category of a finite group. This will be motivated by ideas from topological field theory.
Oct 19	Wed	Karima Khusnutdinova (Loughborough)	Applied Mathematics Colloquium
		The effect of bubbles on internal waves
Oct 19	Wed	Alexander Stasinski (University of East Anglia)	Pure Maths Colloquium
16:00		Representations of reductive groups over finite rings
		Hicks Seminar Room J11
	Abstract: Let $F$ be a local field with finite residue field, ring of integers $O$, and maximal ideal $p$. Let $G$ be a reductive group scheme over $O$ (e.g. $G=GL_n$). We present an approach to the study of representations of the finite groups $G_{r}:=G(O/p^r)$, which for $r=1$ coincides with the theory of Deligne and Lusztig. One reason why such a study is of interest is the close connection between the representation theory of the groups $G_{r}$, and the representation theory of the group $G(F)$. One of the few cases where the representations of $G_{r}$ are known for all $r;eq1$, is when $G=GL_{2}$. This is due to several people, including Kutzko, and the method used is purely algebraic, and quite different from our geometric approach. We show how the two methods can be linked, and in particular how the algebraic method can be used to analyse representations constructed geometrically.
Oct 20	Thu	Victor Snaith (Sheffield)
12:10		Overview of the Beilinson Conjectures II
		Hicks Seminar Room J11
Oct 25	Tue	David Gepner (Sheffield)	Topology Seminar
14:00		Equivariant elliptic cohomology
		Hicks Seminar Room J11
Oct 26	Wed	Reza Raoufi and Alan Zinober (Sheffield)	Applied Mathematics Colloquium
		$C^3$ = Chaos, Cryptography and Control
Oct 26	Wed	Dietrich Notbohm (University of Leicester)	Pure Maths Colloquium
16:00		Homology decompositions and applications
		Hicks Seminar Room J11
	Abstract: A homolgy decomposition is a way to build a space out of 'simpler' space. A CW -complexes is given an iterated building process based on spheres and discs where as the gluing data for homology decompositions is encoded in a functor defined on a 'nice' category with values in the category of topological spaces, and where all simpler spaces are glued together in one step. Homology decompositions are one of the major tools to understand the homotopy theory of classifying spaces. We will apply these ideas in several much more algebraic contexts, Stanley-Reisner algebras associated to simplicial complexes, invariant theory and group cohomology.
Oct 27	Thu	Victor Snaith (Sheffield)	Snaith seminar
12:10		Overview of the Beilinson conjectures III.
		Hicks Seminar Room J11
Oct 28	Fri	Paul Buckingham (Sheffield)	Pure Maths Postgraduate Seminar
11:10		Sheaf Cohomology and hypercohomology
		Hicks Seminar Room J11
Oct 28	Fri	Almar Kaid (Sheffield)	Algebra / Algebraic Geometry seminar
14:00		Unitarily graded field extensions
		Hicks Seminar Room J11
Nov 2	Wed	Prof. Howard Wilson (York)	Applied Mathematics Colloquium
		Explosive instabilities in laboratory fusion plasmas
Nov 2	Wed	Marcus Linckelmann (Aberdeen)	Pure Maths Colloquium
16:00		Fusion Systems and Modular Representation Theory
		Hicks Seminar Room J11
	Abstract: The $p$-local approach to finite group theory tries to understand the structure of a finite group in terms of one of its Sylow-$p$-subgroups $P$ (they are all isomorphic, so it doesn't matter which one we take) and the way in which $P$ is embedded into $G$. This approach goes well back to the early stages of the theory, illustrated by theorems of Burnside and Frobenius, and plays an important role in the context of the classification of finite simple groups. One can describe the p-local structure of $G$ in terms of a category, the fusion system of $G$. As a consequence of work of Alperin and Broue around 1980 it appears that categories with very similar formal properties occur also in modular representation theory, prompting Puig in the 1990's to formalise the notion of fusion systems independently of finite groups and Benson to speculate whether any such fusion system gives rise to a topological space which would play the role of classifying space of the group. Broto, Levi and Oliver developed in recent years the precise framework for topological spaces arising in this way - giving a sense to the concept of classifying spaces of finite groups which don't exist...
Nov 3	Thu	Victor Snaith (Sheffield)	Snaith seminar
12:10		Overview of Beilinson's conjectures IV
		Hicks Seminar Room J11
Nov 4	Fri	Sam Marsh (Sheffield)	Pure Maths Postgraduate Seminar
11:10		TBA
		Hicks Seminar Room J11
Nov 4	Fri	David Jordan (Sheffield)	Algebra / Algebraic Geometry seminar
14:00		Poisson algebras and modules: a case study.
		Hicks Seminar Room J11
Nov 9	Wed	Everett Howe (Center for Communications Research, San Diego)	Pure Maths Colloquium
16:00
		Hicks Seminar Room J11
Nov 10	Thu	Victor Snaith (Sheffield)	Snaith seminar
12:10		Overview of Beilinson's conjectures V
		Hicks Seminar Room J11
Nov 11	Fri	Victor Snaith (Sheffield)	Snaith seminar
10:00		The Arf Invariant One Problem Part I
		Hicks Seminar Room J11
Nov 11	Fri	David Barnes (Sheffield)	Pure Maths Postgraduate Seminar
11:10		Theory of Representations and Stable Homotopy
		Hicks Seminar Room J11
	Abstract: The speaker has been overheard referring to this subject (acronymoniously)as T.R.A.S.H.
Nov 11	Fri	Victor Snaith (Sheffield)	Snaith seminar
14:00		The Arf Invariant One Problem Part II
		Hicks Seminar Room J11
Nov 14	Mon	Prof. Stanley L Jaki (Seton Hall)	Applied Mathematics Colloquium
		A late awakening with a nightmare
Nov 14	Mon	Stanley L. Jaki (Seton Hall University)	Pure Maths Colloquium
16:00		A late awakening with a nightmare
		LT5
	Abstract: According to Godel's theorem, formulated in 1930, no non- trivial theory of arithmetic can have its proof of consistency in terms of the presuppositions of the theory itself. This means that it is not possible to form a final form of mathematics that would be its sole form which is also necessarily true. Since physics has to be heavily mathematical, this also means the end of hopes that a final physical theory could ever be formulated. Contrary to a recent claim of Prof Hawking, this does not mean of the end of physics, though it constitutes a death blow at those hopes, often proposed with great arrogance. Godel's theorem is an assurance that the work of physicists will go on to no end.
Nov 15	Tue	Andrew Stacey (Sheffield)	Topology Seminar
14:00		Delooping Moravian Maps
		Hicks Seminar Room J11
	Abstract: One of the pieces of baggage that comes with a graded cohomology theory is the family of operations. These are self-maps of the cohomology groups obeying certain obvious naturality conditions. There are two main types of operation: stable and unstable. An unstable operation acts only on the cohomology groups of a particular degree whilst a stable operation acts on the cohomology groups of any degree compatibly with the suspension isomorphism. It is clear, therefore, that a stable operation defines a family of unstable ones. However, even if one knows that an unstable operation came from a stable one it may not be easy to reconstruct that stable operation. What is remarkable about the Morava K--theories is that there is a straightforward way to do this. The "delooping" of the title refers to the fact that operations are closely linked to maps between certain spaces and spectra associated to the cohomology theory. In this language, the claim is that there is a simple way to convert an arbitrary map between the representing spaces of the Morava K-theories into an infinite loop map. The mathematics involved is astonishingly simple and I shall endeavour to keep the exposition in a similar vein. Thus the prerequisites are minimal: a familiarity with cohomology theories and their links with spectra. This work is joint with Sarah Whitehouse and is funded as part of the EPSRC project on operations in Morava K--theories.
Nov 16	Wed	Dr A Thyagaraja (Culham Laboratory)	Applied Mathematics Colloquium
		Mesoscale electromagnetic turbulence in tokamaks
Nov 16	Wed	Mark Watkins (Bristol)	Pure Maths Colloquium
16:00		Special values of L-functions: a meeting place of algebra and analysis.
		Hicks Seminar Room J11
Nov 18	Fri	Ian Young (Sheffield)	Pure Maths Postgraduate Seminar
11:10		L-functions and elliptic curves
		Hicks Seminar Room J11
Nov 18	Fri	David Jordan (Sheffield)	Algebra / Algebraic Geometry seminar
14:00		Poisson algebras and modules: a case study II
		Hicks Seminar Room J11
Nov 22	Tue	Ruben Sanchez (Sheffield)	Topology Seminar
14:00		Classifying spaces for proper actions and the Baum-Connes Conjecture
		Hicks Seminar Room J11
	Abstract: I will explain how to generalize the ordinary classifying space of a group G to actions with finite stabilizers. The corresponding classifying space appears in the Baum-Connes Conjecture, which identifies two objects associated to G, one analytical and one topological. The analytical one is the K-theory of the reduced $C^*$-algebra of G, and the topological one is the equivariant K-homology of this classifying space. I will describe how to use Bredon homology and a spectral sequence to obtain the topological side of Baum-Connes. Then I would like to explain how to do this for the groups $SL(3,\mathbb{Z})$ and for some Coxeter groups. The talk may suit two sessions, so if people are not too unhappy, I may also talk the following week.
Nov 23	Wed	Prof. Yurii Sergeev (Newcastle)	Applied Mathematics Colloquium
		Tracer particles in turbulent helium II at low temperatures
Nov 23	Wed	Paul Buckingham (Sheffield)
01:30		Serre's Modularity Conjecture "Recipe for the weight"
		Hicks Seminar Room J11
Nov 23	Wed	Aaron Lauda (Cambridge)	Pure Maths Colloquium
16:00		Frobenius algebras and thick tangles
		Hicks Seminar Room J11
	Abstract: In topological quantum field theory one is interested in studying functors from a topological category of $n$-dimensional cobordisms into the category of vector spaces. In two dimensions such functors are very well understood. In fact, specifying a (symmetric monoidal) functor from the 2-dimensional cobordism category 2-Cob into Vect is equivalent to specifying a commutative Frobenius algebra. This makes the study of 2-dimensional TQFT's particularly simple. Recent developments in string theory have prompted many to consider topological quantum field theories using a more interesting version of the $2$-dimensional cobordism category, namely one that allows for cobordisms between $1$-manifolds with boundary. In this talk I will define a category of planar cobordisms between `open strings' and show that functors from this category into Vect are equivalent to (not necessarily commutative) Frobenius algebras. This result arises naturally by considering adjunctions in 2- categories. If time permits, I will also sketch how this process can be generalized to higher-dimensional surfaces using higher-dimensional category theory. This talk is intended to be accessible; all concepts from higher-dimensional category theory will be introduced in the talk.
Nov 24	Thu	Victor Snaith (Sheffield)	Snaith seminar
12:10		Beilinson conjectures VI: a proof of cases of the Lichtenbaum conjecture.
		Hicks Seminar Room J11
	Abstract: This (possibly!!! -- see the abstract to Beilinson VII) final lecture in this semester's series on the Beilinson conjectures culminates with my ( AD 2000) proof of Lichtenbaum's conjecture for the order of $K_{4k}(Z)$. Mention will also be made of my new formula for the Borel- Beilinson regulator in dimension 3.
Nov 25	Fri	Mary-Jane Strong (Sheffield)	Pure Maths Postgraduate Seminar
11:10		Splittings of cohomology theories
		Hicks Seminar Room J11
Nov 25	Fri	David Jordan (Sheffield)	Algebra / Algebraic Geometry seminar
14:05		Poisson algebras and modules: a case study III
		Hicks Seminar Room J11
Nov 25	Fri	Neil Strickland (Sheffield)
14:10		Cobordism and formal power series
		Lecture Room 6
	Abstract: We will discuss the basic definitions of cobordism theory, and outline a proof of the following result of Thom: the unoriented cobordism ring $MO_*$ is given by $$ \mathbb{Z}/2[x_2,x_4,x_5,x_6,x_8,x_9,\ldots], $$ with one generator $x_k$ in each degree $k$ not of the form $2^i-1$. There will be many pretty pictures.
Nov 29	Tue	Ruben Sanchez (Sheffield)	Topology Seminar
14:00		Equivariant K-homology for $SL(3,\mathbb{Z})$ and Coxeter groups
		Hicks Seminar Room J11
	Abstract: I will show how to compute the topological side of the Baum-Connes conjecture for $SL(3,\mathbb{Z})$ and some Coxeter groups. I will put some illustrative pictures.
Nov 29	Tue	Iakovos Androulidakis (Z)
16:10		Realisation of singular foliations by Lie groupoids
		Hicks Seminar Room J11
	Abstract: Lie groupoids generalise at the same time the notion of a Lie group and a manifold. Every Lie groupoid defines a foliation in a canonical way, which may well have singularities, and in this sense the groupoid can be thought of as a desingularization of this foliation. We address the converse problem in this talk, namely whether every singular foliation in the sense of Stefan and Sussmann comes from a Lie groupoid. In particular we present a construction that provides a positive answer, and discuss its implications in noncommutative geometry and quantization.
Nov 30	Wed	Dr Kiril Kuzanyan (Leeds)	Applied Mathematics Colloquium
		Helicity and Solar dynamo: confront theory and observations
Nov 30	Wed	Ivan Smith (Cambridge)	Pure Maths Colloquium
16:00		Knots, matrices and symplectic topology
		Hicks Seminar Room J11
Dec 1	Thu	Victor Snaith (Sheffield)	Snaith seminar
12:10		Beilinson VII: Borel's regulator, the final mopping-up!!
		Hicks Seminar Room J11
	Abstract: I imagine that Beilinson VI will cover the Lichtenbaum conjecture but not the formula for Borel's regulator - so Beilinson VII is reserved for the latter, if necessary. It will be the last in the series!
Dec 2	Fri	Luis Hernandez-Hernandez (Sheffield)	Pure Maths Postgraduate Seminar
11:10		Cohomology of Projective Bundles
		Hicks Seminar Room J11
Dec 2	Fri	David Jordan (Sheffield)	Algebra / Algebraic Geometry seminar
14:05		Possion algebras and modules: a case study IV
		Hicks Seminar Room J11
Dec 7	Wed	Kari Ragnarsson (Aberdeen)	Pure Maths Colloquium
16:00		Homotopy classifications of p-completed classifying spaces
		Hicks Seminar Room J11
	Abstract: In algebraic topology one typically applies powerful algebraic invariants to encode homotopy properties of topological spaces. In certain cases it is possible and useful to reverse this process by assigning a space to an algebraic object. An instance of this is the assignment to a finite group $G$ of a classifying space $BG$, whence the group $G$ can be recovered as the fundamental group. Furthermore, group homomorphisms between finite groups correspond bijectively to homotopy classes of maps between their classifying spaces. In this talk I will discuss how this correspondence changes when we focus on properties relative to a prime $p$. Topologically this means applying the $p$-completion functor to $BG$. I will present three classification theorems for $p$-completed classifying spaces of finite groups. First, the unstable classification, predicted by Martino- Priddy and proved by Oliver, which classifies the homotopy type of the $p$-completed classifying space of $G$ via the fusion system of $G$. Second, the stable classification, due to Martino-Priddy, which classifies the stable homotopy type of the p-completed classifying space of $G$ via weaker data, which loosely speaking can be regarded as a linearisation of the fusion system. Finally, the partially stable classification, which links the unstable and stable classifications. This is the surprising result that, by keeping track of inclusions of Sylow subgroups, the stable homotopy type of the $p$-completed classifying space of $G$ can again be classified via the fusion data of $G$. This classification also gives a simple description of maps realising stable homotopy equivalences (while preserving the inclusions of Sylow subgroups).
Dec 9	Fri	Yukinobu Toda (Tokyo)	Algebra / Algebraic Geometry seminar
16:00		$A_{\infty}$ structures and Fourier-Mukai transforms (An introduction to A. Polishchuk's work)
		Hicks Seminar Room J11
	Abstract: First I will give an introduction of $A_{\infty}$ algebras and $A_{\infty}$ categories. Then we combine them with the techniques of Fourier-Mukai transforms, and approach the problem of describing Brill-Noether loci. These are generalizations of theta divisors of Jacobian of curves, and we will see that $A_{\infty}$ techniques can be applied to some classical problems in algebraic geometry.
Dec 12	Mon	Alfonso Gracia-Saz (Berkeley)
16:10		The symbol of a function of an operator (or How finding the right notation solves half the problem)
		Hicks Seminar Room J11
	Abstract: In the quantum description of a physical system, the observables (e.g. the energy) are represented by operators on a Hilbert space. In the classical description, they are represented by functions on phase space. Weyl quantization provides a bijection between quantum and classical observables. To every operator (quantum) $\widehat{A}$, we associate a function (classical) $A$, called its symbol. We consider the following problem. Let $\widehat{A}$ be an operator with symbol $A$ and let $f$ be a smooth function. Then $\widehat{B}:=f(\widehat{A})$ is another operator, with symbol $B$. What is $B$ in terms of $A$? We will provide an answer to this question in the form of a formula ``à la Feynman'', i.e. a power series whose terms are labeled by diagrams. This has various applications to quantum mechanics. No knowledge of physics will be assumed. The talk will come with a moral: There is no difficult calculation, only unfortunate notations.
Dec 13	Tue	Dr Fay Dowker (Blackett Laboratory, Imperial College)	Applied Mathematics Colloquium
		Causal Set Phenomenology
Dec 13	Tue	Halvard Fausk (Oslo)	Topology Seminar
14:00		t-model structures
		Hicks Seminar Room J11
	Abstract: For every stable model category $M$ with a certain extra structure, we produce an associated model structure on the pro-category $Pro(M)$ and a spectral sequence, analogous to the Atiyah-Hirzebruch spectral sequence, with reasonably good convergence properties for computing in the homotopy category of $Pro(M)$. Our motivating example is the category of pro-spectra. The extra structure referred to above is a t-model structure. This is a rigidification of the usual notion of a t-structure on a triangulated category. A t-model structure is a proper simplicial stable model category $M$ with a t-structure on its homotopy category together with an additional factorization axiom.
Dec 13	Tue	Fay Dowker (Imperial College)	Pure Maths Colloquium
16:00		Causal Set Phenomenology
		Lecture Theatre G
	Abstract: The hypothesis that the discrete substructure of spacetime is a causal set suggests a straightforward model building technique: invent phenomenological dynamics for matter (particles or fields) on a background causal set that is well approximated by our continuum spacetime. These models can be analysed to see if they predict observable eviations from continuum models. I will describe two examples of such models: "particle swerves" and a model of detector response to the scalar field of a scalar charge source.
Dec 14	Wed	Jon Woolf (Liverpool)	Pure Maths Colloquium
16:00		Signatures and Witt spaces, or, why life is simpler with singularities.
		Hicks Seminar Room J11
	Abstract: The signature of a manifold is an important invariant: it is the basic obstruction to a manifold being the boundary of a manifold of one dimension higher. The talk will survey some classical results for computing signatures and explain how, by introducing a notion of signature for certain singular spaces, we can obtain very geometric proofs and significant extensions of these results.
Jan 16	Mon	Matthew Ando (Urbana-Champaign)	Chromatic homotopy
16:00		TBA
		Hicks Seminar Room J11
Jan 23	Mon	Ruben Sanchez (Sheffield)	Chromatic homotopy
16:00		Orthogonal Spectra II
		Hicks Seminar Room J11
Jan 27	Fri	Johann Sigurdsson (Sheffield)	Chromatic homotopy
16:00		Structured Spectra
		Hicks Seminar Room J11
	Abstract: Now that we have good geometric models for the stable homotopy category it is time to construct spectra representing particular cohomology theories. The point is to do that in such a way that interesting structure of cohomology theories, such as pairings, is already reflected in structure on the spectra. I will in particular focus on the Thom spectra representing the various cobordism theories.
Jan 30	Mon	Johann Sigurdsson (Sheffield)	Chromatic homotopy
16:00		Structured Spectra II
		Hicks Seminar Room J11
Feb 3	Fri	Sam Marsh (Sheffield)	Chromatic homotopy
16:00		Complex Oriented Cohomology Theories I
		Hicks Seminar Room J11
Feb 6	Mon	Sam Marsh (Sheffield)	Chromatic homotopy
16:00		Complex Oriented Cohomology Theories II
		Hicks Seminar Room J11
Feb 8	Wed	Dr Thomas Neukirk (St Andrews)	Applied Mathematics Colloquium
		Current Build-up in Topologically Simple Magnetic Fields
Feb 8	Wed	Alexander Odesskii (Machester)	Pure Maths Colloquium
16:00		Elliptic algebras
		Hicks Seminar Room J11
	Abstract: The talk is devoted to associative N-graded algebras presented by n generators and n(n-1)/2 quadratic relations and satisfying the so-called Poincare-Birkhoff-Witt condition (PBW-algebras). We consider examples of such algebras depending on two continuous parameters (namely, on an elliptic curve and a point on this curve) which are flat deformations of the polynomial ring in n variables. Diverse properties of these algebras will be described, together with their relations to integrable systems, deformation quantization, moduli spaces and other directions of modern investigations.
Feb 10	Fri	James Cranch (Sheffield)	Chromatic homotopy
16:00		The Lazard Ring and Quillen's Theorem
		Hicks Seminar Room J11
Feb 13	Mon	James Cranch (Sheffield)	Chromatic homotopy
16:00		The Lazard Ring and Quillen's Theorem, II
		Hicks Seminar Room J11
Feb 15	Wed	Prof Alexander B. Movchan (Liverpool)	Applied Mathematics Colloquium
		Asymptotic analysis of solutions to singularly perturbed problems in multi-structures
Feb 15	Wed	Victoria Hinchcliffe (Sheffield)	Pure Maths Postgraduate Seminar
12:10		The Filter Dimension and the Inequality of Bernstein
		Hicks Seminar Room J11
Feb 15	Wed	Nikita Markarian (Sheffield)	Algebra / Algebraic Geometry seminar
14:00		Hochschild homology, Atiyah classes and Riemann-Roch theorem I
		Hicks Seminar Room J11
Feb 15	Wed	Balazs Szendroi (Oxford)	Pure Maths Colloquium
16:00		The amazing partition function of local P^1
		Hicks Seminar Room J11
	Abstract: To a manifold M, string theory associates its topological partition function, a finite dimensional approximation to a complicated path integral on M. One of the simplest cases when this function can be computed explicitly is that of local P^1, a certain complex threefold fibred over the projective line. Its partition function can be written in six or seven different ways, as infinite sum or infinite product, related to Gromov-Witten theory, Donaldson-Thomas theory, the combinatorics of partitions, Chern-Simons theory of knots... The talk will introduce these ideas in elementary terms.
Feb 17	Fri	Holger Brenner (Sheffield)	Chromatic homotopy
16:00		Introduction to Algebraic Geometry
		Hicks Seminar Room J11
Feb 20	Mon	David Gepner (Sheffield)	Chromatic homotopy
16:00		Schemes, Sheaves and Topoi
		Hicks Seminar Room J11
	Abstract: We continue our introduction to derived algebraic geometry. In particular, we will define schemes, sheaves, and topoi (not necessarily in that order!) and, time permitting, consider possible homotopy-theoretic generalizations.
Feb 22	Wed	Prof Roger Grimshaw (Loughborough)	Applied Mathematics Colloquium
		Internal solitary waves and undular bores in the atmosphere and ocean
Feb 22	Wed	Zacky Choo (Sheffield)	Pure Maths Postgraduate Seminar
12:10		Borel's Regulator
		Hicks Seminar Room J11
Feb 22	Wed	Nikita Markarian (Sheffield)	Algebra / Algebraic Geometry seminar
14:00		Hochschild homology, Atiyah classes and Riemann-Roch theorem II
		Hicks Seminar Room J11
Feb 22	Wed	Alastair King (University of Bath)	Pure Maths Colloquium
16:00		Moduli of sheaves from moduli of Kronecker modules
		Hicks Seminar Room J11
Feb 24	Fri	David Gepner (Sheffield)	Chromatic homotopy
16:00		Schemes, Sheaves and Topoi II
		Hicks Seminar Room J11
Mar 1	Wed	Dr Andrew Soward (Exeter)	Applied Mathematics Colloquium
		Non-axisymmetric $\alpha^2\Omega$-dynamo waves in thin stellar shells
Mar 1	Wed	Alastair Hamilton (University of Bristol)	Pure Maths Colloquium
16:00		Graph homology classes via infinity-algebras
		Hicks Seminar Room J11
	Abstract: I will discuss the role played by certain aspects of quantum field theory such as the Feynman calculus and the Batalin-Vilkovisky formalism in the construction of graph homology and cohomology classes, as introduced by Kontsevich in his 92/93 papers. I will also give the first example of a nontrivial pairing between a graph homology and cohomology class which arises from the evaluation of a super-integral, more than ten years since the idea was first proposed by Kontsevich.
Mar 3	Fri	David Gepner (Sheffield)	Chromatic homotopy
16:00		The Functor of Points Approach to Algebraic Geometry
		Hicks Seminar Room J11
	Abstract: We will illustrate our ``functor of points'' approach to algebraic geometry through a number of concrete examples. In particular, we will see when a subfunctor of a scheme is itself a (closed or open) subscheme, and we will determine the functor represented by n-dimensional projective space.
Mar 6	Mon	David Gepner (Sheffield)	Chromatic homotopy
16:00		Quasicoherent Sheaves
		Hicks Seminar Room J11
	Abstract: We will introduce the notion of a (quasi)coherent sheaf on a scheme. The (quasi)coherent sheaves play a central role in algebraic geometry, particularly in cohomology theory. We will illustrate with examples of coherent sheaves on projective space.
Mar 8	Wed	Dr Robert Walsh (Central Lancashire)	Applied Mathematics Colloquium
		Taking the Sun's temperature: modelling the pros and cons of EUV rastering spectrometers vs narrow-band imagers
Mar 8	Wed	Marc Lackenby (Oxford)	Pure Maths Colloquium
16:00		Property tau
		Hicks Seminar Room J11
	Abstract: How can one construct computer networks without bottlenecks? Is there a method of efficiently shuffling a pack of cards? How does the spectrum of the Laplacian on a manifold behave under finite-sheeted covers? How can one detect `large' groups? Do hyperbolic 3-manifolds contain essential surfaces? In my talk, I will show how these questions are all related to an intriguing concept known as `Property tau'.
Mar 9	Thu	Holger Brenner (Sheffield)	Algebra / Algebraic Geometry seminar
15:10		Grothendieck topologies and closure operations for ideals I
		Hicks Seminar Room J11
Mar 10	Fri	David Gepner (Sheffield)	Chromatic homotopy
16:00		Quasicoherent Sheaves
		Hicks Seminar Room J11
Mar 13	Mon	Ieke Moerdijk (Sheffield)	Chromatic homotopy
16:00		Operads, Dendroidal Sets and Weak Categories
		Hicks Seminar Room J11
Mar 15	Wed	Prof Leo Brevdo (University of the Mediterranean (Marseille, France))	Applied Mathematics Colloquium
		Absolute instability of spatially developing flows and media
Mar 15	Wed	Bruce Bartlett (Sheffield)	Pure Maths Postgraduate Seminar
12:10		2-representations of groups
		Hicks Seminar Room J11
	Abstract: There is a jigsaw puzzle P of closely related ideas that revolve around topological quantum field theory, n- categories, gerbes, elliptic cohomology, knot theory, and higher gauge theory. Unfortunately, I am not qualified to talk about P. I will however attempt to address one infinitesimal piece of P, which is called the "2-category of 2-representations of a finite group.
Mar 15	Wed	Jonathan Jordan (University of Sheffield, dept. of Probability and Statistics)	Pure Maths Colloquium
16:00		Spectral properties of fractal graphs
		Hicks Seminar Room J11
Mar 16	Thu	Holger Brenner (Sheffield)	Algebra / Algebraic Geometry seminar
15:10		Grothendieck topologies and ideal closure operations II
		Hicks Seminar Room J11
Mar 17	Fri	Ruben Sanchez (Sheffield)	Chromatic homotopy
16:00		Homotopy Limits and Colimits
		Hicks Seminar Room J11
Mar 20	Mon	Ieke Moerdijk (Sheffield)	Chromatic homotopy
16:00		Operads, Dendroidal Seta and Weak Categories.
		Hicks Seminar Room J11
Mar 22	Wed	James Cranch (Sheffield)	Pure Maths Postgraduate Seminar
12:10		Rational Morava E-theory of symmetric groups
		Hicks Seminar Room J11
Mar 22	Wed	Frances Kirwan (Oxford)	Pure Maths Colloquium
16:00		Moduli spaces of bundles over curves revisited
		Hicks Seminar Room J11
	Abstract: Several decades ago the Betti numbers of the moduli spaces of stable vector bundles (with fixed mutually coprime rank and degree) over a Riemann surface were found, first by Harder and Narasimhan using number-theoretic methods and counting objects defined over finite fields, and soon after by Atiyah and Bott using Yang-Mills theory and equivariant Morse theory. This talk will link these two approaches and describe some more recent results on the geometry of the moduli spaces.
Mar 23	Thu	Holger Brenner (Sheffield)	Algebra / Algebraic Geometry seminar
15:10		Grothendieck topologies and ideal closure operations III
		Hicks Seminar Room J11
Mar 24	Fri	Ruben Sanchez (Sheffield)	Chromatic homotopy
16:00		Homotopy Limits and Colimits, II
		Hicks Seminar Room J11
Mar 27	Mon	Ieke Moerdijk (Sheffield)	Chromatic homotopy
16:00		Operads, dendroidal sets and weak categories III
		Hicks Seminar Room J11
Mar 29	Wed	Dr Jacques Vanneste (Edinburgh)	Applied Mathematics Colloquium
		Wave radiation by slow flows
Mar 29	Wed	Almar Kaid (Sheffield)	Pure Maths Postgraduate Seminar
12:10		Syzygy Bundles and the Weak Lefschetz Property
		Hicks Seminar Room J11
Mar 29	Wed	Tom Leinster (Glasgow)	Pure Maths Colloquium
16:00		Another look at Euler characteristic
		Hicks Seminar Room J11
	Abstract: Far beyond the realm where we can count "vertices minus edges", there are spaces that, nevertheless, appear to have a well- defined Euler characteristic. For example, the Julia set of any rational function f seems to have an Euler characteristic, a number giving basic information about the dynamical behaviour of f. But to define the Euler characteristic of such spaces, we first need to define the Euler characteristic of a category. This involves generalizing the Mobius inversion formula of classical number theory. We'll see, for instance, that the Euler characteristic of the category of finite sets and bijections is e = 2.718... . Throughout, our motto is: "Euler characteristic is generalized cardinality".
Mar 31	Fri	Ruben Sanchez (Sheffield)	Chromatic homotopy
16:00		Homotopy Limits and Colimits III
		Hicks Seminar Room J11
Apr 26	Wed	Dr Dave Roscoe (Sheffield)	Applied Mathematics Colloquium
		Redshift phenomenology: A review of Napier's analysis
Apr 26	Wed	Caroline Series (Warwick)	Pure Maths Colloquium
16:00		Taming the unruly hyperbolic jungle
		Hicks Seminar Room J11
	Abstract: The last few years have seens some spectacular developments in our understanding of hyperbolic 3-manifolds. The title of my talk is taken from a recent article in Science magazine on this topic. The problems are equivalent to much simpler sounding questions about what happens when you iterate Mobius maps. I will give an overview of the background and the significance of the new developments, illustrated with many pictures from our book Indra's Pearls (Mumford, Series and Wright, CUP 2002).
Apr 27	Thu	Georg Struth (Sheffield, Department of Computer Science)	Algebra / Algebraic Geometry seminar
15:10		Kleene algebras and program analysis
		Hicks Seminar Room J11
	Abstract: Kleene algebras are non-commutative idempotent semirings with an additional operation for iteration or reflexive transitive closure. They have recently received considerable attention as foundational structures in computer science and for their suitability in different application areas. In this talk I will discuss the basics of Kleene algebras and related structures. I will also try to point out the general benefits of algebraic approaches to software analysis and verification and survey a number of applications in the analysis of programs and software systems.
Apr 28	Fri	James Cranch (Sheffield)	Chromatic homotopy
16:00		Introduction to Stacks
		Hicks Seminar Room J11
May 2	Tue	Neil Dummigan (Sheffield)
11:00		Number Theory Seminar "Modular degrees of elliptic curves"
		Hicks Seminar Room J11
	Abstract: In the first talk I'll look at Neron models of abelian varieties, the Tate p-adic uniformisation of elliptic curves and the modular parametrisations of elliptic curves over the rationals. In the second talk I'll look at the description of the special fiber of the Neron model of the Jacobian of a curve, in terms of the special fiber of a regular model of the curve. Then I'll use all this to prove something about the degrees of modular parametrisations.
May 3	Wed	Dr Sergei Molokov (Coventry)	Applied Mathematics Colloquium
		Interfacial instability in a two-layer system with transverse electric current
May 3	Wed	Rajender Adibhatla (Sheffield)	Pure Maths Postgraduate Seminar
12:10		Deformations of Galois representations
		Hicks Seminar Room J11
May 3	Wed	Simon Donaldson (Imperial College)	Pure Maths Colloquium
16:00		Differential geometry on toric varieties
		Hicks Seminar Room J11
May 5	Fri	James Cranch (Sheffield)	Chromatic homotopy
16:00		Introduction to Stacks, II
		Hicks Seminar Room J11
May 8	Mon	James Cranch (Sheffield)	Chromatic homotopy
16:00		Introduction to Stacks, III
		Hicks Seminar Room J11
May 10	Wed	Prof Basil Hiley (Birkbeck College)	Applied Mathematics Colloquium
		Quantum Field Theory and the Bohm Model: the Role of the Photon
May 10	Wed	Anthony Hignett (Sheffield)	Pure Maths Postgraduate Seminar
12:10		Stable cooperations in complex K-theory
		Hicks Seminar Room J11
May 10	Wed	Fran Burstall (Bath)	Pure Maths Colloquium
16:00		Harmonic Gauss maps
		Hicks Seminar Room J11
	Abstract: I shall give an overview for non-experts of the modern theory of harmonic maps and how it applies to questions of classical (and sometimes unfashionable) differential geometry via an appropriate notion of Gauss map.
May 12	Fri	James Cranch (Sheffield)	Chromatic homotopy
16:00		Introduction to Stacks, IV
		Hicks Seminar Room J11
May 15	Mon	David Gepner (Sheffield)	Chromatic homotopy
16:00		Higher and Derived Stacks, I
		Hicks Seminar Room J11
May 16	Tue	Paul Buckingham (Sheffield)
11:00		TBA - this will be a number theory seminar
		Hicks Seminar Room J11
	Abstract: This talk will deal with the annihilator ideal of the group ring of a Galois group action on a cyclotomic class group.
May 17	Wed	Prof Chris Eilbeck (Heriot Watt)	Applied Mathematics Colloquium
		Breathers in discrete systems
May 17	Wed	Panagiotis Tsaknias (Sheffield)	Pure Maths Postgraduate Seminar
12:10		Modular forms and Fermat's Last Theorem
		Hicks Seminar Room J11
May 18	Thu	Rodney Sharp (Sheffield)	Algebra / Algebraic Geometry seminar
15:00		Artinian modules with a Frobenius action or What I did in my Study Leave
		Hicks Seminar Room J11
May 18	Thu	Luca Stefanini (Zurich)
16:00		Differential Geometry Seminar Integration of LA-Groupoids
		Hicks Seminar Room J11
	Abstract: Many problems regarding second order differential geometry, Poisson geometry, Lie algebroids and Lie groupoids can be formulated in terms of double structures such as double Lie groupoids, LA-groupoids and double Lie groupoids. After overviewing the key facts in Lie theory for Lie algebroids and Lie groupoids, it shall be presented how Lie's theorems extend for LA-groupoids and double Lie groupoids. Apart from a few technicalities, the suitable generalisations are obtained using simple functorial arguments. A few applications to integrability and duality of Poisson groupoids will be briefly described. Note added by Kirill : An LA-groupoid is a groupoid object in the category of Lie algebroids. These structures arise by infinitesimalizing double Lie groupoids, but they also arise in nature as the cotangent bundles of Poisson Lie groups. In that case, they are intermediate between the Drinfel'd double of the corresponding Lie bialgebra and the matched pairs of Lie groups, or symplectic double groupoids, which provide global forms of Poisson Lie groups.
May 19	Fri	David Gepner (Sheffield)	Chromatic homotopy
16:00		Higher and Derived Stacks, II
		Hicks Seminar Room J11
May 24	Wed	Dr David Roscoe (Sheffield)	Applied Mathematics Colloquium
		Electrodynamics: Old theory in a new light
May 26	Fri	David Gepner (Sheffield)	Chromatic homotopy
16:00		Higher and Derived Stacks, III
		Hicks Seminar Room J11
Jun 1	Thu	Dr Manuel Blickle (Essen)	Algebra / Algebraic Geometry seminar
15:00		Witt-rational singularities and rational points
		Hicks Seminar Room J11
	Abstract: I am reporting on joint work with Hélène Esnault. In this talk I will outline the basic properties of a newly introduced class of singularities for varieties in positive characteristic, called Witt-rational singularites. I will attempt to explain how this notion naturally arises in the context of generalizing results on congruences of rational points of a smooth variety over a finite field beyond the smooth case. In fact, our main result roughtly states that a Witt-rational and rationally connected variety has a rational point. Examples of (non) Witt-rational varieties will be discussed as well as the relation of Witt-rational to a Hodge-theoretic consequence of rational singularities in characteristic zero.
Jun 6	Tue	Bertrand Toen (Toulouse)	GATA Seminar
15:00		Stacks and derived categories I
		Hicks Seminar Room J11
	Abstract: The purpose of these two talks is to report on recent works which use stack theory to study derived categories. In the first talk I will discuss the problem of constructing a reasonable moduli space for compact objects in a given triangulated category (or rather a triangulated ``dg-category''). In a first part I will explain some motivations coming from algebraic geometry and representation theory (e.g. the contruction of moduli spaces of complexes of sheaves on an algebraic variety, the definition of ``Hall algebras'' for derived categories). The second part of the talk will be devoted to present a solution to this problem using a notion of ``derived $\infty$-stack'': the main theorem states that the (derived $\infty$-) stack of compact objects in a given ``saturated'' dg-category is algebraic. Some corollaries and possible future applications will be discussed.
Jun 7	Wed	Bertrand Toen (Toulouse)	GATA Seminar
15:00		Stacks and derived categories II
		Hicks Seminar Room J11
	Abstract: The second talk is concerned with the problem of constructing a reasonable moduli space for triangulated (dg)-categories themselves. The main theorem of this second talk states that the (derived $\infty$-) stack of ``saturated dg-categories'' is algebraic. The infinitesimal theory of this moduli stack can be used to explain the relation between the deformation theory of dg-categories and Hochschild cohomology. Two other applications will be discussed. To start with I will describe, for any given rational number p/q, a circle action on the moduli stack of saturated dg-categories whose fixed points are ``Calabi-Yau dg-categories of dimension p/q''. This can be used to prove that the deformation theory of Calabi-Yau dg-categories is controlled by cyclic cohomology. Finally, I will explain how the ``period map'', from the stack of varieties to the stack of saturated dg-categories, can be used to study derived equivalence classes of algebraic varieties.
Jun 14	Wed	Dr Leon Ofman (NASA, USA)	Applied Mathematics Colloquium
		Waves in coronal active regions: observations and models
Sep 27	Wed	Christian Elsholtz (Royal Holloway)	Pure Maths Colloquium
16:00		Combinatorial prime number theory
		Hicks Seminar Room J11
	Abstract: In this talk we study combinatorial questions about primes. In particular, Ostmann asked whether there exist two sets A and B (with at least two elements each) so that their sumset A+B equals the set of primes, for sufficiently large primes. Using a new version of the large sieve method we show, that such sets A and B would need to have counting functions of size $N^{1/2 +o(1)}$, whereas previously only a lower bound of $N^{o(1)}$ and an upper bound of $N^{1+o(1)}$ was known. This implies, for example, that the set of primes cannot be decomposed into three such sets. This talk will give a nontechnical survey of the underlying ideas and show how a new type of the large sieve method and combinatorial counting arguments (including graph theory) can be applied to such problems. Other recent work on primes by Green, Tao, Goldston, Pintz and Yildirim will be mentioned
Oct 4	Wed	Prof. Valentina Zharkova (Bradford)	Applied Mathematics Colloquium
		On the origin of three seismic sources in the 28 October 2003 flare
Oct 5	Thu	John Fry (Sheffield)	Statistics Seminar
14:00		The Mathematics of Financial Crashes
Oct 5	Thu	Keith Harris (Sheffield)	Statistics Seminar
14:00		Statistical Modelling and Inference for Radio-Tracking.
Oct 5	Thu	Holger Brenner (Sheffield)	Topology Seminar
15:10		Continuous solutions to algebraic forcing equations
		Hicks Seminar Room J11
	Abstract: Let $f_1$, ..., $f_n$ and $f$ be polynomials in $C[X_1,...,X_m]$. When is it possible to write $f = q_1f_1 + ... + q_nf_n$ with continuous functions $q_i: C^m \to C$ ($C$=complex numbers). Does there exists an algebraic characterization of this property? The set of polynomials $f$ which can be written in this way form an ideal which we call the continuous closure of $(f_1,...,f_n)$. We give exclusion and inclusion criteria for this closure operation and algebraic apporoximations, in particular in terms of the axes closure (to be introduced). In the case of a monomial ideal we show that the continuous closure and the axes closure have the same combinatorial description and coincide.
Oct 10	Tue	Burt Totaro (Cambridge)	Topology Seminar
14:00		The geometry of Hilbert's fourteenth problem
		Hicks Seminar Room J11
	Abstract: All kinds of classification problems in geometry (going back to Euclid) lead to the problem of finding the ring of polynomial invariant functions for a group acting on a vector space. Hilbert asked whether rings of invariants are always finitely generated. The answer is yes in many cases but no in general, by Nagata. Although the problem is formulated algebraically, Nagata's counterexamples make brilliant use of the geometry of algebraic curves. I will present the latest advances on the problem.
Oct 11	Wed	Andy Tonks (London Metropolitan University)	Pure Maths Colloquium
16:00		On $K_1$ (and $K_0$) of a Waldhausen category
		Hicks Seminar Room J11
Oct 12	Thu	David Jordan (Sheffield)	Algebra / Algebraic Geometry seminar
15:10		Poisson brackets on $\mathbb{C}[x,y,z]$
		Hicks Seminar Room J11
	Abstract: The talk will offer various elementary observations on Poisson brackets on $A:=\mathbb{C}[x,y,z]$. Apparently it is of interest to (some) physicists to know when the sum of two Poisson brackets is again a Poisson bracket, in which case the two are said to be compatible. We consider two types of Poisson brackets on $A$, one (which I call exact) depending on one polynomial $F\in A$ and the other (proximate) depending on two such polynomials $G$ and $H$. Here proximate with $H=1$ is exact. The criterion for one exact and one proximate bracket to be compatible turns out to be symmetric in $F, G, H$. Hopefully someone in the audience will point out why this is geometrically obvious! I will then consider how close sums of these compatible pairs come to giving all Poisson brackets on $A$, referring to an existing classification of quadratic Poisson brackets on $A$. Maybe there will be a vague conjecture. Time permitting, I will look at Poisson brackets that restrict to the zero bracket on $B:=\mathbb{C}[x,y]$ and their connection with simple rings of formal differential operators on $B$.
Oct 18	Wed	Prof Dugald Duncan (Heriot-Watt)	Applied Mathematics Colloquium
		Numerical analysis of a convolution model of phase separation
Oct 18	Wed	Alexey Bondal (Steklov Mathematics Institute)	Pure Maths Colloquium
16:00		Noncommutative deformations of algebraic varieties and Poisson brackets.
		Hicks Seminar Room J11
	Abstract: The first part of the talk will be a short survey on possible approaches to and results on noncommutative deformations of algebraic verieties, in particular, projective spaces. In the second part we will discuss results and conjectures on the geometric structure of Poisson brackets on Fano varieties.
Oct 19	Thu	Neil Dummigan (Sheffield)	Pure Maths Postgraduate Seminar
12:10		Euler and the zeta function
		Hicks Seminar Room J11
Oct 19	Thu	Andrew Stacey (Sheffield)	Algebra / Algebraic Geometry seminar
15:10		A Plethora of Plethories - Describing Unstable Cohomology Operations
		Lecture Theatre 7
	Abstract: Generalised cohomology theories are a useful tool that allow topologists to use algebraic techniques to study topological spaces. One of the bits of baggage that comes with a generalised cohomology theory is the set of operations on said theory. There are several different ways of describing the algebraic structure of a set of operations which vary from the "neat" to the "useful" via the "completely bizarre"; most are described in a paper by Boardman, Johnson, and Wilson in the Handbook of Algebraic Topology. I shall explain some of these descriptions and introduce another one which appears not to have been considered in this context. It uses the notion of a "plethory", which was originally defined (though not by that name) in the 70s by Tall and Wraith.
Oct 25	Wed	Dr Rony Keppens (K.U.Leuven)	Applied Mathematics Colloquium
		Grid-adaptive approaches for computing magnetized plasma dynamics
Oct 25	Wed	John Power (University of Edinburgh)	Pure Maths Colloquium
16:00		The Algebra of Computational Effects
		Hicks Seminar Room J11
	Abstract: Lawvere theories and monads have been the two main category theoretic formulations of universal algebra, Lawvere theories arising in 1963 and the connection with monads being established a few years later. Monads, although mathematically the less direct and less malleable formulation, rapidly gained precedence. A generation later, Eugenio Moggi instigated the use monads in theoretical computer science in order to model computational effects, without reference to universal algebra. But since then, the relevance of universal algebra to computational effects has been recognised, leading to renewed prominence of the notion of Lawvere theory, now in a computational setting. Here, we investigate the history, in particular asking why Lawvere theories were eclipsed by monads in the 1960's, and how the renewed interest in them in a computer science setting has been developing and might continue to develop in future.
Oct 26	Thu	Nikita Markarian (Sheffield)	Algebra / Algebraic Geometry seminar
15:10		Non-abelian Hodge theory in characteristic 0 and p>0"
		Hicks Seminar Room J11
	Abstract: We shall give a short review of the non-abelian Hodge theory as it was introduces in works of Deligne, Simpson and others. Then we shall discuss a possible analog of it (for curves) in positive characteristic.
Oct 31	Tue	Victor Snaith (Sheffield)	Topology Seminar
14:00		Upper Triangle Technology and the Arf Invariant
		Hicks Seminar Room J11
Nov 1	Wed	Dr John Barrett (Nottingham)	Applied Mathematics Colloquium
		Geometry of the standard model and neutrino mass terms
Nov 1	Wed	Paul Turner (Heriot-Watt)	Pure Maths Colloquium
16:00		Khovanov homology for links
		Hicks Seminar Room J11
	Abstract: Khovanov homology is a vector space valued invariant of links whose graded Euler characteristic is the Jones polynomial. It is a stronger invariant than the Jones polynomial, reveals interesting further structure and has nice functorial properties with respect to link cobordisms. In this talk I will endeavour to give an overview of the subject discussing definitions, elementary properties and some applications.
Nov 2	Thu	Nancy Nicholls (Reading)	Statistics Seminar
14:00		Getting Started: Data Assimilation for Very Large Inverse Problems in Environmental Science
Nov 2	Thu	David Stern (Sheffield)	Algebra / Algebraic Geometry seminar
15:10		Exceptional collections and mutations on Del Pezzo surfaces.
		Hicks Seminar Room J11
	Abstract: Abstract: This talk will use special collections of bundles to obtain abelian categories that are derived equivalent to the category of coherent sheaves of a Del Pezzo surface. These abelian categories are the categories of modules of the homomorphism algebra of bundles in the collection which can be described as the path algebra of a quiver. These constructions work on strong exceptional collections and the main focus of the talk will be to describe an operation, called mutation, acting on a closed set of such collections.
Nov 7	Tue	Alastair Craw (Glasgow)	Topology Seminar
14:00
		Hicks Seminar Room J11
Nov 8	Wed	Dr Yasmin Andrew (JET (Culham))	Applied Mathematics Colloquium
		Experimental Studies of the L-H Transition on JET
Nov 8	Wed	Alastair Craw (University of Glasgow)	Pure Maths Colloquium
16:00
		Hicks Seminar Room J11
Nov 9	Thu	Clive Anderson (Sheffield)	Statistics Seminar
14:00		Some Extreme Value Problems in Metal Fatigue
Nov 13	Mon	Mikhail Kapranov (Yale University)	GATA Seminar
14:00		Talk 1: "Spaces of formal loops and gerbes of chiral differential operators"
		Hicks Seminar Room J11
	Abstract: For a complex manifold X physics considerations lead to a construction of certain sheaves of vertex algebras on X called chiral differential operators (CDO). While locally such a sheaf is unique, globally the situation is similar to that of spinor bundles on a Riemannian manifold. In the categorical terminology they form a gerbe. We relate this gerbe with the gerbe describing 'determinantal anomaly' for the space of free loops in X. The calculation of the class of the gerbe of CDO due to Gorbounov, Malikov and Schechtman turns out to be a particular case of a local Riemann-Roch-type theorem for determinantal gerbes.
Nov 14	Tue	Neil Strickland (Sheffield)	Topology Seminar
14:00		Structured ring spectra and the nilpotence theorem
		Hicks Seminar Room J11
	Abstract: One form of the nilpotence theorem says that if $R$ is a ring spectrum and $a\in\pi_dR$ maps to zero in $MU_dR$ then $a^n=0$ for large $n$. This is a very powerful result, which forms the basis for a huge body of work in stable homotopy theory. Strangely, however, little further work has been done with the circle of ideas used in the proof of the nilpotence theorem. In this talk we will revisit these ideas using some newer technology of structured ring spectra.
Nov 15	Wed	Dr Konstantin Ilin (York)	Applied Mathematics Colloquium
		The stability of tangential and rotational discontinuities in MHD
Nov 15	Wed	Peter Jorgensen (Newcastle)	Pure Maths Colloquium
16:00		Interactions between algebra, analysis, and topology
		Hicks Seminar Room J11
Nov 16	Thu	David Scott (Auckland)	Statistics Seminar
14:00		The hyperbolic and related distributions: problems of implementation
Nov 16	Thu	Mikhail Kapranov (Yale University)	GATA Seminar
15:10		Talk 2: "Spaces of formal loops and gerbes of chiral differential operators."
		Hicks Seminar Room J11
	Abstract: For a complex manifold X physics considerations lead to a construction of certain sheaves of vertex algebras on X called chiral differential operators (CDO). While locally such a sheaf is unique, globally the situation is similar to that of spinor bundles on a Riemannian manifold. In the categorical terminology they form a gerbe. We relate this gerbe with the gerbe describing 'determinantal anomaly' for the space of free loops in X. The calculation of the class of the gerbe of CDO due to Gorbounov, Malikov and Schechtman turns out to be a particular case of a local Riemann-Roch-type theorem for determinantal gerbes.
Nov 21	Tue	Mikhail Kapranov (Yale University)	GATA Seminar
14:00		Talk 3: "Spaces of formal loops and gerbes of chiral differential operators."
		Hicks Seminar Room J11
	Abstract: For a complex manifold X physics considerations lead to a construction of certain sheaves of vertex algebras on X called chiral differential operators (CDO). While locally such a sheaf is unique, globally the situation is similar to that of spinor bundles on a Riemannian manifold. In the categorical terminology they form a gerbe. We relate this gerbe with the gerbe describing 'determinantal anomaly' for the space of free loops in X. The calculation of the class of the gerbe of CDO due to Gorbounov, Malikov and Schechtman turns out to be a particular case of a local Riemann-Roch-type theorem for determinantal gerbes.
Nov 22	Wed	Dr Lisa Hall (Sheffield)	Applied Mathematics Colloquium
		Consistent modified gravity models
Nov 22	Wed	Samir Siksek (University of Warwick)	Pure Maths Colloquium
16:00		Classical Diophantine Equations and the Proof of Fermat's Last Theorem
		Hicks Seminar Room J11
	Abstract: Wiles' proof of Fermat's Last Theorem is one of the happiest memories of the 20th century. Unfortunately, Wiles' proof does not readily extend in a way that allows us to solve many other classical Diophantine problems. In this talk, based on joint work with Bugeaud and Mignotte, we explain how the proof of Fermat's Last Theorem can be combined with older analytic techniques due to Baker, in a way that solves several classical Diophantine problems. For example, we show that the only perfect powers in the Fibonacci sequences are 0, 1, 8, 144.
Nov 23	Thu	Stuart Barber (Leeds)	Statistics Seminar
14:00		Signal processing using complex Daubechies wavelets
Nov 23	Thu	Konstantin Ardakov (Sheffield)	Algebra / Algebraic Geometry seminar
15:10		Iwasawa algebras
		Hicks Seminar Room J11
Nov 29	Wed	Dr Duncan Mackay (St. Andrews)	Applied Mathematics Colloquium
		MHD Simulations of Solar Prominences
Nov 29	Wed	Herbert Gangl (University of Durham)	Pure Maths Colloquium
16:00		Multiple polylogarithms, polygons and algebraic cycles.
		Hicks Seminar Room J11
Nov 30	Thu	David Barnes (Sheffield)	Pure Maths Postgraduate Seminar
12:10		Categories with Involution
		Hicks Seminar Room J11
Nov 30	Thu	Goran Peskir (Manchester)	Statistics Seminar
14:00		Optimal stopping
Nov 30	Thu	Konstantin Ardakov (Sheffield)	Algebra / Algebraic Geometry seminar
15:10		Iwasawa algebras II
		Hicks Seminar Room J11
Dec 5	Tue	Andrew Ranicki (Edinburgh)	Topology Seminar
14:00		The geometric Hopf invariant
		Hicks Seminar Room J11
	Abstract: The talk will be a report on an ongoing joint project with Michael Crabb (Aberdeen). The geometric Hopf invariant of a stable map $F:\Sigma^{\infty}X \to \Sigma^{\infty}Y$ is a stable $Z_2$-equivariant map $h(F):X \to (S^{\infty})^+\wedge(Y \wedge Y)$ to the quadratic construction on $Y$. The stable $Z_2$-equivariant homotopy class of $h(F)$ is the primary obstruction to desuspending $F$. The geometric Hopf invariant of the stable Umkehr map $F:\Sigma^{\infty}M^+ \to \Sigma^{\infty}T(\nu_f)$ of an immersion $f:N^n\to M^m$ of manifolds factors through the $Z_2$-equivariant double point set of $f$. The $\pi_1$-equivariant version of the geometric Hopf invariant has an application to Wall's non-simply-connected surgery theory.
Dec 6	Wed	Toby Stafford (University of Michigan)	Pure Maths Colloquium
16:00		Noncommutative Projective Surfaces
		Hicks Seminar Room J11
	Abstract: Noncommutative projective geometry seeks to use the intuition and techniques from classical projective algebraic geometry to understand the structure of noncommutative algebras and related modules categories. In this talk I will survey some of the basic ideas and techniques in the subject and, time permitting, outline recent work that describes a large class of ``noncommutative surfaces'' which have some weird and wonderful properties.
Dec 7	Thu	Raj Bhansali (Liverpool)	Statistics Seminar
14:00		Frequency Analysis of Chaotic Intermittency Maps with Slowly Decaying Correlations
Dec 12	Tue	Simon Willerton (Sheffield)	Topology Seminar
14:00		Hopf Monads
		Hicks Seminar Room J11
	Abstract: Representations of finite groups have various nice properties, you can tensor two representations together to get another representation and you can take the dual of a representation to get a new representation. This makes the category of representations into a `monoidal category with duals' which lifts these structures from the category of vector spaces. More generally this is true of the representations of any Hopf algebra. A monad is a categorical gadget which can be viewed as generalization of an algebra (in a sense I will explain), and which has a category of representations. Motivated by some specific examples you can ask when the category of representations is a monoidal category with duals (ie when the monad is a *Hopf* monad). I will endeavour to explain my pictorial approach to the answer given by Bruguiere and Virilizier.
Dec 13	Wed	Prof Koji Ohkitani (Sheffield)	Applied Mathematics Colloquium
		Blowup and regularity problems of hypoviscous fluid equations.
Dec 13	Wed	Paul Smith (University of Washington)	Pure Maths Colloquium
16:00		Noncommutative Hirzebruch surfaces
		Hicks Seminar Room J11
	Abstract: I will introduce the audience to some of the main ideas and methods in non-commutative algebraic geometry by focusing on a rich class of examples, the spaces of the title, and showing how closely their behavior follows that in the commutative case. Our results about non-commutative Hirzebruch surfaces, $qF_n$, specialize to the commutative case: for example, there is a map, in the sense of non-commutative geometry, to the projective line, there is a curve on $qF_n$ with self-intersection number (defined in terms of the Euler form on the Grothendieck group) $-n$, and contracting that curves provides maps to other well-known non-commutative surfaces that are again analogues of their commutative counterparts. The starting point for the definition and analysis is a non-commutative analogue of Cox's homogeneous coordinate ring of a toric variety.
Dec 14	Thu	Stefanie Biedermann (Southampton)	Statistics Seminar
14:00		Robust optimal designs for dose-response experiments
Dec 14	Thu	Sukhendu Mehrotra (Sheffield)	Algebra / Algebraic Geometry seminar
15:10		Stability Manifolds as Extended Kaehler Moduli Spaces
		Hicks Seminar Room J11
Jan 15	Mon	Sarah Whitehouse (Sheffield)	Chromatic homotopy
14:00		Topological Hochschild Homology
		Hicks Seminar Room J11
Feb 7	Wed	Jitesh S.B. Gajjar (Manchester)	Applied Mathematics Colloquium
16:00		Global stability calculations of some separated flows
Feb 7	Wed	Kevin Buzzard (Imperial College London)	Pure Maths Colloquium
16:15		Artin's conjecture on L-functions
		Hicks Seminar Room J11
Feb 8	Thu	Elke Thonnes (University of Warwick)	Statistics Seminar
14:00		Statistical analysis of pore patterns in fingerprints
Feb 14	Wed	Ivan Fesenko (Nottingham)	Pure Maths Colloquium
16:00		Dealing with noncommutative aspects of 1d number theory in a commutative 2d way
		Hicks Seminar Room J11
Feb 14	Wed	Rich Kerswell (Bristol)	Applied Mathematics Colloquium
16:00		Transition to Turbulence in a Pipe
Feb 16	Fri	Neil Dummigan (Sheffield)	Algebra / Algebraic Geometry seminar
14:10		p-adic Hodge theory I
		Hicks Seminar Room J11
	Abstract: Global and local Galois groups, Frobenius elements, cyclotomic characters, Tate modules of elliptic curves.
Feb 20	Tue	John Greenlees (Sheffield)	Topology Seminar
14:00		Rational cohomology theories on free $G$-spaces
		Hicks Seminar Room J11
	Abstract: I aim to describe a classification for the theories of the title. More precisely, they are classified by free rational $G$-spectra, and I will describe an algebraic model when $G$ is a connected compact Lie group (the category of torsion modules over the polynomial ring $H^*(BG;Q)$). The two ingredients are an Adams spectral sequence and derived Morita theory. (Joint work with Brooke Shipley).
Feb 21	Wed	Silvia Dalla (Manchester)	Applied Mathematics Colloquium
16:00		Solar science with AstroGrid
Feb 22	Thu	Almar Kaid	Pure Maths Postgraduate Seminar
12:10		Detecting semistability of vector bundles on curves
		Hicks Seminar Room J11
Feb 22	Thu	Ed Cripps (Sheffield)	Statistics Seminar
14:00		Variable selection and covariance selection in multivariate Gaussian linear regression
Feb 27	Tue	John Greenlees (Sheffield)	Topology Seminar
14:00		Rational cohomology theories on free $G$-spaces pt II
		Hicks Seminar Room J11
	Abstract: I aim to describe a classification for the theories of the title. More precisely, they are classified by free rational $G$-spectra, and I will describe an algebraic model when $G$ is a connected compact Lie group (the category of torsion modules over the polynomial ring $H^*(BG;Q)$). The two ingredients are an Adams spectral sequence and derived Morita theory. (Joint work with Brooke Shipley).
Feb 28	Wed	Tony Arber (Warwick)	Applied Mathematics Colloquium
16:00		Emergence of flux through into the Solar corona: the effect of partially ionized layers
Feb 28	Wed	Meinolf Geck (Aberdeen)	Pure Maths Colloquium
16:15		Representations of Hecke algebras
		Hicks Seminar Room J11
	Abstract: Hecke algebras arise in various contexts in Mathematics, ranging from knot theory (construction of the famous Jones polynomial) to the theory of finite groups. They possess a rich and involved combinatorial structure. The purpose of the talk is to explain the role that these algebras play in the representation theory of finite groups and to highlight some recent advances.
Mar 2	Fri	Neil Dummigan (Sheffield)	Algebra / Algebraic Geometry seminar
14:10		p-adic Hodge theory II
		Hicks Seminar Room J11
	Abstract: Big rings, comparison theorems, de Rham and crystalline representations.
Mar 5	Mon	Jos (Universidad Nacional Aut)	Topology Seminar
14:00		Characteristic Classes and Transversality
		Hicks Seminar Room J11
	Abstract: Let $\xi$ be a smooth vector bundle over a differentiable manifold $M$. Let $h : \epsilon^{n-i+1}\to \xi$ be a generic bundle morphism from the trivial bundle of rank $n-i+1$ to $\xi$. We give a geometric construction of the Stiefel-Whitney classes when $\xi$ is a real vector bundle, and of the Chern classes when $\xi$ is a complex vector bundle. Using $h$ we define a differentiable closed manifold $Z(h)$ and a map $\phi : Z(h)\to M$ whose image is the singular set of $h$. The $i$-th characteristic class of $\xi$ is the Poincaré dual of the image, under the homomorphism induced in homology by $\phi$, of the fundamental class of the manifold $Z(h)$. We extend this definition for vector bundles over a paracompact space, using that the universal bundle is filtered by smooth vector bundles.
Mar 6	Tue	Martin Crossley (Swansea)	Topology Seminar
14:00		Word Hopf Algebras
		Hicks Seminar Room J11
	Abstract: Hopf algebras of words appear in many contexts, particularly in topology and in combinatorics. I'll discuss a few of these situations a number of results both old, new, false and true about them.
Mar 7	Wed	T. Talipova (Institute of Applied Physics, Russian Academy of Sciences)	Applied Mathematics Colloquium
16:00		The Gardner equation in nonlinear theory of wave motion in stratified medium
Mar 7	Wed	Elmer Rees (Bristol)	Pure Maths Colloquium
16:15		Frobenius's higher characters and some more recent developments
		Hicks Seminar Room J11
Mar 9	Fri	Neil Dummigan (Sheffield)	Algebra / Algebraic Geometry seminar
14:10		p-adic Hodge theory III
		Hicks Seminar Room J11
Mar 13	Tue	Richard Hepworth (Sheffield)	Topology Seminar
14:00		Chen-Ruan Cohomology
		Hicks Seminar Room J11
	Abstract: Chen-Ruan cohomology seems to be the correct notion of cohomology for orbifolds. Sadly, the definition is rather complicated since it involves differential operators on Riemann surfaces. I will motivate and define orbifolds and Chen-Ruan cohomology before explaining how all of the complications can be reduced to a single property of the so-called age grading.
Mar 14	Wed	Andrew Booker (Bristol)	Pure Maths Colloquium
16:00		New twists on an old idea of Turing
		Hicks Seminar Room J11
Mar 16	Fri	Frazer Jarvis (Sheffield)	Algebra / Algebraic Geometry seminar
14:10		Introduction to group schemes
		Hicks Seminar Room J11
Mar 20	Tue	Julia Singer (Bonn)	Topology Seminar
14:00		Equivariant Lambda Rings
		Hicks Seminar Room J11
	Abstract: The existence of commutative multiplications on Moore spectra for certain types of rings leads to algebraic conditions providing additional structure on the rings. I'll explain why this can be thought of as an equivariant generalisation of a lambda ring structure.
Mar 21	Wed	May-Win Thein (New Hampshire)	Applied Mathematics Colloquium
16:00		Celestial Navigation (CelNav): Lunar Surface Navigation
Mar 21	Wed	Harold Stark (California, San Diego)	Pure Maths Colloquium
16:15		The Gauss Class-Number Problems
		Hicks Seminar Room J11
Mar 22	Thu	Panagiotis Tsaknias (Sheffield)	Pure Maths Postgraduate Seminar
12:10		"Constructing Galois representations from modular forms"
		Hicks Seminar Room J11
Mar 22	Thu	Søren Asmussen (Aarhus)	Statistics Seminar
14:00		Tail Probabilities for a Computer Reliability Problem
Mar 23	Fri	Frazer Jarvis (Sheffield)	Algebra / Algebraic Geometry seminar
14:10		To be announced
		Hicks Seminar Room J11
Apr 18	Wed	Jonathan Pila (Bristol)	Pure Maths Colloquium
16:00		Density of rational points
		Hicks Seminar Room J11
	Abstract: The basic questions of diophantine geometry concern rational or integral points on an algebraic variety: do they exist, how can they be described (or found), how are they distributed, etc. Such questions lead to deep theorems (often ineffective in various ways) and far-reaching conjectures. This talk will be about a circle of problems and results on giving simply upper bound estimates for the number of integer or rational points up to a given height. I will describe a quite elementary method that yields results that, while relatively weak for an individual variety, are uniform over large classes of varieties. This uniformity has made the results useful. The same methods are also applicable to certain nonalgebraic sets. I will describe a result about rational points on the graph of a transcendental real-analytic function and a connection with transcendence theory. I will finally describe a result on the rational points of analytic (and more general) sets of arbitrary dimension and further connections with transcendence theory.
Apr 18	Wed	Patrick Fowler (Sheffield (Chemistry Department))	Applied Mathematics Colloquium
16:00		Mapping currents in molecules
Apr 25	Wed	Christian Boehmer (Portsmouth)	Applied Mathematics Colloquium
16:00		Does the cosmological constant imply the existence of a minimal energy density?
Apr 27	Fri	Jayanta Manoharmayum (Sheffield)	Algebra / Algebraic Geometry seminar
14:10		Deformations of Galois representations
		Hicks Seminar Room J11
Apr 30	Mon	Constanze Roitzheim (Sheffield)	Chromatic homotopy
13:00		Hopf Invariant One for Odd Primes
		Hicks Seminar Room J11
May 2	Wed	Tom Van Doorsselaere (Warwick)	Applied Mathematics Colloquium
15:00		Recent results in coronal loop seismology: determination of the non-ideal damping mechanism and the density scale height
May 2	Wed	Simon Wadsley (Cambridge)	Pure Maths Colloquium
16:00		$K_0$ of p-torsion modules for Iwasawa algebras
		Hicks Seminar Room J11
May 3	Thu	Harry Ullman (Sheffield)	Pure Maths Postgraduate Seminar
12:10		The Stable Splitting of $U(n)$
		Hicks Seminar Room J11
May 3	Thu	Chris Williams (Edinburgh)	Statistics Seminar
14:00		Gaussian processes and machine learning
May 4	Fri	Jayanta Manoharmayum (Sheffield)	Algebra / Algebraic Geometry seminar
14:10		Deformations of Galois representations II
		Hicks Seminar Room J11
May 8	Tue	Ruben Sanchez (Sheffield)	Topology Seminar
14:00		Computing Borel's regulator
		Hicks Seminar Room J11
	Abstract: The Borel's regulator map is a useful tool to study the higher algebraic K-theory of the ring of integers of an algebraic number field. In 2000, Hamida proved a formula for the Borel's regulator as an integral of non-commutative differential forms. We will present a formula to approximate this integral which can lead to explicit computations. Finally, we will discuss a p-adic version of this.
May 9	Wed	Jerome Scherer (UAB Barcelona)	Pure Maths Colloquium
16:00
		Hicks Seminar Room J11
May 9	Wed	Sergei Nazarenko (Warwick)	Applied Mathematics Colloquium
16:00		Leith-type model of 2D turbulence and its predictions
May 10	Thu	Simon Tavaré (Southern California)	Statistics Seminar
14:00		Stochastic processes in stem cell evolution
May 11	Fri	Cristina Lopez Martin (University of Salamanca (visiting Warwick))	Algebra / Algebraic Geometry seminar
14:10		Fourier-Mukai transforms and moduli spaces of sheaves on elliptic curves
		Hicks Seminar Room J11
May 15	Tue	Richard Hepworth (Sheffield)	Topology Seminar
14:00		What is a KO object?
		Hicks Seminar Room J11
	Abstract: The real question is "What is an elliptic object?". Stolz and Teichner have been trying to answer this, and along the way they have developed a new perspective on K-theory. In this expository talk I'll try to explain a little bit of this, hopefully ending with a sketch of Stolz-Teichner's theorem describing the KO-theory spectrum in terms of euclidean field theories.
May 16	Wed	Jacek Brodzki (Southampton)	Pure Maths Colloquium
16:00		Why can't metric spaces be more like groups?
		Lecture Theatre 2
	Abstract: Research into the Baum-Connes conjecture and related issues provides examples of non-trivial and fruitful interactions between analysis and geometry of (among others) discrete groups. On the other hand, ideas of Gromov, Roe and others gave rise to a programme of large- scale geometry, where two objects are declared equivalent if they "look the same" from a distance. In this talk I shall describe new ideas and results that arise from efforts to unify certain features of both programmes.
May 16	Wed	Roddy Vann (York)	Applied Mathematics Colloquium
16:00		A burning fusion plasma: theoretical challenges
May 18	Fri	Helena Fischbacher-Weitz (University of Southampton)	Algebra / Algebraic Geometry seminar
14:10		An equivariant Riemann-Roch theorem for curves
		Hicks Seminar Room J11
	Abstract: Let $X$ be an algebraic curve over a field $k$, let $D$ be a divisor on $X$, and let $\mathcal{O}_X(D)$ denote the invertible sheaf (or line bundle) associated to D on X. We are interested in the 0-th cohomology group $H^0(X,\mathcal{O}_X(D))$ of this sheaf, which can be viewed a space of functions on X whose pole and zero orders are bounded by the values of D. Its dimension as a k-vector space is computed by the ``classical'' Riemann-Roch theorem: $$ \dim H^0(X, \mathcal{O}_X(D)) - \dim H^1(X, L(D))= deg D + 1 - g,$$ where $g$ is the genus of $X$. If we now consider the action of a finite group $G$ on $X$, and if we require $D$ to be $G$-stable, then $G$ also acts on the cohomology groups of $\mathcal{O}_X(D)$, and we have Riemann-Roch type theorems which compute the equivariant Euler characteristic $$ [H^0(X, \mathcal{O}_X(D))] - [H^1(X,\mathcal{O}_X(D))]$$ as an element of the Grothendieck group of $k[G]$-modules, and further in the Grothendieck group of projective $k[G]$-modules. The emphasis in this talk will be on the case where the underlying field $k$ is perfect, but not necessarily algebraically closed.
May 21	Mon	Tore Kro (NTNU)	Topology Seminar
14:00		Geometry of elliptic cohomology
		Hicks Seminar Room J11
	Abstract: We review what elliptic cohomology is. Furthermore, we will mention the various attempts to define it geometrically. In the program initiated by Baas, the idea is to consider 2-vector bundles. We will look at their definition, and the related notion of charted 2-bundles, and give examples.
May 22	Tue	Tore Kro (NTNU)	Topology Seminar
14:00		What does the nerve of a 2-category classify?
		Hicks Seminar Room J11
	Abstract: We outline the proof showing that the nerve of a topological 2-category classifies charted 2-bundles structured by this 2-category. As a corollary, we will see that the K-theory associated to Baez and Crans 2-vector bundles splits as two copies of ordinary K-theory.
May 22	Tue	Andrei Caldararu (Wisconsin)	GATA Seminar
15:45		The Mukai pairing on Hochschild homology
		Hicks Seminar Room J11
	Abstract: Given a Calabi-Yau three-fold X, string theory constructs two so-called topological twists, the A-model and the B-model. A piece of the mathematical incarnation of the A-model is the singular cohomology ring of X (or its quantum deformation). The corresponding piece in the B-model is encoded by the Hochschild cohomology ring of X. Physics predicts both sets of data are Frobenius algebras, i.e., they are endowed with a non-degenerate pairing. In the A-model, this is given by the Poincare pairing on cohomology. In my talk I shall discuss the construction of the corresponding pairing on Hochschild (co)homology. I shall also discuss several important properties of this pairing, including the Cardy condition from open-closed topological string theory.
May 23	Wed	Johan Anderson (Sheffield)	Applied Mathematics Colloquium
16:00		Comparison of theoretical models to zonal flow generation and the effects of back-reaction of zonal flows on ITG turbulence
May 23	Wed	Andrei Caldararu (Wisconsin)	GATA Seminar
16:00		The Pfaffian-Grassmannian derived equivalence
		Hicks Seminar Room J11
	Abstract: We argue that there exists a derived equivalence between Calabi-Yau threefolds obtained by taking hyperplane sections (of the appropriate codimension) of the Grassmannian G(2,7) and the Pfaffian Pf(7). The existence of such an equivalence has been conjectured by physicists for almost ten years, as the two families of Calabi-Yau threefolds are believed to have the same mirror. It is the first example of a derived equivalence between Calabi-Yau threefolds which are provably non-birational.
May 25	Fri	Jonathan Elmer (University of Kent)	Algebra / Algebraic Geometry seminar
14:10		Modular Invariant Rings of Minimal Depth
		Hicks Seminar Room J11
	Abstract: Let G be a finite group, V a kG-module over a field k of characteristic p, and R:=S(V^*), and let R^G be the corresponding ring of invariants. It is well known that if p does not divide |G|, then R^G is a Cohen-Macaulay ring. Equivalently, depth(R^G) = dim(R^G), or "R^G has maximal depth". Little is known in general about the depth of modular invariant rings in general, although thanks to Ellingsrud and Skjelbred we do have a lower bound for depth(R^G). A representation V for which this lower bound is attained is called "flat". In this talk we introduce a slightly narrower class of representations (called "strongly flat") and show that although not all flat representations are strongly flat, this notion is sufficiently general to produce a wealth of new examples of flat representations.
May 29	Tue	Ieke Moerdijk (Sheffield)	Topology Seminar
14:00		To what extent is Lie theory for groupoids like that for groups?
		Hicks Seminar Room J11
	Abstract: Lie groupoids play an increasingly important role in foliation theory, symplectic and Poisson geometry, and non-commutative geometry. In this lecture, we explain how some basic properties of Lie groups extend to groupoids, and how some other properties don't. The talk will only presuppose some basic familiarity with Lie groups, and in particular should be understandable to the students who attended my recent RTP course.
May 30	Wed	Ruben Sanchez (Sheffield)	Topology Seminar
16:00		Computing Borel's regulator II
		Hicks Seminar Room J11
	Abstract: The Borel's regulator map is a useful tool to study the higher algebraic K-theory of the ring of integers of an algebraic number field. In 2000, Hamida proved a formula for the Borel's regulator as an integral of non-commutative differential forms. We will present a formula to approximate this integral which can lead to explicit computations. Note: This talk is independent of the first one except some knowledge of algebraic K-theory and motivation.
May 30	Wed	Daniel Brown (Aberystwyth)	Applied Mathematics Colloquium
16:00		The onset of x-ray bright points in the solar corona
May 31	Thu	Mark Davis (Imperial)	Statistics Seminar
14:00
Jun 6	Wed	Shunsuke Takagi (Fukuoka)
13:30		Finiteness properties of rings with finite F-representation type
		Hicks Seminar Room J11
Jun 6	Wed	Rodney Sharp (Sheffield)
14:40		Further interactions between graded annihilators and tight closure
		Hicks Seminar Room J11
Jun 6	Wed	Reza Tavakol (Queen Mary)	Applied Mathematics Colloquium
16:00		Dynamo models and differential rotation in the Sun and late-type rapidly rotating stars
Jun 6	Wed	Craig Huneke (University of Kansas)	GATA Seminar
16:00		How many times does a polynomial vanish at a point? (GATA lecture I)
		Hicks Seminar Room J11
Jun 7	Thu	Shunsuke Takagi (Fukuoka)
11:00		Rationality of F-jumping exponents on singular varieties
		Hicks Seminar Room J11
Jun 7	Thu	Yuji Yoshino (Okayama)
13:30		Non-commutative parameter algebras of universal liftings of chain complexes
		Hicks Seminar Room J11
Jun 7	Thu	Holger Brenner (Sheffield)
14:40		Some challenging examples for the localization problem in tight closure
Jun 7	Thu	Craig Huneke (University of Kansas)	GATA Seminar
16:00		Reduction to characteristic p, and further refinements of vanishing along algebraic subsets (GATA lecture II)
		Hicks Seminar Room J11
Jun 8	Fri	Vladimir Bavula (Sheffield)
11:00		The Jacobian map, the Jacobian group and the group of automorphisms of the Grassmann algebra
		Hicks Seminar Room J11
Jun 8	Fri	Yuji Yoshino (Okayama)
13:30		Local cohomologies with non-closed supports
		Hicks Seminar Room J11
Jun 8	Fri	Moty Katzman (Sheffield)
14:40		Frobenius structures on injective hulls and their applications
		Hicks Seminar Room J11
Jun 8	Fri	Craig Huneke (University of Kansas)	GATA Seminar
16:00		Absolute integral closures in mixed characteristic and characteristic p (GATA lecture III)
		Hicks Seminar Room J11
Sep 25	Tue	Birgit Richter (Hamburg)
16:00		K-theory of 2-vector spaces
Sep 26	Wed	Birgit Richter (Hamburg)
14:00		K-theory of bipermutative categories I
Sep 27	Thu	Birgit Richter (Hamburg)
14:00		K-theory of bipermutative categories II
Oct 2	Tue	Eugenia Cheng (Sheffield)	Topology Seminar
14:00		An operadic approach to $n$-categories
		Hicks Seminar Room J11
	Abstract: Operads provide a way of studying loop spaces, by giving a formalism for keeping track of weakly associative multiplication. In this talk I will discuss how this is related to study of weak $n$-categories, where now we must keep track of weakly associative composition. I will present the definition of weak $n$-category proposed by Trimble, which uses one specific and very straightforward topological operad. This can be generalised so that we can use other operads such as the little intervals operad and possibly many of your favourite loop space operads.
Oct 3	Wed	Vic Snaith (Sheffield)	Pure Maths Colloquium
16:30		From Algebraic Cobordism to Algebraic Cobordism in only 31 Years
		Hicks Seminar Room J11
Oct 4	Thu	Kirill Mackenzie (Sheffield)
12:10		Lie algebras: integration by paths
		Hicks Seminar Room J11
	Abstract: There are several distinct proofs of the integrability of (finite dimensional, real) Lie algebras, but the main purpose of this seminar is to describe the proof of Duistermaat using path spaces. This method is the foundation of the solution of the integrability problem for Lie algebroids and in retrospect can also be seen as underlying the construction by Cattaneo and Felder of a symplectic realization for any Poisson manifold, using Poisson sigma models. If time and interest are available there will be a second talk on (Poisson) sigma models which I hope will provide some background for Cattaneo's talk in Sheffield on October 24th.
Oct 5	Fri	David Gepner (Sheffield)	Higher Category Theory
13:00		Organisational meeting
		Hicks Lecture Room 10
Oct 5	Fri	Mykola Gordovskyy (Sheffield)
13:05
		Lecture Theatre 9
Oct 9	Tue	Paul Mitchener (Sheffield)	Topology Seminar
14:00		Coarse Geometry
		Hicks Seminar Room J11
	Abstract: Topology arises from the study of continuous maps, and essentially what happens at very small distances. Coarse geometry, by contrast, ignores all local structure, and only examines very large scale details. Essentially, all that matters in coarse geometry is what is going on `at infinity'. In this talk we will introduce the basic notions of coarse geometry, along with a number of examples and coarse invariants that are analogous to standard invariants in algebraic topology.
Oct 9	Tue	David Applebaum (Sheffield)
17:00		Some Random Thoughts on the Laplacian
		Hicks Lecture Theatre 7
	Abstract: The Laplacian is one of the most important linear operators in mathematics. One reason for this is its ubiquitous role in important second order partial differential equations (pdes) and this lecture will focus mainly on the heat equation. I'll describe the probabilistic method of solving this pde using Brownian motion and show how this relates to the modern analytical approach via semigroup theory. In the last part of the talk, we'll bring in some geometry and I'll describe how the Laplacian on a compact Riemannian manifold can yield information about the curvature.
Oct 10	Wed	Tim Dokchitser (Cambridge)	Pure Maths Colloquium
16:00		Parity Conjecture for elliptic curves
		Hicks Seminar Room J11
Oct 10	Wed	Dr Matthew P.Juniper (University of Cambridge)	Applied Mathematics Colloquium
16:00		'Absolute Stability in Fuel Injectors'
		Hicks Lecture Theatre 6
Oct 11	Thu	Richard Jacques (University of Sheffield)	Statistics Seminar
14:00		Classification Methods for the Analysis of High Content Screening Data
		Hicks Room K14
	Abstract: The current paradigm for the identification of candidate drugs within the pharmaceutical industry typically involves the use of high throughput screens. A high throughput screen allows a large number of compounds to be tested in a biological assay in order to identify any activity inhibiting or activating a biological process. From each of the assays run through a high throughput screen a high content screen image is produced which can be analysed using advanced imaging algorithms to produce a set of variables which reflect the observed activity of the cells within the image. Classification methods have important applications in the analysis of high content screening data where they are used to predict which compounds have the potential to be developed into new drugs. Statistical approaches have been developed that enable classification using a single parameter. However, approaches for multi-parametric selection are still in their infancy. Furthermore, proper exploitation of the information contained within each high content screen image will enable more refined compound selection. A new classification technique for the analysis of data from high content screening experiments will be presented and the methodology illustrated on an example data set using a random forest classifier.
Oct 11	Thu	Michailina Siakalli (University of Sheffield)	Statistics Seminar
14:00		Stochastic Stabilization
		Hicks Room K14
	Abstract: In simple words stability of a dynamic system means sensitivity of the system to changes. Consider a first order non-linear differential equation system dx(t)\dt=f(x(t)). Investigating what happens when noise is added, it has so far been observed that Brownian motion noise can stabilize an unstable system or destabilize it in the case that is stable. In my talk I will describe what is happening when the given non-linear system is perturbed by different types of Poisson noise.
Oct 12	Fri	Eugenia Cheng (Sheffield)	Higher Category Theory
13:00		Introduction
		Hicks Seminar Room J11
Oct 12	Fri	Johan Anderson (Sheffield)
13:05
		Lecture Theatre 9
Oct 12	Fri	Simon Willerton (Sheffield)	Algebra / Algebraic Geometry seminar
14:10		Low-dimensional algebra
		Hicks Seminar Room J11
Oct 15	Mon	Kirill Mackenzie (Sheffield)
14:30		Integration of Lie algebras, continued
		Hicks Seminar Room J11
Oct 16	Tue	Teimuraz Pirashvili (Leicester)	Topology Seminar
14:00		Second Hochschild cohomology and triangulated categories
		Hicks Seminar Room J11
Oct 17	Wed	David Rydh (Stockholm)	Algebra / Algebraic Geometry seminar
13:10		Submersions and effective descent of etale morphisms
		Hicks Seminar Room J11
Oct 17	Wed	Elizabeth Allman (Fairbanks, visiting Newton institute)	Pure Maths Colloquium
16:00		Models of DNA site substitution
		Hicks Seminar Room J11
	Abstract: Molecular phylogenetics is concerned with inferring evolutionary relationships (phylogenetic trees) from biological sequences (such as aligned DNA sequences for a gene shared by a collection of species). The probabilistic models of sequence evolution that underly statistical approaches in this field exhibit a rich algebraic structure. After an introduction to the inference problem and phylogenetic models, this talk will survey some of the highlights of current algebraic understanding. Results on the important statistical issue of identifiability of phylogenetic models will be emphasized, as the algebraic viewpoint has been crucial to obtaining such results.
Oct 18	Thu	Steve Buckland (The National Centre for Statistical Ecology)	RSS Seminar
14:30		Embedding population dynamics models in inference
		Hicks Room K14
	Abstract: Increasing pressures on the environment are generating an ever-increasing need to manage animal and plant populations sustainably, and to protect and rebuild endangered populations. Effective management requires reliable mathematical models, so that the consequences of management action can be predicted, and the uncertainty in these predictions quantified. These models must be able to predict the response of populations to anthropogenic change, while handling the major sources of uncertainty. We describe a simple Â'building blockÂ' approach to formulating discrete-time models. These models may include demographic stochasticity, environmental variability through covariates or random effects, multi-species dynamics such as in predator-prey and competition models, movement such as in metapopulation models, non-linear effects such as density dependence, and mating models. We discuss methods for fitting such models to time series of data, and quantifying uncertainty in parameter estimates and population states, including model uncertainty, using computer-intensive Bayesian methods.
Oct 18	Thu	Rachel Borysiewicz (The National Centre for Statistical Ecology)	RSS Seminar
14:30		Integrated population modelling for multi-site data
		Hicks Room K14
	Abstract: The statistical analysis of mark-recapture-recovery (MRR) data collected on wild animal populations dates back to the 1960s, when the foundation was laid for stochastic models fitted to data by the method of maximum likelihood. In recent years an active area of research has developed which combines MRR data with census data. The census data can be described by state-space models and the Kalman filter provides a mechanism for forming the census likelihood. Model fitting then follows by maximising a combined likelihood that is the product of component likelihoods. By combining multiple data sources it has been found that as well as increasing precision of common parameters, it is also possible to estimate parameters which would be inestimable from the analysis of the separate data alone. This methodology is termed integrated population modelling. A particular focus of this talk will be to discuss integrated population modelling for multi-site data, which arises when animals live in and move between different locations. By making use of movement information provided by MRR data, it is possible to avoid flat likelihood surfaces, thus allowing the estimation of site-dependent parameters. The benefits of performing integrated population modelling on multi-site data will be highlighted through both simulated and real data applications.
Oct 18	Thu	Toby Reynolds (The National Centre for Statistical Ecology)	RSS Seminar
14:30		Integrated data analysis in the presence of emigration and tag loss: A study of common guillemots on (and off) the Isle of May
		Hicks Room K14
	Abstract: In recent years, many UK seabird populations have experienced dramatic breeding failures and lower than average survival. The common guillemot (Uria aalge) is among those species to suffer. The causes of these events are likely due to a combination of over-fishing and environmental change affecting their primary prey species, the lesser sandeel (Ammodytes marinus). We need to understand the dynamics of seabird populations, in order to determine the implications of future breeding failures and enable us to monitor or predict the effects of future changes in the marine environment. Integrated population modelling provides a useful and robust means to achieve this. An integrated analysis will be presented of four long-term datasets relating to a single guillemot colony on the Isle of May, southeast Scotland (a population of about 20,000 breeding pairs). These comprise abundance, MRR (two datasets) and productivity data. A particular complication with guillemot population dynamics arises due to unobservable emigration of immature birds. In traditional analyses using only MRR data, emigration is confounded with tag loss in the estimation of `fidelity' probabilities, and it is only possible to estimate their product. By combining all available data for the Isle of May guillemots, we are able to provide separate estimates for emigration and tag loss. This model provides a framework which may be used for prediction under various future scenarios.
Oct 19	Fri	Urmila Mitra-Kraev (Sheffield)
13:05
		Lecture Theatre 9
Oct 22	Mon	Paul Mitchener (Sheffield)	Non-commutative Geometry, Analysis and Groups
17:00		Motivation and Introduction to the Index Theorem
		Hicks Seminar Room J11
	Abstract: We will look at de Rham cohomology, the Euler characteristic, differential operators, and the Gauss-Bonnet formula in an attempt to motivate the Atiyah-Singer index theorem before stating the theorem in its general form. The plan is for this to be a short talk; we will work out organisational details for the rest of the semester afterwards.
Oct 26	Fri	Sergei Zharkov (Sheffield)
13:05
		Lecture Theatre 9
Oct 26	Fri	Almar Kaid (Sheffield)	Algebra / Algebraic Geometry seminar
14:10		Frobenius descent for vector bundles
		Hicks Seminar Room J11
Oct 29	Mon	Bruce Bartlett	Higher Category Theory
16:00		Degenerate Higher Categories II
		Hicks Seminar Room J11
	Abstract: This is part II of the talk from last week. I will recap the idea of the periodic table and what the stabilization hypothesis is about. Then we'll relate the ideas of suspension, looping, and stabilization in higher categories to the corresponding ideas in topology. Finally we'll look at the "second column" of the periodic table, explaining the kinds of algebraic structures which appear there - with plenty of examples (*) - and also explain how suspension and looping work on these structures. (*) One of the algebraic structures appearing in the second column of the periodic table is a "braided monoidal category". I will try to mention the idea due to Grothendieck and Drinfeld, once explained to me by Frazer, that the "group of deformations" of a certain natural braided monoidal category is somehow isomorphic to the absolute Galois group from number theory.
Oct 29	Mon	John Greenlees (Sheffield)	Non-commutative Geometry, Analysis and Groups
17:00		Characteristic Classes
		Hicks Seminar Room J11
Oct 30	Tue	Shoham Shamir (Sheffield)	Topology Seminar
14:00		Cellular approximations and the Eilenberg-Moore spectral sequence
		Hicks Seminar Room J11
	Abstract: Given chain-complexes k and M over a ring R, a k-cellular approximation to M is the "closest approximation" of M that can be glued together from copies of suspensions of k. I will discuss this concept (due to Dwyer, Greenlees and Iyengar) and how is can be used to study the Eilenberg-Moore cohomology spectral sequence for a fibration.
Oct 31	Wed	Wilhelm Klingenberg (Durham)	Pure Maths Colloquium
16:00		Fibrations by geodesics, spacelike surfaces, and the standard tight contact structure
		Hicks Seminar Room J11
	Abstract: A regular fibration by geodesics of a three-dimensional space form is represented by a spacelike surface in four-dimensional moduli space of geodesics. In the euclidean case, the standard contact structure is perpendicular to such a fibration. Solemn undertaking: "I would make it accessible to any math grad student..."
Oct 31	Wed	Professor Alan Zinober (Sheffield)	Applied Mathematics Colloquium
16:00		'Optimal Control and Some Applications in Operations Research'
		Hicks Lecture Theatre 6
Nov 2	Fri	Gemma Attrill (MSSL)
13:05
		Lecture Theatre 9
Nov 2	Fri	Barrie Cooper (Sheffield)	Algebra / Algebraic Geometry seminar
14:10		Almost Koszul algebras and rational conformal field theory I
		Hicks Seminar Room J11
	Abstract: The preprojective algebra of a non-Dynkin graph is Koszul and can be identified with the functorial image of a Koszul ``universal preprojective algebra object'' in the Temperley-Lieb category. This line of thought also helps identify what happens to make the Dynkin preprojective algebras ``almost Koszul'' and elicits interesting connections to conformal field theory and quantum subgroups of sl(2). In the second talk I will discuss the sl(3) case and use these connections to construct new examples of almost Koszul algebras. The talk will be pretty basic, with the aim of rendering the abstract comprehensible to a graduate student.
Nov 5	Mon	Richard Hepworth (Sheffield)	Non-commutative Geometry, Analysis and Groups
17:00		Dirac Operators
		Hicks Seminar Room J11
Nov 6	Tue	James Cranch (Sheffield)	Topology Seminar
14:00		Spannish for beginners
		Hicks Seminar Room J11
	Abstract: I will say something about the notion of a span category, the appropriate analogue in the language of quasicategories, and what all this is supposed to have to do with homotopy theory.
Nov 7	Wed	Bob Coecke (Oxford)	Pure Maths Colloquium
16:00		Kindergarten Quantum Mechanics
		Hicks Seminar Room J11
Nov 7	Wed	Dr C.J.Howls (Southampton)	Applied Mathematics Colloquium
16:00		'Why is a Shock Not a Caustic?
		Hicks Lecture Theatre 6
Nov 8	Thu	Markus Riedle (University of Manchester)	Statistics Seminar
14:00		Introduction to stochastic delay differential equations
		Hicks Room K14
	Abstract: In the last years stochastic functional differential equations or stochastic differential equations with delay have gained increasing attention in several scientific areas such as economy, biology, physics and medicine. The reason can be found in the observation that in a huge variety of models the evolution of the process describing the dynamics in the model under consideration not only depends on the current state of the process but also on its former states. This effect is due to various reasons such as time to maturity, incubation time, time to build, time to transport, hysteresis, delayed feedback and past dependent volatility. In the beginning of the talk we present some of these applications of stochastic functional differential equations. We introduce the basic ideas of ordinary stochastic differential equations not depending on the past and explain how these equations can be generalised to functional equations covering the examples presented before. The fundamental theory of stochastic functional differential equations are introduced and in particular compared with the situation of ordinary stochastic differential equations. In the remaining part of the talk we distinguish several cases how the random noise and past dependence enter the equation and we focus here on asymptotic aspects of the solution. We present some phenomena only known from delay equations. We also introduce some results which explain the relation of functional and partial stochastic differential equations.
Nov 9	Fri	Youra Taroyan (Sheffield)
13:05
		Lecture Theatre 9
Nov 14	Wed	Alexander J McNeil (Heriot-Watt University)	Statistics Seminar
14:00		A New Perspective on Archimedean Copulas
		Hicks Room K14
	Abstract: The Archimedean copula family is used in a number of actuarial applications, ranging from the construction of multivariate loss distributions to frailty models for dependent lifetimes. We present some new results that contribute to a greater understanding of this family and point the way to improved simulation and estimation procedures. We derive necessary and sufficient conditions for an Archimedean generator function (a continuous, decreasing mapping of the positive half-line to the unit interval) to generate a copula in a given dimension d. We also show how the Archimedean family coincides with the class of survival copulas of L1-norm symmetric distributions. These results allow us to construct a rich variety of new Archimedean copulas in different dimensions and to solve in principle the problem of generating samples from any Archimedean copula. The practical consequences include new models for negatively dependent risks, simple formulas for rank correlation coefficients and diagnostic tests for Archimedean dependence.
Nov 14	Wed	Keiichi Ueda (Kyoto University)	Applied Mathematics Colloquium
16:00		Stripe splitting in reaction-diffusion systems on uniformly growing domains
		Hicks Lecture Theatre 6
Nov 15	Thu	John Harthman (South Yorkshire Fire & Rescue Service)	RSS Seminar
16:30		Registering Risk - The Community Risk Register
		Hicks Room K14
	Abstract: Under the Civil Contingencies Act 2004, local authorities and the emergency services are required to assemble and publish a "register" of local hazards and the risks they pose to their communities as a basis for informing emergency planning. This talk will examine the principles widely adopted across the UK in fulfilling this legal duty and illustrate some areas of concern, with particular reference to the supposedly 'unprecedented' floods in Sheffield and South Yorkshire of June 2007.
Nov 16	Fri	Viktor Fedun (Sheffield)
13:05
		Lecture Theatre 9
Nov 16	Fri	Barrie Cooper (Sheffield)	Algebra / Algebraic Geometry seminar
14:10		Almost Koszul algebras and rational conformal field theory II
		Hicks Seminar Room J11
Nov 16	Fri	Helena Fischbacher-Weitz (Sheffield)	Algebra / Algebraic Geometry seminar
15:20		Geometric Galois module theory: A result of Chinburg revisited
		Hicks Seminar Room J11
	Abstract: Geometric Galois module theory deals with the problem of computing the equivariant Euler characteristic of bounded complexes of sheaves on a finite cover of noetherian schemes. In this talk, we concentrate on the following special case. Let X be a nonsingular, irreducible projective curve over a finite field k, and let G be a finite subgroup of Aut(X/k). Assume that the cover X--> X/G is tamely ramified. Then the equivariant Euler characteristic of the de Rham complex of X is the class [H^0 (X, O_X)] - [H^1(X, O_X)] in the Grothendieck group of projective kG-modules. Chinburg has proved a formula for this (which also generalizes to higher dimensions) in terms of epsilon constants (Artin root numbers) of representations of G. We will see that there is an alternative description of the equivariant Euler characteristic of the de Rham complex, which may be viewed as an equivariant Hurwitz formula. This can be used, together with various results on epsilon constants, to give an alternative, more elementary proof of Chinburg's formula.
Nov 19	Mon	J.F. Jardine (University of Western Ontario)
16:00		The parabolic groupoid
		Hicks Seminar Room J11
	Abstract: This talk gives a description of a simplicial groupoid object $\mathbf{Par}$ which collects together the parabolic subgroups of the general linear groups. The parabolic groups appear as automorphism groups of objects in the various simplicial degrees. One recovers Quillen's $K$-theory space for vector bundles from $\mathbf{Par}$ by applying Zariski stack completion in each simplicial degree. The method of proof involves cocycle categories used as models for stack completion, in the context of the homotopy theoretic approach to the theory of stacks.
Nov 19	Mon	Dave Applebaum (Sheffield)	Non-commutative Geometry, Analysis and Groups
17:00		The Analytic Index
		Hicks Seminar Room J11
Nov 20	Tue	Christian Ausoni (Bonn)	Topology Seminar
14:00		On rational algebraic K-theory
		Hicks Seminar Room J11
	Abstract: I will present a strategy for computing the rational algebraic K-theory of connective S-algebras. I will illustrate it in the cases where the algebra is connective complex or real topological K-theory. This is joint work with John Rognes (Oslo).
Nov 21	Wed	Harry Ullman (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Invertible objects in the equivariant stable homotopy category.
		Hicks Seminar Room J11
	Abstract: Invertible objects in the equivariant stable homotopy category. In classical algebra, for a commutative ring R an R-module M is said to be invertible if there exists an R-module N such that M tensor N is isomorphic to R as R-modules. The isomorphism classes of invertible R-modules form a group, called the Picard group of R, Pic(R). This is an example of the Picard group of a closed symmetric monoidal category. The first half of the talk will comprise of the definitions of a closed symmetric monoidal category, invertible objects of a category and the Picard group of a category. In the second half of the talk I will discuss work of Fausk, Lewis and May on calculating the invertible elements of the equivariant stable homotopy category by constructing a similar but simpler category to work from. I will assume everyone knows what a category, functor and natural transformation is, but not much else from there.
Nov 21	Wed	Alexander Vishik (Nottingham)	Pure Maths Colloquium
16:00		u-invariant of fields and Algebraic Cobordism
		Hicks Seminar Room J11
Nov 21	Wed	Mahesan Niranjan (Sheffield)	Applied Mathematics Colloquium
16:00		Some fun problems that simultaneously excite Biologists, Applied Mathematicians and Computer Scientists
		Hicks Lecture Theatre 6
Nov 22	Thu	Qiwei Yao (London School of Economics)	Statistics Seminar
14:00		Modelling Multiple Time Series via Common Factors
		Hicks Room K14
	Abstract: We propose a new method for estimating common factors of multiple time series. One distinctive feature of the new approach is that it is applicable to nonstationary time series. The unobservable (nonstationary) factors are identified via expanding the orthoganal complement of the factor loading space step by step; therefore solving a high-dimensional optimization problem by many low-dimensional sub-problems. Asymptotic properties of the estimation were investigated. The proposed methodology was illustrated with both simulated and real data sets.
Nov 23	Fri	Stephen Fletcher (Sheffield Hallam)
13:05
		Lecture Theatre 9
Nov 23	Fri	Larry Smith (Goettingen, visiting Sheffield)	Algebra / Algebraic Geometry seminar
14:10		Cohomology Automorphisms and Ore's q-Power Series Ring
		Hicks Seminar Room J11
	Abstract: A cohomology automorphism is just that, an automorphism of the functor that assigns to a topological space X its total(say for definiteness singular) cohomology algebra H^{**} (X ; F) = \prod_{i=1}^\infty H^i (X ; F), where F is say a field. For the case of F = F_p these were introduced and studied by Atiyah and Hirzebruch in connection with Wu's Formula concerning the action of Steenrod operations on H^{*}(X ; F_p)when X is a closed (oriented) manifold. There is a surprising connection between cohomology automorphisms (which may be expressed in terms of Steenrod operations) and a certain ring introduced by O.Ore, the ring of q-power series. This leads to a description of the Steenrod group (i.e., the group of invertible elements in the total Steenrod algebra) {\cal P}^{**} = \prod_{i=0^\infty {\cal P}^i. Several amusing problems in this connection remain open as far as I know. I will also mention one application to topology : An extension of Thom's theorem: There are no non trivial rational cohomology operations. In some sense this holds for any infinite field.
Nov 26	Mon	Paul Mitchener (Sheffield)	Non-commutative Geometry, Analysis and Groups
17:00		Sobolev Spaces
		Hicks Seminar Room J11
Nov 27	Tue	David Barnes (Sheffield)	Topology Seminar
14:00		Rational Equivariant Cohomology Theories
		Hicks Seminar Room J11
	Abstract: If one wants to study spaces, one can use cohomology theories. For spaces with a group action, one uses equivariant cohomology theories which provide more refined information about the group action. By requiring that these cohomology theories are rational, one can study the collection of rational equivariant cohomology theories as a whole. In the case of a finite group, SO(2) or O(2) one can replace the collection of rational equivariant cohomology theories by an explicit and easy to understand algebraic category. I will talk about how, according to the group structure, the collection of rational equivariant cohomology theories splits into several disjoint collections. Thus one can study each of these pieces separately. I will also discuss how one can relate rational O(2) cohomology theories to rational SO(2) cohomology theories via the notion of a category with involution. This work is an overview of my thesis, supervised by John Greenlees.
Nov 28	Wed	James Cranch (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Arithmetic with monads
		Hicks Seminar Room J11
	Abstract: Abstract: "This talk will be a report on the work of Durov, who has been trying to do number theory using a certain sort of monads as a generalisation of commutative rings. I will review some basic arithmetical constructions, motivate the generalisations, and make the necessary definitions. Then we will have some fun with examples. These will include the local ring of Z at infinity (and its completion), the field with one element, and the ring of integers congruent to 1 mod 10."
Nov 28	Wed	Professor John Brown (Glasgow)	Applied Mathematics Colloquium
15:00		\'The High Energy Sun and NASA\'s Award Winning RHESSI Mission\'
		Hicks Lecture Theatre 6
Nov 28	Wed	Neil Strickland (Sheffield)	Pure Maths Colloquium
16:00		Symmetric powers of spheres
		Hicks Seminar Room J11
	Abstract: This talk will report on a project to understand, extend and consolidate a dense network of connections between a wide range of ideas in stable homotopy theory. One way into the maze is to consider the symmetric powers of the sphere spectrum, which interpolate between the sphere spectrum itself and the integer Eilenberg-Mac Lane spectrum. The quotients in this filtration are interesting spectra that arise naturally in a number of other contexts, involving the theory of Steinberg modules and Hecke algebras and the combinatorics of partition complexes. The same partition complexes are also relevant in the theory of the Goodwillie tower of the identity functor. There are other connections with power operations in Morava E-theory, as well as the classical Dyer-Lashof algebra and Lambda algebra. A great deal is already known about these ideas, but there are some hints that important parts of the puzzle have yet to fall into place.
Nov 29	Thu	Boris Mitavskiy (University of Sheffield)	Statistics Seminar
14:00		Complexity of Evaluating the Probability Distribution of State Cycles in Finite State Update Networks
		Hicks Room K14
	Abstract: In many situations in biology (gene interactions, metabolic pathways, etc) and communications (mobile phones, WWW) an appropriate model is provided by a digraph in which the nodes (genes, metabolites, phones, computers) are in various states, and these states are updated (at times $t=0, \, 1, \, 2, \ldots$) as a response to the states of the ``incoming nodes". Assuming synchronous updating then the state of the system as a whole $U(t)$ say is some function of $U(t-1)$. The dynamics of the system (i.e. the sequence of $U(t)$) can then be described by a directed graph over the possible states, where two states $\mathbf{x}$ and $\mathbf{y}$ are joined if $U(t-1)=\mathbf{x}$ implies $U(t)=\mathbf{y}$. Since the system is finite this directed graph consists of a set of cycles, and a set of trees each rooted (the edges of each tree pointing towards the root) on the cycles. There is much known (but little understood) about these dynamics. In this talk I'll introduce a rigorous simplified model of this scenario and study its basic properties with respect to the distribution of cycle lengths. It turns out that the distribution of fixed points is rather straightforward to compute (and it is the uniform distribution regardless of the network topology!) while the distribution of cycles of length $k$ for any fixed $k \geq 2$ is already an NP-hard question with respect to the size of the underlying digraph. I will provide a brief introduction to the theory of NP-completeness which is sufficient to understand the proofs. If time allows, I will also discuss a constant time algorithm to solve the subproblem where the underlying digraph is an $r$-input regular one.
Nov 30	Fri	Philippe Caillol (Sheffield)
13:05
		Lecture Theatre 9
Nov 30	Fri	John Greenlees (Sheffield)	Algebra / Algebraic Geometry seminar
14:10		Commutative algebra of groups and spaces
		Hicks Seminar Room J11
Dec 3	Mon	Paul Mitchener (Sheffield)	Non-commutative Geometry, Analysis and Groups
17:00		Analysis of Dirac Operators
		Hicks Seminar Room J11
Dec 5	Wed	Bruce Bartlett (Sheffield)	Pure Maths Postgraduate Seminar
14:00		The geometry of 2-representations of groups
		Hicks Seminar Room J11
	Abstract: A "2-representation" of a group is a group acting on a suitable linear category. In this sense they are a categorification of ordinary group representations, which are groups acting on linear sets (vector spaces). These structures appear to emerge in topological quantum field theory as well as in elliptic cohomology, and so they are an interesting application of higher category ideas to other branches of mathematics. The 2-representations of a group form a 2-category 2Rep(G), whose objects, morphisms and 2-morphisms have explicit geometric descriptions in terms of "equivariant gerbes". One can also take the "2-character" of a 2-representation, this also has a natural interpretation. The aim of the talk is hopefully to explain these ideas, and to show how simple categorical notions translate into interesting geometric structures.
Dec 5	Wed	Tamas Hausel (Oxford)	Pure Maths Colloquium
16:00		Arithmetic harmonic analysis on holomorphic symplectic quotients
		Hicks Seminar Room J11
Dec 7	Fri	Simon Willerton (Sheffield)	Higher Category Theory
13:00		Higher Duals in Higher Categories
		Hicks Seminar Room J11
Dec 7	Fri	Daniel Rees (Sheffield)
13:05
		Lecture Theatre 9
Dec 7	Fri	Vladimir Bavula	Algebra / Algebraic Geometry seminar
14:10		Dimension, multiplicity, holonomic modules, and an analogue of the inequality of Bernstein for rings of differential operators in prime characteristic
		Hicks Seminar Room J11
Dec 10	Mon	Dave Applebaum (Sheffield)	Non-commutative Geometry, Analysis and Groups
17:00		The Heat Equation
		Hicks Seminar Room J11
Dec 11	Tue	Tony Hignett (Sheffield)	Topology Seminar
14:00		Discrete module categories
		Hicks Seminar Room J11
	Abstract: A module over a topological ring is `discrete' if it is continuous when given the discrete topology. This concept is closely related to the coalgebra-algebra duality and hence to the cooperations-operations duality for a (decent) (co)homology theory E. I will talk about discrete module categories in general and the case E = K.
Dec 12	Wed	Norbert Peyerimhoff (Durham)	Pure Maths Colloquium
16:00		On Pompeius problem for Damek-Ricci spaces
		Hicks Seminar Room J11
Dec 12	Wed	Norbert Peyerimhoff (Durham)	Pure Maths Colloquium
16:00		Random walks, Archimedean solids and finite Coxeter groups
		Hicks Seminar Room J11
	Abstract: I will give a geometric characterisation of critical points of eigenvalue functions of the transition probability matrix of random walks on finite, vertex transitive graphs in the case of higher multiplicity. I will also  explain applications to Archimedean solids and to the Cayley graphs of finite Coxeter groups. These are joint results with Ioannis Ivrissimtzis.Â
Dec 12	Wed	Professor Steve Decent (Birmingham)	Applied Mathematics Colloquium
16:00		Unstable Jets, Threads and Curtains
		Hicks Lecture Theatre 6
Dec 14	Fri	Eamon Scullion (Sheffield)
13:05
		Lecture Theatre 9
Dec 14	Fri	David Jordan (Sheffield)	Algebra / Algebraic Geometry seminar
14:10		Simple Poisson modules, singularities and Poisson invariants.
		Hicks Seminar Room J11
Jan 15	Tue	Bob Bruner (Wayne State)	Topology Seminar
14:00		Higher Leibniz Formulas
		Hicks Seminar Room J11
	Abstract: The Leibniz formula tells us how differentials behave on products. When considering an S-algebra, there are higher order operations (Dyer-Lashof operations and their generalizations) and it is possible to work out formulas for differentials on these. They have been worked out in detail in two important cases, the Adams spectral sequence and the spectral sequence(s) for the homology of the homotopy fixed points, orbits or Tate construction of an $S^1$ equivariant S-algebra. In both cases, they provide a great deal of information about the differentials and extensions in the spectral sequence.
Jan 17	Thu	Markus Brodmann (Zurich)	Algebra / Algebraic Geometry seminar
14:00		Cohomological stability of projective schemes over surfaces
		Hicks Seminar Room J11
	Abstract: Let $p: X\to Y$ be a projective morphism of schemes such that $Y$ is a surface of finite type over a field. Let $L$ be an ample sheaf of $O_X$-modules and let F be a coherent sheaf of $O_X$-modules. We show that for each $i > 0$ the set of $Y$-associated primes of the $i$-th direct image $G^i_n := R^i{p_*}(F \otimes L^n)$ ultimately becomes constant if n converges to $-\infty$. We extend this to a stabilty result for the depth of the sheaves $G^i_n$ along a closed zubset $Z$ of $Y$. We also present examples of Singh-Swanson, and more recent ones of Chardin-Cutkosky-Herzog-Srinivasan which show that these stability results fail if the base scheme $Y$ is not a surface. It is noteworthy, that the latter examples show that even ``cohomological tameness'' may fail if $Y$ is of dimension > 2. In purely algebraic terms, our result may be formulated (and proved) as results on the asymptotic behaviour of graded components of certain local cohomology modules.
Jan 29	Tue	Wajid Mannan (Sheffield)	Topology Seminar
14:00		The dimension 2 problem
		Hicks Seminar Room J11
	Abstract: This problem is an example of a phenomena which has long been known to hold in sufficiently high dimensions but is not known to hold in all low dimensions (in this case dimension 2). For n not equal to two, a finite cell complex of cohomological dimension n is homotopy equivalent to an n-complex. It is unknown whether this holds when n=2. I will discuss the problem and explain what I have done so far (proving that it holds sometimes) and mention what I am doing now (Vic's idea for finding a counterexample).
Jan 30	Wed	Jesse Andries (Katholieke Universiteit Leuven, Belgium)	Applied Mathematics Colloquium
14:00		Decoherence of MHD wave packets: a simple example
		Hicks Lecture Theatre A
	Abstract: Magnetohydrodynamic waves have been studied extensively in the literature. They have received much attention lately in efforts to indirectly extract information about the solar coronal plasma by combining theoretical models with data of (spaceborne) instruments that record ample evidence of MHD waves in the solar atmosphere. We will provide a rigorous treatment of linear MHD oscillations in a very simple model emphasizing the self-adjointness and the origin and implications of the existence of continuous parts in the eigenmode spectrum. This will illustrate an important idea which is mathematically and conceptually very easy to understand but which has not yet received enough attention in the context of 'coronal seismology'. Roughly speaking, the output of a system is a convolution between the input and the system. So if you want to draw conclusions based on the output of a system, either you need some information about the input which allows to determine the system, or you need some information on the system in order to draw conclusions on the input. 'Coronal seismology' has so far mainly focussed on discrete trapped waveguide modes and has therefore not payed much attention to this. However, it provides a unifying conceptual framework for the interpretation and comparison of several mechanisms which are often invoked to explain the observed wave behavior and which are often interpreted as being conceptually different (e.g. phase mixing, resonant absorption and leakage). Certainly, within the current understanding that coronal waves are coupled and driven by oscillations in the lower layers of the solar atmosphere and at the solar surface, it is important to appreciate that the characteristics of the solar coronal waves may depend crucially on the characteristics of the driver/exciter and not only on the characteristics of the medium itself.
Feb 5	Tue	Johann Sigurdsson (Sheffield)	Topology Seminar
14:00		Homotopy operations
		Hicks Seminar Room J11
	Abstract: I'll give a leisurely introduction to the theory of homotopy operations on categories of ring spectra.
Feb 6	Wed	Yi Li (Sheffield)	Applied Mathematics Colloquium
14:00		A restricted Euler model for small scale intermittency in fluid turbulence
		Hicks Lecture Theatre A
	Abstract: Small-scale intermittency in fluid turbulence refers to the infrequent but strong bursts in the signals of small scale parameters. These bursts display highly non-Gaussian statistics, and its prediction poses serious challenges to turbulence research. Based on the restricted Euler approximation, we derive in this talk a simple system of equations for the short-time Langrangian evolution of velocity and passive scalar increments. The system reproduces several important intermittency trends observed in turbulence, and thus provides a simple dynamic explanation for the observations.
Feb 7	Thu	John Haslett (Dublin Trinity College)	Statistics Seminar
14:00		Monotone smoothing: application of a compound Poisson- Gamma process to modelling radiocarbon-dated depth chronologies
		Hicks Room K14
	Abstract: We propose a new and simple continuous Markov monotone stochastic process and use it for Bayesian monotone smoothing. The process is piece-wise linear, based on additive independent Gamma increments arriving in a Poisson fashion. A special case allows very simple conditional simulation of sample paths given known values of the process. We take advantage of a re-parameterisation involving the Tweedie distribution to provide efficient MCMC computation. The motivating problem is the establishment of a chronology for samples taken from lake sediment cores; that is, the attribution of a set of dates to samples of the core given their depths, knowing that the age-depth relationship is monotone. The chronological information arises from radiocarbon (14C) dating at a subset of depths. We use the process to model the stochastically varying sedimentation rate.
Feb 7	Thu	Vic Snaith (Sheffield)	Snaith seminar
15:00		Functoriality of the canonical fractional Galois ideal
		Hicks Seminar Room J11
	Abstract: This is a number theory seminar. A famous conjecture in number theory is the Stark conjecture, which concerns the leading term of the Taylor series for Artin L-functions at $s=0$. A few years ago, en route to giving a proof of the Coates-Sinnott conjecture, I constructed a canonical fractional ideal inside the rational group-ring of a finite, abelian Galois group of a number field extension. It's role in life was to annihilate algebraic K-groups of number rings, in a way which imitated and extended Stickelberger's famous theorem from the 1890's. Recently, in number theory, some very eminent professionals have been studying non-commutative Iwasawa theory. In this one makes an Iwasawa algebra out of an infinite Galois extension with such Galois groups as $GL_{n}{\mathbb{Z}}_{p}$. This talk will (i) describe the canonical (abelian) fractional Galois ideal (ii) its naturality properties (iii) how to make a canonical non-abelian fractional Galois ideal and (iv) it leads conjecturally to a two-sided ideal in the Iwasawa algebra. This is joint work with Paul Buckingham.
Feb 12	Tue	Tom Bridgeland (Sheffield)	Topology Seminar
14:00		Wall-crossing and holomorphic generating functions
		Hicks Seminar Room J11
	Abstract: To get nice moduli spaces for objects in algebraic geometry (e.g. vector bundles) one first has to choose a stability condition. As one varies this stability condition the moduli space of stable objects undergoes discontinuous changes. This is called wall-crossing behaviour. I will explain how this works in a simple example and describe some recent work of Joyce which allows one to make holomorphic generating functions for invariants associated to the moduli spaces using special functions related to multilogarithms.
Feb 13	Wed	Philippe Caillol (Sheffield)	Applied Mathematics Colloquium
14:00		Nonlinear singular Kelvin modes within a barotropic vortex
		Hicks Lecture Theatre A
	Abstract: This study considers the propagation of helical neutral modes within a barotropic and axisymmetric vortex with an arbitrary azimuthal velocity profile. The singular mode/mean flow interaction leads to strongly nonlinear critical layers around the radius where the angular velocity of the mean flow and the disturbance frequency are comparable. Strong analogies can be done with the theory of critical layers in a stratified flow. We formulate a theory valid when the analogous local Richardson number is small at the critical radius but is nevertheless larger than the mode amplitude, and at a long time asymptotic steady state after the formation of the critical layer. The problem is tackled by removing the apparent singularity by retaining nonlinear terms in the equations of motion inside the critical layer. Viscosity is also introduced in order to render the nonlinear critical layer solution unique, but the inviscid limit is eventually taken. The result from the interaction is the emergence of a multipolar vortex whose poles are located on the critical radius, spiral around the basic vortex axis and are embedded in a distorted mean flow caused by a slow diffusion of the three-dimensional vorticity field from the critical layer in a transitional stage due to the very weak viscosity of the flow. This study gives an analytical description of these vortices.
Feb 13	Wed	Raphael Rouquier (Oxford)	Pure Maths Colloquium
16:15		Dunkl operators, microlocalization and quantization
		Hicks Seminar Room J11
	Abstract: We introduce certain algebras of deformed differential operators on a vector space. Their representation theory can be studied via monodromy representations, leading to Hecke algebras. On the other hand, these algebras can be microlocalized. This microlocalization provides a quantization of the Hilbert schemes of points on the complex plane.
Feb 14	Thu	Rita Zapata-Vasquez (University of Sheffield)	Statistics Seminar
14:00		Bayesian cost-effectiveness analysis based on a decision analytic model
		Hicks Room K14
	Abstract: The purpose of economic evaluations relating to cost-effectiveness analysis is to provide decision-makers with sufficient evidence to establish the relevance or pertinence of one treatment or strategy over another, or to adjust the results to his/her location of interest. Cost-effectiveness studies based on decision models involve highlighting specific features of previously published studies. However, the lack of evidence or of consistent reports is common in many fields. In medicine this is complicated by the fact that it is ethically unacceptable to implement clinical trials that put patients under a high risk, or because the cost of such trial is not affordable. Apart from the specialized literature, another source of information is that which can be obtained from experts through the use of elicitation. Regardless of the origin, from this knowledge judgements are established to represent the uncertainty of the data through the use of probability distributions. A model for assessing the cost-effectiveness of two management strategies for the treatment of intracranial hypertension in children with severe traumatic brain injury is outlined. Some parts of the model structure will be presented, but I will focus on the way that the uncertainty of the parameters (inputs) of the model were formulated as probability distributions, based on the corresponding judgements. Certain dependence relations among inputs will be shown, and how learning from one aspect may change our beliefs. Further, I will comment on how the dependence can be conceived when cost and effects come from different sources.
Feb 14	Thu	Theresa Cain (University of Sheffield)	Statistics Seminar
14:00		Bayesian Inference for health state utilities using pairwise comparison data
		Hicks Room K14
	Abstract: The National Institute for Health and Clinical Excellence (NICE) makes recommendations about which drugs should be available on the NHS. An important part of this decision is performing a cost-effectiveness analysis. When evaluating the cost-effectiveness of a treatment, it is important to consider the quality of life a patient experiences. The quality of life is described by utility, a measure of preference for a particular health condition. Conventional methods of eliciting utilities such as the Standard Gamble and Time Trade-off involve questions that some respondents might find difficult to answer. An alternative method is to collect discrete choice data, in which respondents simply state which health state they prefer from two alternatives, rather than provide actual utilities. The underlying utilities must be determined given these pair-wise choices. We consider Bayesian approaches for inference about population utilities given such pair-wise choice data.
Feb 18	Mon		Non-commutative Geometry, Analysis and Groups
16:00		Organisational Meeting
		Hicks Seminar Room J11
Feb 19	Tue	Dirk Schuetz (Durham)	Topology Seminar
14:00		Cohomology of planar polygon spaces
		Hicks Seminar Room J11
	Abstract: We study the topology of the moduli space of polygonal planar curves with given side-length vector. By a conjecture of Walker the side-lengths are determined by the cohomology ring of the moduli space. We show that this conjecture is true for a large class of length vectors, and that an analogous conjecture holds if one considers polygonal curves in 3-space. This is joint work with Michael Farber and Jean-Claude Hausmann.
Feb 19	Tue	Ezra Getzler (Northwestern)	GATA Seminar
16:00		Open-closed topological field theory in 2 dimensions
		Hicks Seminar Room J11
	Abstract: We use Deligne and Mumford's compactification of moduli spaces of Riemann surfaces, and its generalization to Riemann surfaces with boundary introduced by Liu, to analyse the structure of two-dimensional topological field theories.
Feb 20	Wed	Chris Jones (Leeds)	Applied Mathematics Colloquium
14:00		Convection driven zonal flows in giant planets
		Hicks Lecture Theatre A
	Abstract: The large scale zonal flows on Jupiter and Saturn may be due either to deep convection or to forcing in the stably stratified zone near the surface. Boussinesq simulations of deep convection in a rapidly rotating spherical shell have been successful in reproducing the strong eastward flowing current and the alternating bands of eastward and westward flow. We are currently developing an anelastic compressible model to see how the large density variation between the deep interior and the near-surface layers affects these results. A further issue is whether the magnetic field can affect the nature of the surface flows on giant planets.
Feb 20	Wed	Ezra Getzler (Northwestern)	GATA Seminar
14:00		Lie theory for L-infinity algebras
		Hicks Seminar Room J11
	Abstract: I show how to associate to a nilpotent differential graded Lie algebra (or, more generally, L-infinity algebra) concentrated in degrees >-n an n-groupoid. This construction generalizes the case of a Lie algebra (it gives the associated Lie group) and when the dg Lie algebra is abelian (i.e. a chain complex), it becomes the Eilenberg-MacLane space of the complex.
Feb 20	Wed	Tony Hignett (Sheffield)	Pure Maths Postgraduate Seminar
15:00		Iwasawa theory and topological K-theory
		Hicks Seminar Room J11
	Abstract: Finitely generated modules over the Iwasawa algebra $\mathbb{Z}_p[[T]]$ have long been classified up to "pseudo-isomorphism". This can be translated into a statement about p-adic K-theory, because the Iwasawa algebra is almost the ring of operations for this theory. I'll explain this and a possible passage to p-local K-theory.
Feb 20	Wed	Holger Brenner (Sheffield)	Pure Maths Colloquium
16:00		Tight closure is dead - long live tight closure
		Hicks Seminar Room J11
	Abstract: I describe an example, based on a joint work with Paul Monsky, showing that tight closure does not commute with localization. The example is given by a normal hypersurface domain in dimension three in characteristic two and the ideal is generated by three elements. It is a geometric deformation of a two-dimensional tight closure problem and it is analogous to an example of an arithmetic deformation constructed together with Moty Katzman. The geometry in the background of this example is the existence of a vector bundle on a family of smooth projective curves parametrized by the affine line, such that the bundle on the generic curve is strongly semistable, but not so on any special curve. I will also discuss some new developments, discussed with Helena Fischbacher-Weitz, indicating that a certain generic ideal inclusion, which is based on the Froeberg conjecture and which holds for the polynomial ring in three variables, has a tight closure version for graded three-dimensional Cohen-Macaulay domains.
Feb 22	Fri	Youra Taroyan (Sheffield)
13:05
		Lecture Theatre 10
Feb 22	Fri	Neil Dummigan (Sheffield)	Muggle-MAGIC number theory seminar
14:00		Sato-Tate Conjecture, I
		Hicks Seminar Room J11
Feb 25	Mon	Paul Mitchener (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:00		The Heat Equation Proof of the Index Theorem
		Hicks Seminar Room J11
	Abstract: The plan is to give a clear statement of the Atiyah-Singer index theorem and to at least sketch how the methods developed in the seminars last semester enable us to prove the result.
Feb 26	Tue	Constanze Roitzheim (Sheffield)	Topology Seminar
14:00		Morita theory in stable homotopy theory
		Hicks Seminar Room J11
	Abstract: In classical Morita theory, one uses the endomorphisms of a ring R to study the derived category of R-modules. We see how this generalises to studying the homotopy category of a stable model category by endomorphism ring specra. Further, we look at how Morita theory might help us classify algebraic models of the K-local stable homotopy category at odd primes.
Feb 26	Tue	Michael Thompson (Sheffield)
17:00		Forward and Inverse Problems of Solar Seismology
		Hicks Lecture Theatre 7
	Abstract: The Sun oscillates simultaneously in more than a million resonant modes, the oscillations being manifest in small-amplitude motions of the Sun's surface. The measured properties of the observed oscillations can be used to infer conditions inside the Sun, a study known as helioseismology. In this colloquium I shall describe the forward problem of modelling the oscillations and the inverse problems that arise in using the oscillations to infer properties of the solar interior and its physics.
Feb 27	Wed	Srilakshmi Krishnamoorthy (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Modular curves as algebraic curves over Q
		Hicks Seminar Room J11
Feb 28	Thu	Michael Papathomas (Imperial College London)	Statistics Seminar
14:00		Obtaining proposal distributions for reversible jump MCMC
		Hicks Room K14
	Abstract: A major difficulty when implementing the reversible jump Markov chain Monte Carlo methodology lies in the choice of good proposals for the parameters of the competing statistical models. We focus on the comparison of non-nested log-linear models and present a novel approach for the construction of proposal distributions.
Feb 29	Fri	James McLaughlin (St Andrews University)
13:05
		Lecture Theatre 10
Feb 29	Fri	Neil Dummigan (Sheffield)	Muggle-MAGIC number theory seminar
14:00		Sato-Tate Conjecture, II
		Hicks Seminar Room J11
Mar 3	Mon	Dr Helena Fischbacher-Weitz (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:00		The Riemann-Roch Theorem
		Hicks Seminar Room J11
Mar 4	Tue	Ezra Getzler (Northwestern)	GATA Seminar
14:00		Lie theory for L-infinity algebras (Part II)
		Hicks Seminar Room J11
Mar 4	Tue	Andrey Lazarev (Leicester)	Topology Seminar
15:30
		Hicks Seminar Room J11
Mar 5	Wed	Gene Ryan (Bath)	Applied Mathematics Colloquium
13:30		Input-to-State Stability of Differential Inclusions with Application to Hysteretic Feedback Systems
		Hicks Lecture Theatre 7
	Abstract: Input-to-state stability is a concept that captures ``nice'' properties of dynamical systems with input (e.g. bounded input implies bounded state, input ``eventually small'' implies state ``eventually small'', input convergent to zero implies state convergent to zero). Input-to- state stability (ISS) of a class of differential inclusions is described. Every system in the class is of Lur'e-type: a feedback interconnection of a linear system and a (set-valued) nonlinearity. Applications of the ISS results, in the context of feedback interconnections with a hysteresis operator in the feedback path, are developed.
Mar 5	Wed	Ezra Getzler (Northwestern)	GATA Seminar
14:00		Operads revisited
		Hicks Seminar Room J11
	Abstract: I give a new formulation of the axioms for operads, which covers all of the variants of the theory, such as cyclic operads, modular operads, PROPs, wheeled PROPs, as well as simplicially enriched variants, such as topological field theories of different types.
Mar 5	Wed	Zacky Choo (Sheffield)	Pure Maths Postgraduate Seminar
15:00		Finding an element in $H_{3}$
		Hicks Seminar Room J11
Mar 5	Wed	Gennady Puninskiy (University of Manchester)	Pure Maths Colloquium
16:00		Nonfinitely generated projective modules over generalized Weyl algebras
		Hicks Seminar Room J11
	Abstract: The class of generalized Weyl algebras was introduced by V.Bavula in early 90s. Quite a lot is known about finitely generated projective modules over GWAs (say their Grotendieck groups and the zeroth cohomology groups were calculated by T.Hodges). In this talk we discuss a recent classification of infinitely generated projective module over GWAs.
Mar 6	Thu	Neil Dummigan (Sheffield)	Muggle-MAGIC number theory seminar
14:00		Sato-Tate Conjecture, III
		Hicks Seminar Room J11
Mar 7	Fri	Nicolas Leprovost (Sheffield)
13:05
		Lecture Theatre 10
Mar 10	Mon	Helena Fishbacher-Weitz	Algebra / Algebraic Geometry seminar
15:10		Bounds for membership in the Frobenius closure and tight closure
		Hicks Seminar Room J11
	Abstract: Let R be a standard-graded algebra of dimension d+1 over a field of positive characteristic, and let I be an ideal in R. We seek to describe the Frobenius closure I^F and the tight closure I* of the ideal I. In particular, we are interested to find the smallest m such that R_m is contained in I^F or in I*, respectively. This "degree bound" depends on the minimal number of generators of I and on their degrees. Using geometric methods, one can reduce the original problem to finding the smallest zero of the Hilbert function associated to an ideal in a polynomial ring. The Froberg conjecture states that the Hilbert function coincides with a certain combinatorial function, whose zeroes can be computed explicitly. In the cases where the conjecture is known to hold true, in particular for d=2, this leads us to an explicit formula for the degree bound. This talk is based on joint work with Holger Brenner, with further contributions from Thomas Fischbacher.
Mar 10	Mon	Richard Hepworth (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:10		The Hirzebruch Signature Theorem
		Hicks Seminar Room J11
Mar 12	Wed	Ingo Runkel (King's College London)	Pure Maths Colloquium
16:15		Frobenius algebras in braided tensor categories
		Hicks Seminar Room J11
Mar 13	Thu	Robert Gramacy (University of Cambridge)	Statistics Seminar
14:00		Importance Tempering
		Hicks Room K14
	Abstract: Simulated tempering (ST) is an established Markov Chain Monte Carlo (MCMC) methodology for sampling from a multimodal density $\pi(\theta)$. The technique involves introducing an auxiliary variable k taking values in a finite subset of [0,1] and indexing a set of tempered distributions, say $\pi_k(\theta) = \pi(\theta)^k$. Small values of k encourage better mixing, but samples from $\pi$ are only obtained when the joint chain for $(\theta,k)$ reaches k=1. However, the entire chain can be used to estimate expectations under pi of functions of interest, provided that importance sampling (IS) weights are calculated. Unfortunately this method, which we call importance tempering (IT), has tended not work well in practice. This is partly because the most immediately obvious implementation is naïve and can lead to high variance estimators. We derive a new optimal method for combining multiple IS estimators and prove that this optimal combination has a highly desirable property related to the notion of effective sample size. The methodology is applied in two modelling scenarios requiring reversible-jump MCMC, where the naïve approach to IT fails: model averaging in treed models, and model selection for mark--recapture data.
Mar 13	Thu	Russ Bentley, Carol Calvert, Will Driskell, Mike Jones, Nicky Tarry (Department for Work & Pensions)	RSS Seminar
16:15		Statisticians from DWP talk about their work
		Conference room 1 - Moorfoot Building
	Abstract: Statisticians from the Department for Work and Pensions' Information Directorate will provide an insight into the impact statisticians have in the UK's largest Government Department. They will show the contribution statisticians can make to producing accurate intelligence on fraud and migration, how their work has supported policy development and describe how their career as a professional statistician has had an impact and been rewarding.
Mar 14	Fri	Sergey Shelyag (Sheffield)
13:05
		Lecture Theatre 10
Mar 14	Fri	Neil Dummigan (Sheffield)	Muggle-MAGIC number theory seminar
14:00		Sato-Tate Conjecture, IV
		Hicks Seminar Room J11
Mar 18	Tue	Neil Dummigan (Sheffield)	Muggle-MAGIC number theory seminar
14:00		Sato-Tate conjecture V (and final)
		Hicks Seminar Room J11
Mar 18	Tue	Alastair King (Bath)	GATA Seminar
15:00		Dimers, quivers and Calabi-Yau algebras
		Hicks Seminar Room J11
Mar 19	Wed	Anne Juel (Manchester)	Applied Mathematics Colloquium
14:00		Interfacial wave growth in oscillating two-phase flow
		Hicks Lecture Theatre A
	Abstract: When a closed vessel containing two stably stratified, immiscible liquids is oscillated sinusoidally in the horizontal direction, the at interface between the two liquids loses stability to two-dimensional `frozen waves' through a mech- anism analogous to that of the Kelvin{Helmholtz instability). The onset of `frozen waves' occurs through a supercritical pitchfork bifurcation, but for larger values of the forcing parameters, a qualitative change in the wave growth takes place. In terms of the inverse vibrational Froude number, W (ratio of vibrational to gravity forces, proportional to the square of the forcing velocity), there is a critical value, Wc, beyond which the experimental data collapses onto a single curve that exibits a linear dependence on W. We find that this collapse is indicative of a bifurcation to an inviscid solution at Wc. Our investigation of the evolution of the interface shape suggests that this second bifurcation is associated with a transition from gravity to capillary dominated waves, which is consistent with the wavelength reaching a minimum for W = Wc. For larger values of the forcing parameters, the two-dimensional array of waves becomes unstable to three-dimensional oscillatory waves through a sub-critical bifurca- tion. The response frequency of the three-dimensional oscillatory waves is found to be locked to the forcing frequency. Secondary transition to three-dimensional waves underpin the dynamics of a variety of fluid flows, e.g. the oscillatory instability of rolls in thermal convection and the formation of streamwise vortices in mixing layers. We characterise the secondary instability of our oscillating interface by comparison with these systems and discuss the physical mechanism that leads to the onset of three-dimensional waves.
Apr 4	Fri	Daniel Rees (Sheffield)
13:05
		Lecture Theatre 10
Apr 8	Tue	Sarah Whitehouse (Sheffield)	Topology Seminar
14:00		Robinson's bicomplex and Taylor towers
		Hicks Seminar Room J11
	Abstract: Robinson's bicomplex was introduced to provide an obstruction theory for E-infinity structures on ring spectra. For suitable functors taking values in an abelian category, one can define a Taylor tower approximating the functor. In this expository talk, I will explain the relationship between Robinson's bicomplex and Taylor towers, namely the bicomplex is a model for the first layer of the tower. I will discuss recent work of Intermont-Johnson-McCarthy interpreting the rank filtration of functors in terms of the Robinson complex.
Apr 9	Wed	Roald Koudenburg (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Graph complexes of cyclic operads and Outer space.
		Hicks Seminar Room J11
	Abstract: Following the article 'On a theorem of Kontsevich', by Conant and Vogtmann, we will construct a graph complex OG = (OG_*, d) for a cyclic operad O. If O is the Lie-operad then there is a subcomplex of OG whose homology groups are isomorphic to the cohomology groups of Outer space X_n. The latter was introduced by Culler and Vogtmann in their article 'Moduli of graphs and automorphisms of free groups'. Among other things, X_n can be used to compute the rational cohomology of Out(F_n), the group of outer automorphisms of the free group of rank n.
Apr 9	Wed	Zhivko Stoyanov (Bath)	Applied Mathematics Colloquium
14:00		Clustering and ordering of large networks, and sensitivity analysis
		Hicks Lecture Theatre A
	Abstract: Clustering is the problem of dividing a network into two or more balanced and well-connected subnetworks with only a few links between them. This is a discrete problem, which is intractable for most real-life networks, due to their size. We give a brief overview of some of the methods, available in the literature, for clustering large networks. Another discrete problem on networks, which can not be solved exactly in real-life examples, is that of ordering. For example, the problem which Google solves is that of ordering the webpages in the internet, respecting the criteria of their authority, that is, how many webpages link to a given webpage. We give a brief overview of the basics of the techique, which Google uses, in order to solve the problem of ordering. In the second half of the talk we motivate the sensitivity analysis of networks and consider the effects, which small perturbations of the data can produce on the clustering of the network.
Apr 9	Wed	Volodymyr Mazorchuk (the University of Glasgow)	Pure Maths Colloquium
16:15		Konstant's problem
		Hicks Seminar Room J11
	Abstract: Kostant's problem can be formulated as follows: for which modules M over the universal enveloping algebra U(g) of a semi-simple complex finite-dimensional algebra g does the algebra U(g) surject onto the vector space of all linear endomorphisms of M, which are locally finite with respect to the adjoint action of g. This question is not yet answered even for simple highest weight modules. In the talk we plan to survey the classical results on this problem and present some recent results and applications.
Apr 10	Thu	Oliver Johnson (University of Bristol)	Statistics Seminar
14:00		Maximum entropy and Poisson approximation
		Hicks Room K14
	Abstract: I will show that the Poisson distribution maximises entropy in the class of ultra log-concave distributions (a class which includes sums of Bernoulli variables). I will also explain how this result relates to bounds in Poisson and compound Poisson approximation.
Apr 11	Fri	Philippe Caillol (Sheffield)
13:05
		Lecture Theatre 10
Apr 14	Mon	Richard Hepworth (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:10		The Hirzebruch Signature Theorem, Part 2
		Hicks Seminar Room J11
Apr 15	Tue	Paul Mitchener (Sheffield)	Topology Seminar
14:00		What is the Baum-Connes conjecture and why should we care?
		Hicks Seminar Room J11
	Abstract: This talk should be a fairly gentle introduction to the formulation of the Baum-Connes conjecture, some generalisations and analogues, and topological implications of the conjecture, such as the Novikov conjecture, and the question of the existence of positive scalar curvature metrics on certain manifolds.
Apr 16	Wed	Arjun Malhotra (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Exotic 7-Spheres
		Hicks Seminar Room J11
	Abstract: The talk will describe the general notion of exotic spheres, and explain Milnor's initial construction of them in dimension 7.
Apr 16	Wed	A Thyagaraja (UKAEA/EURATOM Fusion Association, Culham Science Centre)	Applied Mathematics Colloquium
14:00		Two-fluid theory of axisymmetric toroidal equilibria
		Hicks Lecture Theatre A
	Abstract: An introduction to key issues in the magnetic confinement to fusion power production will be given. This is followed by an overview account of a recently developed, novel approach to axisymmetric toroidal equilibria with strong flows will be presented, essentially from an analytical point of view.
Apr 16	Wed	Jonathan Pridham (Cambridge)	Pure Maths Colloquium
16:15		Derived deformation theory
		Hicks Seminar Room J11
	Abstract: Deformation theory is the local study of moduli stacks in algebraic geometry. Derived moduli stacks were introduced by Deligne, Drinfel'd and Kontsevich as a generalisation. I will show how strong homotopy algebras and coalgebras over various monads and comonads can be used to construct derived deformation groupoids in many cases.
Apr 17	Thu	Vappu Reijonen (Helsinki)
13:00
		E39, Hicks Building
Apr 17	Thu	Adam Butler (BioSS Edinburgh)	Statistics Seminar
14:00		A latent Gaussian model for compositional data with many zeros
		Hicks Room K14
	Abstract: Compositional data record the relative proportions of different components within a mixture, and arise frequently in many fields, including geology, ecology and human health. Standard statistical techniques for the analysis of such data assume the absence of proportions which are genuinely zero, but real data may contain a substantial number of zero values. In this talk I will present a latent Gaussian model for the analysis of compositional data which contain zero values, based on assuming that the data arise from a (deterministic) Euclidean projection of a multivariate Gaussian random variable onto the unit simplex. A simulation study is used to compare three difference methods of inference - maximum likelihood estimation, MCMC and approximate Bayesian computation - and the methodology is illustrated using real data on dietary intake.
Apr 18	Fri	Sergei Zharkov (Sheffield)
13:05
		Lecture Theatre 10
Apr 21	Mon	Vladimir Bavula (Sheffield)	Algebra / Algebraic Geometry seminar
15:10		The Jacobian Algebra
		Hicks Seminar Room J11
	Abstract: The Jacobian algebras are obtained from the Weyl algebras by inverting (not in the sense of Ore) of certain elements. Surprisingly, the Jacobian algebras and the Weyl algebras have little in common. Moreover, they have almost opposite properties. The Jacobian algebras appeared in my study of the group of polynomial automorphisms and the Jacobian Conjecture, which is a conjecture that makes sense only for polynomial algebras in the class of all commutative algebras. In order to solve the Jacobian Conjecture, it is reasonable to believe that one should create technique which makes sense only for polynomials; the Jacobian algebras are a step in this direction (they exist for polynomials but make no sense even for Laurent polynomials).
Apr 21	Mon	Bruce Bartlett (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:10		Spin groups, spin structures and the Lichnerowicz formula
		Hicks Seminar Room J11
	Abstract: I will be talking about what the spin group is, explaining the idea of a ``spin structure'' and derive the Lichnerowicz formula, which links the square of the Dirac operator to the scalar curvature of the manifold. This has important applications which John will hopefully tell us more about in his talk.
Apr 22	Tue	John Hunton (Leicester)	Topology Seminar
14:00		Cohomology of spaces of substitution tilings
		Hicks Seminar Room J11
	Abstract: One of the main tools that have proved effective in studying aperiodic tilings has been the algebraic topology (cohomology or K-theory) of an associated moduli space of tilings locally equivalent to the individual tiling considered. A special class of examples are the tilings generated by substitutions, and although these are far from being generic examples, they include most of the well known and historically early examples (Fibonacci, Thue-Morse, Penrose, Amman-Beenker, etc). This talk will describe new techniques for understanding the cohomology of their associated spaces.
Apr 23	Wed	Nicolas Leprovost (Sheffield)	Applied Mathematics Colloquium
14:00		Shear stabilisation and turbulent mixing
		Hicks Lecture Theatre A
	Abstract: In order to explain the turbulent mixing in the solar tachocline and also the occurrence of differential rotation in the convection zone, we study the effect of rotation on sheared turbulence. By solving quasi-linear equations for the fluctuating fields, we derive turbulence amplitude and turbulent transport coefficients (turbulent viscosity and diffusivity), taking into account the effects of shear and rotation on turbulence. The interaction between the shear and the rotation is shown to give rise to a novel non-diffusive flux of angular momentum (known as the Lambda effect), possibly offering a mechanism for the occurrence of a strong shear region in the solar interior. We also discuss the effect of stratification and magnetic fields on turbulent mixing."
Apr 23	Wed	Alice Rogers (King's College London)	Pure Maths Colloquium
16:15		Multisymplectic geometry in classical and quantum field theory
		Hicks Seminar Room J11
	Abstract: Symplectic geometry provides the geometric setting for the Hamiltonian formulation of classical mechanics, and its quantization. Multisymplectic geometry is a generalisation of symplectic geometry which allows an analogous formulation for classical field theory. I will describe this formulation, together with some rather tentative steps towards quantization, with particular reference to functional integrals.
Apr 24	Thu	Leszek Roszkowski (University of Sheffield)	Statistics Seminar
14:00		Bayesian Statistics in Cosmology and Particle Physics
		Hicks Room K14
	Abstract: I will describe two recent applications of Bayesian statistics. In one, main features of our Universe are extracted from studies of cosmic background radiation. In the other, current data is used to speculate about properties of ``new physics'' models based on supersymmetry that will soon be tested in particle physics experiments at the Large Hadron Collider (LHC) at CERN near Geneva.
Apr 25	Fri	Mark Douglas (Sheffield)
13:05
		Lecture Theatre 10
Apr 28	Mon	Morten Brun (Bergen)	Topology Seminar
14:00		Covering Homology
		Hicks Seminar Room J11
	Abstract: Given a topological space $X$ and an abelian group $A$ there is a free topological abelian group $A \otimes X$ which morally it is the $X$-fold sum of copies of $A$. The homotopy of the undlying space of this topological abelian group is the homology of $X$ with coefficients in $A$. This approach to homology also works in other contexts. For example, if $A$ is a commutative ring then the commutative ring $A \otimes S^1$ is version of Hochschild homology. In the talk I shall focus on the situation where $A$ is a commutative ring-spectrum, and I shall explain how covering projections $X \to Y$ allow us to use this construction to obtain variations of Bökstedt, Hsiang and Madsen's topological cyclic homology.
Apr 28	Mon	Simon Willerton (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:10		K-theory
		Hicks Seminar Room J11
Apr 29	Tue	Mark Grant (Durham)	Topology Seminar
14:00		Topological aspects of motion planning
		Hicks Seminar Room J11
	Abstract: Inspired by the motion planning problem in robotics, M. Farber recently introduced a new numerical homotopy invariant, called the Topological Complexity, which provides a measure of the navigational complexity of a space when viewed as the configuration space of a mechanical system. As well as its practical motivation, computation of this invariant presents a challenge to homotopy theorists, which may be likened to computation of the Lusternik-Schnirelmann category. I will survey the best known lower and upper bounds for Topological Complexity, using plenty of examples. I also hope to discuss a recently obtained upper bound based on the homology coalgebra structure of the space.
Apr 29	Tue	Morten Brun (Bergen)	Topology Seminar
16:10		Equivariant multilinearity in algebra and topology
		Hicks Seminar Room J11
	Abstract: The ring of (big) Witt vectors over a commutative ring appears naturally in the description of certain algebraic K-theory groups. These K-groups are related to equivariant stable homotopy via the topological Hochschild homology construction. It has been known for twenty years, that that given a (pro-)finite group G there is a G-typical version of the ring of Witt vectors. This G-typical Witt ring is related to commutative G-ring spectra, that is, commutative monoids in the G-equivariant stable homotopy category. In the talk I will propose a generalization of the concept of multilinearity that gives a new approach to both Witt vector constructions and certain G-equivariant stable homotopy groups. In particular it can be used to describe the lowest homotopy group of G-fold smash-powers of G-spectra.
Apr 30	Wed	Leigh Shepperson (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Spectra, Rings and The Generating Hypothesis
		Hicks Seminar Room J11
	Abstract: The aim of my talk will be to give a brief introduction to an important conjecture in stable homotopy theory known as `The Generating Hypothesis.' In particular, it will follow the order of the title, insofar as it will start with a standard exposition of (finite) spectra, moving on to a brief discussion of the ring $\pi_*(S)$ (with a few more or less general definitions) and then ending with the Generating Hypothesis and what the former have to do with it.
Apr 30	Wed	Robert Rothschild (Lancaster)	Applied Mathematics Colloquium
14:00		Should airlines code-share or should they merge?
		Hicks Lecture Theatre A
	Abstract: This seminar compares the profits from 'contractual' relationships amongst competing firms, with those obtainable when the parties formally merge. The emphasis throughout is on the essentially game-theoretic nature of the decision, and the strategic equilibria that result.
May 2	Fri	Kara Burke (Sheffield)
13:05
		Lecture Theatre 10
May 6	Tue	Jeff Giansiracusa (Oxford)	Topology Seminar
14:00		Pontrjagin-Thom maps and the Deligne-Mumford compactification.
		Hicks Seminar Room J11
	Abstract: This is joint work with Johannes Ebert. We extend the classical construction of Pontrjagin-Thom wrong way maps to the setting of topological stacks. This construction applied to the boundary divisors of the Deligne-Mumford compactification produces many new mod p cohomology classes.
May 7	Wed	Laura Stanley (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Dyer-Lashof operations
		Hicks Seminar Room J11
	Abstract: This talk will present an introduction to the Dyer-Lashof homology operations used in the study of the homology of infinite loop spaces. I intend to outline their construction and some of their properties and to give an application and an example of their use.
May 7	Wed	Remi Tailleux (Reading)	Applied Mathematics Colloquium
14:00		Are incompressible Navier-Stokes equations valid for describing turbulent diabatic motions?
		Hicks Lecture Theatre A
	Abstract: According to classical turbulence theory, there exists two possible pathways to dissipation for kinetic energy in a turbulent stratified fluid, a viscous and a diffusive one. The viscous pathway is well known and associated with the work of molecular viscous stresses. The second one is envisioned as a two steps process. In the first step, kinetic energy is converted into available potential energy (APE) adiabatically, without modification of the mean gravitational potential energy (GPEr). In a second step, lateral molecular diffusion is thought to irreversibly convert the APE into GPEr. Thus, according to the diffusive pathway, kinetic energy is dissipated into mean GPE. In this talk, I will present different line of arguments aiming at demonstrating that this view is invalid. Ultimately, the arguments will lead to the conclusion that the incompressible description of hydrodynamics of fluid flows at low Mach number must be invalid too for representing diabatic irreversible motions. A modification of the incompressible Navier-Stokes equations will be proposed that is more physically consistent, and how existing incompressible hydrodynamics codes can be modified will be discussed. We will also show that the above results provide a simple solution to the existing ``ocean heat engine controversy".
May 7	Wed	Kirill Zainoulline (Munchen)	Pure Maths Colloquium
16:00		Special correspondences and Chow traces of Landweber-Novikov operations.
		Hicks Seminar Room J11
	Abstract: We prove that the function field of a variety which possesses a special correspondence in the sense of M. Rost preserves the rationality of cycles of small codimensions. This fact was proven by Vishik in the case of quadrics and played the crucial role in his construction of fields with $u$-invariant $2^r+1$. The main technical tools are algebraic cobordism of Levine-Morel, generalized Rost degree formula and divisibility of Chow traces of certain Landweber-Novikov operations. As a direct application of our methods we prove the Vishik's Theorem for all $F_4$-varieties.
May 8	Thu	Owen Jones (University of Melbourne)	Statistics Seminar
14:00		Looking for continuous local martingales
		Hicks Room K14
	Abstract: Continuous local martingales, or equivalently time-changed Brownian motion, are a popular class of models in finance. We present a set of statistical tests for whether or not an observed process is a continuous time-changed Brownian motion, based on the concept of the crossing tree. We apply our methodology to five currency exchange rates---AUD-USD, JPY-USD, EUR-USD, GBP-USD and EUR-GBP---and show that in each case, when viewed at a moderately large time scale, the log-transformed series is consistent with a continuous local martingale model.
May 9	Fri	Carlos Jaimes (Sheffield)
13:05
		Lecture Theatre 10
May 12	Mon	John Greenlees (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:10		The Positive Scalar Curvature Problem
		Hicks Seminar Room J11
May 13	Tue	Simon Willerton (Sheffield)	Topology Seminar
14:00		The cardinality of a metric space.
		Hicks Seminar Room J11
	Abstract: Hadwiger's Theorem says for a finite union of convex subsets in some Euclidean space that the Euler characteristic, perimeter, and so on up to the volume, are the only `additive', `invariant' measures. Note that lots of interesting spaces such as spheres and fractals are not finite unions of convex sets. The aim of the talk is to describe one way of trying to look at such measures on more general spaces. Tom Leinster defined the notion of Euler characteristic for a subclass of finite categories and has extended this idea to finite metric spaces by considering them as a certain type of enriched category. I will explain a conjectural connection with Hadwiger measures.
May 14	Wed	Rodney Sharp (Sheffield)	Pure Maths Colloquium
16:15		Generalized fractions, complexes, local cohomology and the Frobenius homomorphism
		Hicks Seminar Room J11
May 15	Thu	Jenny Freeman (University of Sheffield)	RSS Seminar
16:30		How to Display Data
		John Pemberton Room, 2nd Floor, ScHARR
	Abstract: The speaker will illustrate various good and poor methods of displaying data, particularly in medical research, taken in part from her recent book. She will give tips on how to improve the way data are displayed, both in publications and in talks.
May 16	Fri	Alan Zinober (Sheffield)
13:05		The Big Picture in Control and Estimation with Application to Satellite Attitude Control
		Lecture Theatre 10
May 20	Tue	Kirill Mackenzie (Sheffield)	Topology Seminar
14:00		Lie Theory for Multiple Structures
		Hicks Seminar Room J11
	Abstract: I plan to do two, perhaps three, main things in this talk: -- describe the Lie theory of (ordinary) Lie groupoids and its relation to connection theory; -- describe how Poisson group theory leads to multiple Lie structures; -- outline the Lie theory of double Lie groupoids. This will be an overview, not a technical talk. I'll recall notions from Poisson geometry and connection theory.
May 21	Wed	Michael Atiyah (Edinburgh)	SoMaS Launch Event
09:00		Soliton dynamics
		Lecture theatre 7
	Abstract: Many important physical problems involve non-linear PDE. Simplified models may admit exact analytical solutions, which can provide some guidance, but usually this has to be augmented by simulation, backed by physical insight. There is scope here for a really interdisciplinary approach. I will illustrate this by the example of magnetic monopoles and the Skyrmion model of protons and neutrons, showing in particular the underlying role of topology.
May 21	Wed	Douglas Gough (Cambridge)	SoMaS Launch Event
10:00		Resonant waves in a deformed sphere
		Lecture theatre 7
	Abstract: The resonance conditions for one-dimensional waves on a line are easy to derive and state. Brillouin, and perhaps Einstein, tried to generalize them to three dimensions in the early days of quantum theory. Unfortunately, their analyses were incomplete. It was only after Keller, nearly forty years later, recognized the importance of caustic surfaces that useful estimates of the eigenvalues of wave-like boundary-value problems were obtained, and then the resonance procedure became widely used to solve complicated problems. But I shall keep it simple. After describing the basic procedure, and applying it to acoustic waves in a spherical system, which could be a nonrotating star, I shall demonstrate how small deformations caused by rotation or a magnetic field can be accounted for, yielding asymptotic formulae which provide more insight than do more accurate numerical solutions.
May 21	Wed	Terry Lyons (Oxford)	SoMaS Launch Event
11:30		Rough paths
		Lecture theatre 7
	Abstract: Calculus is the main mathematical tool used to describe systems with a local interaction. Examples of this abound throughout mathematics. Even the simplest case of a control problem without feedback has a huge importance. Differential equations of the form $dy^i = \sum_i f^{i,j} dx_i$ express the relationship between a controlling process x and a response y; x could be a path in a Lie algebra and y its development into a Lie group; x could represent the evolution of massive particles exerting a gravitational influence on the evolution of a satellite, whose state is represented by y. However, an examination of many real world situations leads one to conclude that in many contexts, the controls that influence evolution are highly oscillatory and not at all adequately modelled on normal scales by classical tools of calculus. The theory of rough paths considers the relationship between the control and the response, and identifies natural metrics making this functional uniformly continuous, and so well-defined on the completion. The completion of the smooth paths in these metrics are called rough paths; they are tractable and not particularly abstract objects (it is important to understand that they are a generalisation of the concept of a smooth path, rather than a restriction of the concept of a continuous path). They allow one to describe what is important about x on normal scales and to do numerical analysis on these scales, rather than tunnel deep into fine structure to use classical calculus. A key feature of this approach is a natural and universal representation of the class of paths in $\mathbb{R}^n$ with concatenation into a subgroup of the free tensor algebra.
May 21	Wed	Jon Keating (Bristol)	SoMaS Launch Event
14:00		Random matrices and number theory
		Lecture theatre 7
	Abstract: I will review some conjectural connections between the zeros of the Riemann zeta function and random matrix theory, which underpins our understanding of complex quantum systems. I will then describe how these conjectures shed interesting new light on some deep and long-standing problems relating to the size of the Riemann zeta function and other L-functions, and the number of rational points on elliptic curves.
May 21	Wed	Paul Blackwell (Sheffield)	SoMaS Launch Event
15:00		Random tessellations - models, inference and applications
		Lecture theatre 7
	Abstract: Tessellations with various kinds of symmetry and regularity are well known in mathematics and in art, but tessellations generated by random processes are also important, and have been widely used as models of observed spatial patterns. Statistical inference for such processes can enable us to choose between models or theories, to reconstruct patterns or images, or to estimate underlying parameters. I will talk about a range of tessellations of the plane, including the well-known (and often re-invented) Dirichlet or Voronoi tessellation and variants obtained by for example varying the distance function used, regarding the plane as a section of a three-dimensional space, or using a form of duality---giving the Delaunay triangulation. The random process driving the tessellation will typically be a point process on some suitable space; in practice, a further modelling step is needed to describe the way in which the tessellation is observed, for example the `noise' in an image. Carrying out the actual inference involves modern computer-intensive `Markov chain Monte Carlo' techniques, which are partly derived from simulation techniques in physics. I will illustrate the models and methods with examples from ecology and a selection of possible other areas including material science, physiology, geography and astronomy.
May 21	Wed	Koji Ohkitani (Sheffield)	SoMaS Launch Event
16:10		Recent progress in the basic problems of fluid equations
		Lecture theatre 7
	Abstract: In this talk geared for non-specialists, we address the fundamental issues of fluid dynamics. Besides their mathematical interest as nonlinear PDEs, we explain the esoteric connection with developed fluid turbulence, centering on the so-called Onsager's conjecture. We then review what have been known mathematically regarding the 3D incompressible Euler and Navier-Stokes equations and point out the differences from what physicists and engineers expect about them. We recall how the existing methods fail to show, for example, regularity of the Navier-Stokes equations or singularity of the Euler equations. We also emphasise how studying the Euler equations may help in making possible progress in the Navier-Stokes theory. Some examples of numerical experiments are shown for illustration, where appropriate.
May 21	Wed	Neil Strickland (Sheffield)	SoMaS Launch Event
16:50		Thoughts on toric topology
		Lecture theatre 7
	Abstract: In this talk I'll discuss a construction that starts with some combinatorial and algebraic data and produces a manifold, called a toric variety. There are many beautiful examples, and connections with combinatorics, commutative algebra, geometry, topology and physics, so this topic lies in the intersection of many of the most active areas of research in the pure mathematics department.
May 22	Thu	Neil O'Connell (University of Warwick)	Statistics Seminar
14:00		Exponential functionals of Brownian motion and class one Whittaker functions
		Hicks Room K14
	Abstract: Motivated by a problem concerning scaling limits for directed polymers, and recent extensions of Pitman's `2M-X' theorem including an analogue, due to Matsumoto and Yor, for exponential functionals of Brownian motion, we consider (multi-dimensional) Brownian motion conditioned on the asymptotic law of a family of exponential functionals and identify which laws give rise to diffusion processes. For particular families (with a lot of symmetry) these conditioned processes are related to class one Whittaker functions associated with semisimple Lie groups. The work of Matsumoto and Yor corresponds to the group GL(2,R) and the class one Whittaker function in this case is essentially the Macdonald function (or modified Bessel function of the second kind). For the group GL(3,R) many explicit formulae are available for understanding the behaviour of these processes. The directed polymer problem should correspond to the group GL(n,R) and the asymptotics of the corresponding Whittaker functions for large n, but there are significant technical hurdles to overcome before this can be made fully rigourous. This is based on joint work with Fabrice Baudoin.
May 23	Fri	Andrew Newton (Sheffield)
13:05
		Lecture Theatre 10
May 27	Tue	Richard Hepworth (Sheffield)	Topology Seminar
14:00		Orbifold Morse Homology
		Hicks Seminar Room J11
	Abstract: Morse theory is a geometric way to understand the homology of manifolds. Orbifolds are spaces that locally look like the quotient of a manifold by a finite group. I will explain how Morse theory generalizes to orbifolds, giving methods to compute several different notions of "the homology of an orbifold" using generalizations of the Witten Complex.
May 28	Wed	Rekha Jain (Sheffield)	Applied Mathematics Colloquium
14:00		Interaction of p Modes with a Thin Magnetic Flux Tube
		Hicks Lecture Theatre A
	Abstract: The Sun's magnetic active regions, composed of sunspots and plage, are topologically complex. The magnetic field is highly structured, forming a tangle of fibrils within the plage and more compact, regimented bundles within sunspot umbrae. The fragmented nature of the field makes helioseismic observations within active regions rather difficult to interpret. We choose to study the propagation of acoustic waves through regions of plage, modelling the magnetic field therein as a collection of thin flux tubes. In this talk I will present the first results of this research; the computation of the absorption coefficient from a single tube. The incoming acoustic waves interact with the flux tube, exciting sausage and kink tube waves which propagate downward and upward carrying away energy, thereby producing absorption. The tube response further scatters the incoming wave into a variety of f modes and p modes. We treat plage as a collection of noninteracting flux tubes. I will present the resulting theoretically calculated absorption coefficients and compare with the most recent observations.
May 28	Wed	Rekha Jain (Sheffield)	Applied Mathematics Colloquium
14:00		tbd
		Hicks Lecture Theatre A
May 30	Fri	Jamie Douglas (Sheffield)
13:05
		Lecture Theatre 11
Jun 2	Mon	Tatiana Gateva-Ivanova (The Bulgarian Academy of Science/Cambridge)	Algebra / Algebraic Geometry seminar
16:00		Multipermutation solutions of the Yang Baxter Equation.
		Hicks Seminar Room J11
Jun 3	Tue	Ieke Moerdijk (Sheffield)	Topology Seminar
14:00		A Milnor-Moore Theorem for Lie-Rinehart algebras
		Hicks Seminar Room J11
	Abstract: Lie-Rinehart algebras arise naturally as the algebraic counterpart of Lie algebroids(which are the infinitesimal structures related to Lie groupoids). I will discuss to what extent the enveloping algebra of a Lie-Rinehart algebra carries a structure like that of a Hopf algebra, and discuss a Milnor-Moore type theorem for these structures.(The talk is based on a joint paper with J. Mrcun, available on the ArXiv.)
Jun 4	Wed	Yuri Shtessel (Alabama)	Applied Mathematics Colloquium
14:00		Higher Order Sliding Mode Control with Application to Blood Glucose Level Regulation
		Hicks Lecture Theatre A
	Abstract: Control under uncertainty is one of the main topics of the modern control theory. In spite of the extensive and successful development of robust adaptive control and backstepping technique, sliding mode control (SMC) stays, probably, the main choice in handling bounded uncertainties/disturbances and unmodeled dynamics. The idea is in stirring the system trajectory to properly chosen constraints (sliding manifold) and keeping it thereafter by means of high-frequency switching control, exploiting the main features of the sliding mode: its insensitivity to external and internal disturbances matched by control and ultimate accuracy and finite-time reaching transient. Stabilization of the sliding variable in SISO systems by means of the traditional SMC, designed as a switching control with respect to the so-called sliding variable, requires the system relative degree to be equal to one with respect to the sliding variable. Also, high frequency control switching leads to the so-called chattering effect, which is exhibited by high frequency vibration of the controlled plant that can be dangerous in applications and difficult to avoid or attenuate. The intrinsic difficulties of the traditional SMC are mitigated by the higher order sliding mode control (HOSM) that stabilizes at zero not only the sliding variable, but also its successive derivatives (kth order HOSM). HOSM is a new generation of SMC that is based on a general discontinuous-control approach. The unique power of the approach is revealed by the development of practical arbitrary-order real-time robust exact differentiator, which performance is proved to be asymptotically optimal in the presence of small Lebesgue-measurable input noises. 1k- Applications of HOSM control and observation to blood glucose regulation (diabetes control) are discussed.
Jun 5	Thu	David Lucy (University of Lancaster)	Statistics Seminar
14:00
		Hicks Room K14
Jun 6	Fri	Marialejandra Luna (Sheffield)
13:05
		Lecture Theatre 10
Jun 11	Wed	John Greenlees (Sheffield)	Topology Seminar
14:00
		Hicks Seminar Room J11
Jun 18	Wed	Leonard Scott (Virginia)	Pure Maths Colloquium
16:00		Group actions, representations, and cohomology
		Hicks Seminar Room J11
	Abstract: There will be two themes to this talk. One is the general interaction of finite, continuous and algebraic group representation theory, together with related roles of representations of Lie algebras and quantum groups. My point of view will mostly be that of finite and algebraic groups. The second theme is the intereaction of linear and nonlinear actions of these groups and the intereactions of the study of these actions with group cohomology and homological algebra. Finally I will discuss some recent examples and results related to some issues raised by Bob Guralnick on the asymptotic behavior of 1-cohomology for finite groups.
Jun 26	Thu	Sharon Hollander (Lisbon)	Topology Seminar
14:00		Applications of Homotopy Theory of Stacks
		Hicks Seminar Room J11
	Abstract: I will describe the homotopy theory of stacks and explain how algebraic stacks can be naturaly seen in this context. A consequence of this perspective will be certain criteria for the algebraicity of a stack.
Jun 26	Thu	Alex Usvyatsov (Lisbon)
16:00		Introduction to Model Theory
		Hicks Seminar Room J11
	Abstract: I will give a very light introduction to Model Theory (which is an area of Mathematical Logic). I will try to explain some of the main questions and goals of the field, as well as several major results.
Sep 25	Thu	Brian Sawford (Monash)	Applied Mathematics Colloquium
14:00		Relative Dispersion and Richardson's Constant
		Hicks Lecture Theatre 5
	Abstract: This talk will describe some very recent analysis of Direct Numerical Simulation results for turbulent relative dispersion over a wide range of Reynolds numbers. We will start with some background discussion of the nature and significance of relative dispersion and of the role of Kolmogorov's similarity theory, leading to the introduction of Richardson's constant as a fundamental parameter of relative dispersion. Although it is of great fundamental and practical significance, Richardson's constant has not been well-quantified, and model estimates for it range from 0.01 to 4. We will describe first a traditional analysis of relative dispersion data, concluding that this approach does not yield a good estimate for Richardson's constant even at the highest Reynolds number currently available. We then use a modified version of a new approach developed by Ott and Mann (JFM, 422, 207, (2000)) to show that a welldefined Richardson scaling range exists in our data. We estimate Richardson's constant over a range of Reynolds numbers showing that it decreases weakly with Reynolds number to an asymptotic value at large Reynolds number of 0.55 - 0.57.
Sep 30	Tue	Paul Mitchener (Sheffield)	Topology Seminar
14:00		Coarse Homotopy Theory
		Hicks Seminar Room J11
	Abstract: The category of metric spaces and coarse maps does not carry the structure of a Quillen model category in any obvious way, for the simple reason that we do not know how to form products in the coarse category. However, the coarse category can be equipped with a weaker structure- that of a Baues cofibration category. We show how to do this in this talk. The cofibration category structure gives us an abstract notion of coarse homotopy groups. This abstract notion is closely related to something more geometric- the plan is to define this ``something'' in the talk and compute some simple examples.
Oct 1	Wed	Professor Keke Zhang (Exeter)	Applied Mathematics Colloquium
14:00		Linear and nonlinear instabilities in rotating cylindrical Rayleigh-Bénard convection
		Hicks Lecture Theatre A
	Abstract: Motivated by the wish to understand the fundamental dynamics taking place in planetary/stellar fluid interiors and atmospheres, convection in rotating cylindrical geometry has been extensively studied. We shall present some new analytical and numerical results on linear and nonlinear convection in cylindrical systems heated from below and rotating about its vertical axis. In particular, we shall discuss asymptotic solutions of inertial convection in rotating cylinders and nonlinear counter-traveling waves in connection with the Eckhaus-Benjamin-Feir-type instability and with the saddle-node-type bifurcation in rotating cylindrical channels.
Oct 3	Fri	Istvan Ballai (Sheffield)
13:05		Ten years of solar physics at Sheffield University
		Lecture Theatre 9
Oct 3	Fri	Vladimir Bavula (Sheffield)	Algebra / Algebraic Geometry seminar
13:10		Weil divisors and reflexive rank one modules
		Hicks Seminar Room J11
Oct 7	Tue	Richard Hepworth (Sheffield)	Topology Seminar
14:00		2-Vector Bundles and Differentiable Stacks
		Hicks Seminar Room J11
	Abstract: This seminar is an account of Alan Weinstein's recent paper The Volume of a Differentiable Stack. I'll explain that differentiable stacks are a generalization of smooth manifolds and that they crop up in many interesting situations, like the study of of orbifolds or the study of flat connections. Just as every manifold has a tangent bundle, every stack has a tangent something, and I'll explain that the something in question is a bundle of Baez-Crans 2-vector spaces. These 2-vector bundles are often horrible compared with vector bundles, but they still admit a 'top exterior power'. We'll see that sections of this top exterior power can be treated just like volume forms on a manifold, and in particular can be integrated to define the volume of a stack.
Oct 7	Tue	Tom Bridgeland (Sheffield)
17:00		Mirror Symmetry
		LT7
	Abstract: Since its discovery by string theorists in the early 90s mirror symmetry has become a huge area of research with connections to many areas of mathematics. I'll try to give a rough feel for the subject by introducing Calabi-Yau manifolds and explaining what it means for two such manifolds to be mirror.
Oct 9	Thu	Richard Wilkinson (Sheffield)	Statistics Seminar
14:00		Estimating Species Divergence Times Using the Fossil Record
		Hicks Room K14
	Abstract: In this talk I will show how to estimate species divergence times using the fossil record. I will describe how branching process models can be conditioned to contain subtrees originating at a given point in time, and how these can be used to model evolution taking some known phylogenetic structure into account. Inference can be performed using Approximate Bayesian Computation (ABC) and I will describe a hybrid ABC-Gibbs algorithm that can improve the efficiency of the basic ABC algorithm.
Oct 10	Fri	Takashi Sakajo (Department of Mathematics at Hokkaido University, JAPAN)
13:05		N-vortex problem on a sphere
		Lecture Theatre 9
Oct 10	Fri	Vladimir Bavula (Sheffield)	Algebra / Algebraic Geometry seminar
13:10		Weil divisors and reflexive rank one modules, II
		Hicks Seminar Room J11
Oct 13	Mon	Paul Mitchener (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:00		Introduction
		Hicks Seminar Room J11
	Abstract: The plan is to show that topological obstructions exist to the existence of a metric of positive scalar curvature on a manifold, and to look at some examples where such a metric does and does not exist.
Oct 14	Tue	Neil Strickland (Sheffield)	Topology Seminar
14:00		Rational spectra and chain complexes
		Hicks Seminar Room J11
	Abstract: In stable homotopy theory we study spectra with various kinds of structure, such as group actions or ring structures. Often it is illuminating to restrict attention to spectra whose homotopy groups are rational vector spaces, as many things become simpler and more algebraic in that context. Indeed, rational spectra without extra structure are essentially the same as rational chain complexes. The word 'essentially' hides some subtleties, which previously made it difficult to incorporate extra structures in the picture. I will report on a way to resolve this difficulty, which makes contact with de Rham theory in an unexpected way.
Oct 14	Tue	Kazuma Shimomoto (Japan)	Algebra / Algebraic Geometry seminar
17:10		On the system of parameters of local rings in mixed characteristic
		Hicks Seminar Room J11
	Abstract: In this talk, we propose an approach towards the construction of big Cohen-Macaulay algebras in mixed characteristic based upon techniques developed by G. Dietz in his thesis along with systematic use of various kinds of alfgebra modifications. This talk is also meant to give some reasonable evidence to the existence of big Cohen-Macaulay algebras.
Oct 15	Wed	Jonathan Woolf (Liverpool)	Pure Maths Colloquium
16:15		What should be the fundamental group of a stratified space?
		Hicks Seminar Room J11
Oct 16	Thu	Leo Bastos (University of Sheffield)	Statistics Seminar
14:00		Diagnostics for Gaussian Process Emulators
		Hicks Room K14
	Abstract: This work presents some diagnostics to validate and assess the adequacy of a Gaussian process emulator as surrogate for a computer model. These diagnostics are based on comparisons between simulator outputs and Gaussian process emulator outputs for some test data, known as validation data, defined by a sample of simulator runs not used to build the emulator. Our diagnostics take care to account for correlation between the validation data. In order to illustrate a validation procedure, these diagnostics are applied to two different data sets.
Oct 16	Thu	Tom Fricker (University of Sheffield)	Statistics Seminar
14:00		Prior specification in Gaussian process emulators: What do we mean by the mean?
		Hicks Room K14
	Abstract: When building an emulator for a computer model, we treat the model output as an unknown deterministic function of the inputs. The data we have are observations of the computer model output at a number of input points, and our task is to make inference about the function using this noiseless data. We use a semiparametric regression model, a priori describing the function as the sum of a parametric mean function and a zero-mean Gaussian process. Often in past a very basic regression function has been used for the mean (either constant or linear in the inputs), and most of the effort has been spent in correctly specifying the Gaussian process to model the residuals. However, in some quarters it is believed that we should attempt to build more prior information about the computer model into the emulator via the mean function. But individual realisations of a zero-mean Gaussian process do not necessarily have a mean value of zero, so what exactly is meant when we talk about `the prior mean' of the model? How far should we go in the mean function's complexity? What happens if we overfit it? And does this extra effort actually improve the emulator's predictions of the computer model? In this talk I shall use some very simple toy examples to explore these questions (but without necessarily offering any answers...)
Oct 17	Fri	Eun-Jin Kim (Sheffield)
13:05
		Lecture Theatre 9
Oct 17	Fri	Vladimir Bavula (Sheffield)	Algebra / Algebraic Geometry seminar
13:10		Weil divisors and reflexive rank one modules, III
		Hicks Seminar Room J11
Oct 20	Mon	Richard Hepworth (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:00		Constructions of Manifolds with Positive Scalar Curvature
		Hicks Seminar Room J11
Oct 21	Tue	Hadi Zare (Manchester)	Topology Seminar
14:00		On spherical classes in $H_{\ast}QS^1$.
		Hicks Seminar Room J11
	Abstract: This talk is about spherical classes in $H_{\ast}QS^1$. Inspired by work of Curtis and Wellington, we give an upper bound on the type of classes in $H_{\ast}QX$ which can be spherical. Specialising to $X=S^1$, the results can be refined. I will explain the motivation for studying this problem, and recall some results about this.
Oct 22	Wed	Harry Ullman (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Equivariant K-theory of projective representations
		Hicks Seminar Room J11
	Abstract: watch this space
Oct 22	Wed	Dr Rosa Diaz-Sandoval (Sheffield)	Applied Mathematics Colloquium
14:00		Solar activity and human health
		Hicks Lecture Theatre A
	Abstract: We will show the most important results of statistical studies regarding the relationship between solar activity and cardiac and mental diseases, as well as the physiological parameters of healthy individuals. In order to establish a plausible physical mechanism, the whole system from the sun to the human body is studied. The methodology used to find correlations between solar and health parameters is based mainly upon the spectral analysis of solar and medical data because it has been suggested that a possible physical mechanism might be related to solar periodicities. To compare the geomagnetic activity, caused by the solar activity itself, and health parameters, the Superposed Epochs Method is used. The Forbush decreases in cosmic rays and the geomagnetic index Ap are the phenomena most commonly analyzed because of previous results reported in the literature. We will show, based on the Mexican results, that solar activity could well be a risk factor that affects the vulnerable population by a factor of 2 in the occurrence of myocardial infarction diseases.
Oct 22	Wed	Tom Lenagan (Edinburgh)	Pure Maths Colloquium
16:15		Totally positive matrices
		Hicks Seminar Room J11
Oct 23	Thu	Lucy Morecroft & Nick Fieller (Sheffield)	RSS Seminar
16:30		Faces and Statistics
		Hicks Room K14
	Abstract: The study described here was undertaken to develop a statistical method for measuring the quality of match of photographs of faces taken at a scene of crime to that of a suspect. The objective was to provide evidential information of use in a court of law. The method is based on landmark identification of facial features and routine techniques of shape analysis to model their joint distribution, thus allowing a statistical assessment of facial identification.
Oct 24	Fri	Sergey Shelyag (Sheffield)
13:05
		Lecture Theatre 9
Oct 24	Fri	Kevin Buzzard (Imperial)	Muggle-MAGIC number theory seminar
15:00		Galois representations and automorphic forms: a non-expert struggles
		Hicks Seminar Room J11
Oct 27	Mon	John Greenlees (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:00		The Gromov-Lawson-Rosenberg Conjecture
		Hicks Seminar Room J11
Oct 28	Tue	Kathryn Hess (Lausanne)	Topology Seminar
14:00		Power maps in algebra and topology
		Hicks Seminar Room J11
	Abstract: (Joint work with J. Rognes) Let $t:C\to A$ be a twisting cochain, where $C$ is a connected, coaugmented chain coalgebra and $A$ is an augmented chain algebra over an arbitrary PID $R$. I'll explain the construction of a twisted extension of chain complexes $$A\to H(t)\to C$$ of which both the Hochschild complex of an associative algebra and the coHochschild complex of a coassociative coalgebra are special cases. We call $H(t)$ the Hochschild complex of $t$. When $A$ is a chain Hopf algebra, I'll give conditions under which $H(t)$ admits an $r^{\text{th}}$-power map extending the usual $r^{\text{th}}$-power map on $A$ and lifting the identity on $C$. In particular, both the Hochschild complex of any cocommutative Hopf algebra and the coHochschild complex of the normalized chain complex of a double suspension admit power maps. Moreover, if $K$ is a double suspension, then the power map on the coHochschild complex of the normalized chain complex of $K$ is a model for the topological power map on the free loops on $K$, illustrating the topological relevance of our algebraic construction. This algebraic model of the topological power map is a crucial element of the construction of our model for computing spectrum homology of topological cyclic homology of spaces.
Oct 29	Wed	Elizabeth Winstanley (Sheffield)	Applied Mathematics Colloquium
14:00		Furry black holes
		Hicks Lecture Theatre A
	Abstract: My aim in this seminar is to explain what furry black holes are, and why they might be interesting. There will not be a lot of detail on the relativity side of things, but I will explain the mathematics behind the proof of the existence and stability of furry black holes in a particular matter model.
Oct 31	Fri	Nicolas Leprovost (Sheffield)
13:05
		Lecture Theatre 9
Oct 31	Fri	Tom Bridgeland (Sheffield)	Algebra / Algebraic Geometry seminar
14:10		CY3 algebras
		Hicks Seminar Room J11
	Abstract: CY3 algebras are a class of non-commutative algebras whose module categories mimic the properties of coherent sheaves on three-dimensional Calabi-Yau algebras. As such they provide a baby model for many things of interest in mirror symmetry and string theory. Several people asked me to say something about them, so I'm planning to give two or three lectures at an introductory level, covering algebras defined by a quiver with potential, the CY3 condition and Donaldson-Thomas invariants. There are lots of things I don't understand in this subject, so I hope that people might be inspired to take up the baton and provide some of the missing details.
Oct 31	Fri	Neil Dummigan (Sheffield)	Muggle-MAGIC number theory seminar
15:00		Saito-Kurokawa lifts, Harder's conjecture and ratios of standard zeta values
		Hicks Seminar Room J11
Nov 4	Tue	Shoham Shamir (Sheffield)	Topology Seminar
14:00		Loops on a p-complete space and hereditary torsion theories
		Hicks Seminar Room J11
	Abstract: Benson constructs a purely algebraic model for $H^*(\Omega (BG^\wedge_p);p)$, where $G$ is a finite group, $(-)^\wedge_p$ denotes the Bousfield-Kan $p$-completion. This construction can be generalized for the classifying space of any discrete monoid $M$, as long as $M$ is "nice". This gives an excuse to present some algebra, since Benson's construction uses the old algebraic notion of a hereditary torsion theory to calculate a certain localization functor on the derived category of $k[M]$, where $k$ is the field of $p$-elements. I will explain these notions, why they are interesting, and present the construction.
Nov 5	Wed	Kijti Rodtes (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Connective K-theory of finite groups
		Hicks Seminar Room J11
	Abstract: This talk will fix on ku*(BG) about meaning and how to compute them, where G is a finite group.
Nov 5	Wed	Peter Constantin (Chicago)	Applied Mathematics Colloquium
14:00		Complex Fluids
		LTA
	Abstract: I will describe recent results concerning melts of complex particles. Time permitting, I will describe some mathematical results concerning suspensions in fluids.
Nov 5	Wed	Jens Funke (Durham)	Pure Maths Colloquium
16:15		Quadratic Forms and Modular Forms: An invitation to number theory
		Hicks Seminar Room J11
	Abstract: In this talk, we explore the relationship between integral quadratic forms, both positive definite and indefinite, to modular forms. Modular forms play an increasingly central role in modern number theory. We give an introduction to the subject concentrating on the case of quadratic forms with $3$ variables. Among the topics we discuss are class numbers of imaginary quadratic fields, representation numbers for the sum of three squares, and the values of the famous j-invariant at quadratic irrationalities in the upper half plane.
Nov 6	Thu	Mark Steel (University of Warwick)	Statistics Seminar
14:00		Time-Dependent Stick-Breaking Processes
		Hicks Room K14
	Abstract: This paper considers the problem of defining a time-dependent nonparametric prior. A recursive construction allows the definition of priors whose marginals have a stick-breaking form. The processes with Poisson-Dirichlet and Dirichlet process marginals have interesting interpretations that are further investigated. We develop a general conditional MCMC method for inference in a wide subclass of these models. We derive a Polya urn scheme type representation of the Dirichlet process construction. This allows us to develop a marginal MCMC method for this case. The result section shows the relative performance of the two MCMC schemes for the Dirichlet process case and looks at two data examples.
Nov 7	Fri	Gary Verth (Sheffield)
13:05
		Lecture Theatre 9
Nov 7	Fri	Tom Bridgeland (Sheffield)	Algebra / Algebraic Geometry seminar
13:10		CY3 algebras, II
		Hicks Seminar Room J11
Nov 7	Fri	Samir Siksek (Warwick)	Muggle-MAGIC number theory seminar
15:00		Integral points on curves of higher genus
		Hicks Seminar Room J11
Nov 11	Tue	Ian Leary (Ohio and Bristol)	Topology Seminar
14:00		New Smith groups and Kropholler's hierarchy
		Hicks Seminar Room J11
	Abstract: We construct an infinite group that has a very strong fixed point property for actions on finite-dimensional contractible spaces. Using similar techniques we show that Kropholler's hierarchy of groups is as long as it possibly could be: previously only the first four levels of the hierarchy were known to contain groups.
Nov 12	Wed	Jennifer Waters (Sheffield)	Applied Mathematics Colloquium
14:00		Data Assimilation into the Wavewatch III model
		Hicks Lecture Theatre A
	Abstract: The assimilation of data into wave models aims to improve the performance of the model by correcting the model state with observations. The area considered in this study is the Celtic Sea region off the coast of South Wales were a Pisces HF radar was deployed between 2002 and 2005. The ultimate aim is to assimilate the HF radar data into Wavewatch III and an initial study is presented where perturbed buoy data is assimilated into the model to test the assimilation scheme configuration.
Nov 12	Wed	Noel Robertson (SheffieldSheffield)	Applied Mathematics Colloquium
14:00		Modelling of the effect of snow on the hydrology and carbon budget of boreal regions
		Hicks Lecture Theatre A
	Abstract: In the study of global carbon dynamics, the carbon and water cycles are closely related. In order to act as an effective carbon sink, plants must have water as well as sunlight to perform photosynthesis. In cold boreal regions, where some of the world's largest forests are located, we therefore need to quantify the role of snow water dynamics in the carbon cycle. In this talk I particularly discuss the effect of climate-driven model predictions of snow water equivalent on the hydrology and carbon budget of boreal zones such as Siberia.
Nov 12	Wed	Theodore Voronov (Manchester)	Pure Maths Colloquium
16:15		Differential Forms and Higher Poisson Brackets
		Hicks Seminar Room J11
	Abstract: The relation between symplectic 2-forms and Poisson structures is well known. We shall show how this relation can be extended to the case of inhomogeneous multivector fields and inhomogeneous differential forms (or pseudodifferential forms). As a starting point we take a transformation from the de Rham complex to the Poisson-Lichnerowicz complex existing on an arbitrary Poisson manifold and, using some analogy with classical mechanics, show how it generalizes to the "non-quadratic" case. The role of inverting a matrix of a 2-form or a contravariant 2-tensor is taken by the Legendre transform. In particular we arrive at a notion which is a generalization of a symplectic structure and gives rise to higher Poisson brackets. We shall discuss homotopy Poisson structures (such a structure makes the space of functions on a manifold an L-infinity algebra) and show how one obtains Koszul type brackets in this setting. The Koszul bracket on an ordinary Poisson manifold is an odd Poisson bracket on the algebra of forms. In particular, it makes the cotangent bundle T*M a Lie algebroid. For a homotopy Poisson structure we give a construction of higher Koszul brackets. The induced structure on T*M will be that of an "L-infinity algebroid". (I shall explain what it means.) The talk is based on a work in progress with H. M. Khudaverdian. See http://arxiv.org/abs/0808.3406.
Nov 13	Thu	Dan Crisan (Imperial College)	Statistics Seminar
14:00		Sequential Monte Carlo methods - a theoretical perspective
		Hicks Room K14
	Abstract: The aim of the talk is to present a bird's-eye view of sequential Monte carlo methods (including the SIR algorithm and branching algorithms) with emphasis on classical convergence results. Additionally, some recent uniformly convergent particle filters will be discussed. The second part of the talk is based on joint work with K. Heine (see http://www.ma.ic.ac.uk/~dcrisan/crihei2.pdf for details)
Nov 14	Fri	Sergey Zharkov (Sheffield)
13:05
		Lecture Theatre 9
Nov 14	Fri	Tom Bridgeland (Sheffield)	Algebra / Algebraic Geometry seminar
13:10		CY3 algebras, III
		Hicks Seminar Room J11
Nov 14	Fri	Ambrus Pal (Imperial)	Muggle-MAGIC number theory seminar
15:00
		Hicks Seminar Room J11
Nov 17	Mon	Arjun Malhotra (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:10		Counterexamples to the Gromov-Lawson-Rosenberg Conjecture: I
		Hicks Seminar Room J11
Nov 19	Wed	Kiyoshi Igusa (Brandeis)	Topology Seminar
14:00		Higher Reidemeister Torsion I:\\ Sphere Bundles
		Hicks Seminar Room J11
	Abstract: Higher Reidemeister torsion can be defined using Morse theory (Igusa- Klein approach), homotopy theory (Dwyer-Weiss-Williams and Dorabiala) and analytically (Bismut-Lott and Goette). It is a challenge to see if these are equivalent. These talks are aimed at relating the Morse theory and homotopy theory points of view. The object of study is a smooth fiber bundle: $$ M\to E\to B $$ where $M,E,B$ are all compact smooth manifolds and the action of $ \pi_1B$ on the rational homology of $M$ is trivial. In this case all three invariants are defined. The easiest example is and oriented sphere bundle. 1) Sphere bundles By classical results about Euclidean bundles, topological sphere bundles have well-defined rational Pontrjagin classes. Smooth oriented sphere bundles have higher Reidemeister torsion invariants which are proportional to the topological Pontrjagin character for linear sphere bundles and for all even dimensional sphere bundles. When the fiber is an odd dimensional sphere, these invariants can differ and the difference measures the exotic smooth structure on the sphere bundles. I will discuss the theory of these exotic structures using Morse theory and the Dwyer-Weiss-Williams homotopy theoretic calculation of the group of fiberwise stable smooth structures on smooth bundles. I will also discuss the recent results of S. Goette comparing higher analytic torsion and the Morse theory version (IK-torsion) and the results of Goette and myself comparing IK-torsion and DWW-torsion.
Nov 19	Wed	Francesca Ticconi (Universita degli Studi Roma Tre)	Applied Mathematics Colloquium
14:00		Synthetic aperture radar: its role in remote sensing
		Hicks Lecture Theatre A
	Abstract: The Synthetic Aperture Radar (SAR) is an active sensor that transmits a beam of electromagnetic radiation, in the microwave region of the electromagnetic spectrum, providing high quality image of the Earth's surface, with a fine resolution independent of the sensor altitude or wavelength. By proper selection of operating frequency, the microwave signal can penetrate clouds, haze, rain, fog and precipitation with very little attenuation, thus allowing operation in unfavourable weather conditions that preclude the use of visible/infrared system. Being an active sensor, that is providing its own source of illumination, SAR is not dependent on light from Sun and therefore it can operate day or night. Moreover, it is able to illuminate with variable look angle and can select wide area coverage. The net result is an instrument that is capable of continuously monitoring geophysical parameters related to the structural and electrical properties of Earth's surface and also it is capable of observing dynamic phenomena, such as ocean currents, sea ice motion or changing of land cover vegetation. In addition, the topography change can be derived from phase difference between measurement using radar interferometry, achievable due the coherent character of the SAR system that retains both phase and magnitude of the backscattered echo signal. Even if the interpretation on the SAR images is less intuitive compared to the optical ones, SAR has been shown to be very useful over a wide range of applications, including sea and ice monitoring, oil pollution monitoring, oceanography, snow monitoring, forest monitoring and classification of Earth terrain.
Nov 19	Wed	Anatol Odzijewicz (University of Bialystok (Poland))	Pure Maths Colloquium
16:15		BANACH LIE-POISSON AND GROUPOID STRUCTURES ASSOCIATED WITH VON NEUMANN ALGEBRAS
		Hicks Seminar Room J11
	Abstract: The von Neumann algebras (or $W^*$-algebras) were introduced by John von Neumann in 1929 for the needs of quantum mechanics. They make a very important class of operator algebras. There are several equivalent ways of defining them. In particular, von Neumann algebras can be characterized by the existence of the predual, i.e., a Banach space such that the dual of it is the algebra. We shall give an introduction to von Neumann algebras and show that with any von Neumann algebra $M$ one can canonically associate the following structures: the structure of a Banach Lie-Poisson space on the Banach space $M_*$ predual to $M$; various groupoid structures including a groupoid structure on the set $U(M)\subseteq M$ of partial isometries; an inverse semigroup structure on some canonically chosen subsets of $M$. These structures play an important role for the description of a von Neumann algebra $M$. They also give a link between the theory of von Neumann algebras and the Banach Poisson geometry. In particular, they give a link with the theory of infinite-dimensional Hamiltonian systems. We shall present some theorems to justify this claim. References: A. Odzijewicz, T. Ratiu, Banach Lie-Poisson spaces and reduction, Commun. Math. Phys. 243, 1-54 (2003). A. Odzijewicz, A. Sliżewska, Groupoids and inverse semigroups related to a W*-algebra (in preparation).
Nov 20	Thu	Kiyoshi Igusa (Brandeis)	Topology Seminar
14:00		Higher Reidemeister Torsion II:\\ Dwyer-Weiss-Williams higher torsion and a construction of Hatcher.
		Hicks Seminar Room J11
	Abstract: Higher Reidemeister torsion can be defined using Morse theory (Igusa- Klein approach), homotopy theory (Dwyer-Weiss-Williams and Dorabiala) and analytically (Bismut-Lott and Goette). It is a challenge to see if these are equivalent. These talks are aimed at relating the Morse theory and homotopy theory points of view. The object of study is a smooth fiber bundle: $$ M\to E\to B $$ where $M,E,B$ are all compact smooth manifolds and the action of $ \pi_1B$ on the rational homology of $M$ is trivial. In this case all three invariants are defined. 2) Dwyer-Weiss-Williams higher torsion and a construction of Hatcher In the second talk I will give my version of the Dwyer-Weiss-Williams theory of higher torsion. Basically, they show that the stable smooth structures on a topological manifold bundle $E\to B$ with prescribed vertical tangent bundle are classified by sections of the associated $H^{%}$-bundle (the bundle over $B$ whose fibers are $\Omega^ \infty(M_+\wedge \mathcal H(\ast))$ where $\mathcal H(X)$ is the stable smooth concordance space of $X$. In the case when $M,E,B$ are all closed manifolds, this is given rationally by a homology class in $E$ which we call the stable smooth structure class. The Poincaré dual of the image of this class in the homology of $B$ is the higher DWW-torsion. Using a generalization of a construction of Hatcher, Goette and I constructed sufficiently many exotic smooth structures on any bundle and calculated their IK-torsion and we concluded that IK- torsion and DWW-torsion agree up to a constant. (However, this is not the complete answer since we prescribed the vertical tangent bundle.)
Nov 20	Thu	Martin Hairer (University of Warwick)	Statistics Seminar
14:00		A weak form of Harris's theorem
		Hicks Room K14
	Abstract: Harris' theorem gives easily verifiable conditions for a Markov operator to have a spectral gap in a weighted supremum norm. We are going to show a new elementary proof of this result. This proof can then be generalised to situations where Harris' theorem fails in order to prove a 'weak' form of it. The range of possible applications includes a number of stochastic PDEs and stochastic delay equations.
Nov 21	Fri	Tom Bridgeland (Sheffield)	Algebra / Algebraic Geometry seminar
13:00		Donaldson-Thomas invariants
		Hicks Seminar Room J11
Nov 21	Fri	Johan Anderson (Sheffield)
13:05
		Lecture Theatre 9
Nov 21	Fri	Kiyoshi Igusa (Brandeis)	Topology Seminar
14:00		Higher Reidemeister Torsion III:\\ Iterated integrals, superconnections and higher torsion
		Hicks Seminar Room J11
	Abstract: Higher Reidemeister torsion can be defined using Morse theory (Igusa- Klein approach), homotopy theory (Dwyer-Weiss-Williams and Dorabiala) and analytically (Bismut-Lott and Goette). It is a challenge to see if these are equivalent. These talks are aimed at relating the Morse theory and homotopy theory points of view. The object of study is a smooth fiber bundle: $$ M\to E\to B $$ where $M,E,B$ are all compact smooth manifolds and the action of $ \pi_1B$ on the rational homology of $M$ is trivial. In this case all three invariants are defined. The easiest example is and oriented sphere bundle. 3) Iterated integrals, superconnections and higher torsion This talk explains how iterated integrals are used in the definition and calculation of higher torsion. Given a smooth fiber bundle, we can construct an $A_\infty$-functor from the category of smooth simplices in the base to the $A_\infty$-category of finitely generated chain complexes over a field. Taking the limit as the size of the simplices go to zero we get a flat $\mathbb Z$-graded superconnection on the base. Conversely, such a superconnection can be integrated using Chen's iterated integrals to recover the $A_\infty$-functor. The higher Reidemeister torsion can be defined categorically using the $A_ \infty$-functor. However, to calculate it one needs an explicit formula for the flat superconnection. I will talk about the relation between these three concepts.
Nov 24	Mon	Arjun Malhotra (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:10		Counterexamples to the Gromov-Lawson-Rosenberg Conjecture: II
		Hicks Seminar Room J11
Nov 25	Tue	Nick Wright (Southampton)	Topology Seminar
14:00		Property A and dimension for CAT(0) cube complexes.
		Hicks Seminar Room J11
	Abstract: Yu's property A is a property of a space which is a geometric analogue of amenability for groups. I will present a result on property A for CAT(0) cube complexes, and discuss strengthening this result in terms of the large-scale dimension of these spaces. These questions are motivated in part by open questions about Thompson's group F.
Nov 26	Wed	Laura Stanley (Sheffield)	Pure Maths Postgraduate Seminar
14:00		The Adams Splitting of p-local K-Theory
		Hicks Seminar Room J11
Nov 26	Wed	Dr Balazs Pinter (Aberystwyth)	Applied Mathematics Colloquium
14:00		Local Helioseismology -- How far can we see?
		Hicks Lecture Theatre A
	Abstract: We can see clusters of galaxies millions of light years away in the deep space. However, looking into the interior of the nearest star is impossible even to the deservedly celebrated Hubble Space Telescope. Helioseismology is the only field of physics which offers means to discover the hidden world of the Sun. We will briefly review different techniques together with the greatest results of local helioseismology. The power of observing and analysing oscillations will be apparent also in the second part, which will be a case study in coronal seismology. A filament was visible in the Sun's atmosphere on 15th October 2002. A part of it was clearly oscillating until the filament erupted. The spatial structure and the temporal variation of the filament oscillations will be studied by using the techniques of wavelet analysis.
Nov 26	Wed	Baptiste Calmes (Cambridge)	Pure Maths Colloquium
16:15		Formal group laws and the cohomology of flag varieties
		Hicks Seminar Room J11
Nov 27	Thu	Jon Pitchford (University of York)	Statistics Seminar
14:00		Is there something fishy about Lévy processes?
		Hicks Room K14
	Abstract: Lévy flights are loosely defined as random walks in which the step lengths are drawn from some underlying power law distribution. In biology, detecting Lévy-like behaviour is worryingly fashionable and interestingly controversial. Do Lévy flights really occur? If so, then why have they evolved? I will discuss possible answers to these questions, arguing that there may be a role for more general Lévy processes in biology and ecology. I will draw on two examples from my recent research: superspreading in epidemics, and stochastic foraging in patchy environments.
Nov 28	Fri	Koji Ohkitani (Sheffield)
13:05		Magnetic reconnection observed in the Eulerian-Lagrangian analysis of magnetohydrodynamics equations
		Lecture Theatre 9
Nov 28	Fri	Lassina Dembele (Essen)	Muggle-MAGIC number theory seminar
15:00		A non-solvable Galois extension of Q that is ramified at 2 only
		Hicks Seminar Room J11
Dec 1	Mon	Paul Mitchener (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:10		The Stable Gromov-Lawson-Rosenberg Conjecture
		Hicks Seminar Room J11
Dec 2	Tue	Bruce Bartlett (Sheffield)	Topology Seminar
14:00		Pivotal structures on fusion categories
		Hicks Seminar Room J11
	Abstract: A fusion category is a monoidal category whose hom-sets are finite-dimensional vector spaces and which is semisimple --- in the sense that there are a finite bunch of 'simple' objects, and every other object is a direct sum of them. Fusion categories arise in several areas of mathematics and physics: conformal field theory, operator algebras, representations of quantum groups, and so on. A conjecture was made by Etingof, Nikshych and Ostrik that ''every fusion category admits a pivotal structure''. In this talk I will explain what that means, and I will present some work which might help in settling this conjecture. Specifically, I will use a string diagram argument first discovered by Hagge and Hong, similar to the Dirac belt trick, which shows that the hom-sets in a fusion category carry involution operators, which must be "trivial" in order for the category to admit a pivotal structure.
Dec 3	Wed	Arjun Malhotra (Sheffield)	Pure Maths Postgraduate Seminar
14:00		The H-cobordism theorem and the Poincare conjecture
		Hicks Seminar Room J11
	Abstract: The talk will be a basic introduction the H-cobordism theorem, briefly indicating how to prove it. I'll then describe the Poincare conjecture and apply the theorem to prove it in dimension 6 and above.
Dec 3	Wed	Dmitriy Rumynin (Warwick)	Pure Maths Colloquium
16:15		Irreducible Characters, from Weyl to Lusztig and beyond
		Hicks Seminar Room J11
	Abstract: We discuss Weyl's character formula, then Lusztig's conjecture. We discuss why it is still open and what tools modern Algebraic Geometry have to facilitate settling it.
Dec 4	Thu	Mike Campbell (University of Sheffield)	Statistics Seminar
14:00		A statistician on a NICE appraisals committee
		Hicks Room K14
	Abstract: NICE stands for the National Institute for Health and Clinical Excellence. The speaker has been on a NICE Appraisals committee for 7 years. He will describe what the committee does and how NICE makes decisions. Much of the evidence to NICE is statistical and a statistician is an important member of the committee. A number of roles for a statistician will be described. One role is checking for errors and he will describe some he has come across.
Dec 5	Fri	Viktor Fedun (Sheffield)
13:05
		Lecture Theatre 9
Dec 5	Fri	Martin Huxley (Cardiff)	Muggle-MAGIC number theory seminar
15:00
		Hicks Seminar Room J11
Dec 8	Mon	Bruce Bartlett (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:10		Scalar Curvature and Path Integrals
		Hicks Seminar Room J11
Dec 9	Tue	Oscar Randal-Williams (Oxford)
14:00		Transpennine Topology Triangle:\\ Homology of the stable non-orientable mapping class group
		Hicks Seminar Room J11
	Abstract: The mapping class group of a surface F is the group of isotopy classes of self-diffeomorphisms of F. Harer proved that for oriented surfaces the homology of these groups stabilises: in any fixed degree, increasing the genus of the underlying surface beyond a certain number does not change the homology of its mapping class group. This was used crucially by Madsen and Weiss in their proof of the Mumford conjecture on the homology of mapping class groups of oriented surfaces. Later, Wahl proved a stability result for unoriented surfaces, which implies a Madsen--Weiss theorem for their mapping class groups. This identifies the stable homology of mapping class groups of unoriented surfaces with the homology of a certain infinite loop space, corresponding to the spectrum sometimes known as MTO(2). In this talk I will introduce this homotopy-theoretic approach to mapping class groups, and discuss a calculation of the stable homology.
Dec 9	Tue	Larry Smith (Goettingen)
16:00		Transpennine Topology Triangle:\\ Poincare duality algebras and binary quadratic forms modulo 2
		Hicks Seminar Room J11
Dec 10	Wed	Roald Koudenberg (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Simplicial sets.
		Hicks Seminar Room J11
Dec 10	Wed	Dr Anne Juel (Manchester)	Applied Mathematics Colloquium
14:00		Steep capillary-gravity waves in oscillatory shear flows
		LTA
	Abstract: Nonlinear waves in uids are associated with a rich variety of dynamics that often underpin important natural phenomena. Examples range from internal solitary-like waves that are ubiquitous features of coastal oceans to the surface ocean spectra, whose interpretation relies on the nonlinear interaction between surface water waves and wind. We study steep capillary-gravity waves that form at the interface between two stably stratied layers of immiscible liquids in a horizontally oscillating vessel, and are commonly referred to as frozen waves. The oscillatory nature of the external forcing prevents the waves from over- turning, and thus enables the development of steep shear-driven waves at large forcing. The onset of `frozen waves' occurs through a supercritical pitchfork bi- furcation, with a non-monotonic dependence on the viscosity ratio between the layers. Thus, increasing the viscosity of one of the uids often results in a more unstable interface. For larger values of the forcing parameters, a qualitative change in the wave growth takes place. Beyond a critical value of Wc (ratio of vibrational to gravity forces, proportional to the square of the forcing velocity), the experimental data collapses onto a single curve that exibits a linear depen- dence on W. The evolution of the interface shape suggests a transition from gravity to capillary dominated waves, which is consistent with the wavelength reaching a minimum for W = Wc. For larger values of the forcing parameter, the two-dimensional array of waves becomes unstable to three-dimensional oscil- latory waves through a sub-critical bifurcation that exhibits a viscosity depen- dence opposite to the primary instability. The existence of a global bifurcation point is investigated.
Dec 11	Thu	Jon Nicholl (University of Sheffield)	RSS Seminar
16:30		What direction of travel? Reconfiguring emergency and urgent care
		Pemberton Lecture Theatre, 2nd Floor, Regent Court
Dec 12	Fri	Youra Taroyan (Sheffield)
13:05
		Lecture Theatre 9
Dec 17	Wed	Dr Dave Roscoe (Sheffield)	Applied Mathematics Colloquium
14:00		Via Aristotle, Leibniz, Berkeley and Mach to necessarily large-scale fractal structure in the Universe
		Hicks Lecture Theatre A
	Abstract: Abstract The claim that the large scale structure of the Universe is hierarchical has a very long history going back at least to Charlier's papers of the early 20th century. In recent years, the debate has centered largely on the works of Sylos Labini, Joyce, Pietronero and others, who have made the quantative claim that the large scale structure of the Universe is quasi-fractal with fractal dimension D=2. There is now a concensus that this is the case on medium scales, with the main debate revolving around what happens on the scales of the largest available modern surveys. Apart from the (essentially sociological) problem that their thesis is in absolute conflict with any concept of a Universe with an age of 14 billion years or, indeed, of any finite age, the major generic difficulty faced by the proponents of the hierarchical hypothesis is that, beyond hypothesizing the case (eg: Nottale's Scale Gravity), there is no obvious mechanism which would lead to large scale structure being non-trivially fractal. This talk describes a surprising resolution to this problem: in effect, the conflict between a homogeneous vs fractal universe is shown, at root, to be a conflict between two opposing views of ``space". One has its roots in ideas which can be traced from Democritus, through Newton to Einstein whilst the other has its roots in ideas which can be traced from Aristotle through Leibniz, and Berkeley to Mach.
Dec 18	Thu	George Streftaris (Heriot-Watt University)	Statistics Seminar
14:00		Bayesian inference for stochastic epidemic models with non-exponential tolerance to infection
		Hicks Room K14
	Abstract: The transmission dynamics of an infectious disease during the outbreak of an epidemic can be stochastically described through a time-inhomogeneous Poisson process, thus assuming exponentially distributed levels of disease tolerance, following the so-called Sellke (1983) construction. In this talk I will present generalisations of the Sellke structure under the susceptible-exposed-infectious-removed (SEIR) class of epidemic models, and focus on a model with Weibull individual tolerance thresholds. Examples of simulated and real epidemic data are discussed, where inference is carried out using MCMC methods following a Bayesian approach to tackle the issue of the partial observation of the temporal course of the epidemic. The adequacy of the models is assessed using methodology based on the properties of Bayesian latent residuals, demonstrating problems with more commonly used model checking techniques.
Dec 19	Fri	Daniel Reese (Sheffield)
13:05
		Lecture Theatre 9
Jan 29	Thu	Caitlin Buck (Sheffield)	RSS Seminar
14:00		Quantifying uncertainty on the chronologies of palaeoclimate reconstructions from ice cores
		Hicks Room K14
	Abstract: Compacted snow and ice that form huge ice sheets in polar regions preserve valuable information about past environment and climate. Cores that are drilled through these ice deposits are analysed for physical and chemical properties, which reveal information about climate at the time the deposits were laid down. A pivotal part of interpreting the information held within these sequences is to build ice core chronologies i.e. to relate time to depth. Various approaches (and combinations thereof) are taken when constructing such chronologies: (1) layer counting using the seasonality in signals, (2) glaciological modelling describing processes such as snow accumulation and plastic deformation of ice, and (3) linking parameters in the ice core to other dated events or records. Conventionally, implementation of these approaches does not use statistical methods; this talk describes recent collaborative work in this area using a Bayesian model-based approach.
Jan 29	Thu	Marian Scott (Glasgow)	RSS Seminar
14:45		Dating tools and measuring rates: essential ingredients for reconstructing past climate
		Hicks Room K14
	Abstract: Underpinning our ability to reconstruct past climate is our ability to measure time using 'clocks' based on the principle of radioactive decay or on counting atoms. These measurements and procedures are complex and may require sophisticated models for the measurement errors. Some examples of measurements errors and their estimation (as well as the statistical models used) from cosmogenic isotope dating using C-14, Be- 10, Al-26 and Cl-36 will be presented.
Jan 29	Thu	Andrew Parnell (Univerisity College Dublin)	RSS Seminar
16:00		Estimating the synchroneity of past climate changes
		Hicks Room K14
	Abstract: Radiocarbon dating techniques allow us to estimate the timing of climatic shifts as evidenced by changes in pollen compositions. We use some recently developed Bayesian chronology models (Haslett and Parnell, 2008; Parnell et al 2008) to provide a framework to answer questions about the synchroneity of these shifts across Europe. This talk will discuss the statistical background to the chronology models as well as issues concerning the identification of a climatic 'event'.
Feb 5	Thu	Eugenia Cheng (Sheffield)	Topology Seminar
15:05		Ubiquitous Yoneda: universal operads
		Hicks Seminar Room J11
	Abstract: We show how to build operads for n-categories that are informally analogous to the universal loop space operads. We will make this universal property precise by showing that it is in fact the Yoneda Lemma in disguise. We will then explain how this constitutes a win in the Australian version of "Mornington Crescent".
Feb 11	Wed	Philippa Browning (Manchester)	Applied Mathematics Colloquium
14:00		Magnetic reconnection and the active solar corona
		Hicks Lecture Theatre A
	Abstract: Magnetic reconnection is a process by which the topology of magnetic fields can change, even in a highly conducting plasma, and which allows efficient dissipation of magnetic energy. One of the major outstanding problems in solar physics is to explain the high temperature of coronal plasma, and a strong candidate is the dissipation of free magnetic energy by magnetic reconnection. The physical process is then essentially the same as in solar flares - dramatic energy-releasing events in the solar atmosphere - and coronal heating can be viewed as a superposition of many small flare-like events. A key feature of solar flares is the presence of non-thermal high energy charged particles, and understanding the origin of these is a challenge for theorists. These high energy particles provide an important diagnostic of the magnetic reconnection process. After an introduction to coronal heating and solar flares, some recent work concerning acceleration of high energy particles by magnetic reconnection in solar flares will be presented. Also, a new model of coronal heating by reconnection, occurring during the nonlinear phase of kink instability of coronal loops, will be described. A theoretical model based on a minimum energy principle will be described, complemented by numerical simulations.
Feb 12	Thu	Lindsay Collins (Sheffield)	Statistics Seminar
14:00		Climate variability and its effect on atmosphere/terrestrial-biosphere carbon fluxes
		Hicks LT7
	Abstract: In my PhD I will study the effect of climate uncertainty and variability on vegetation carbon dynamics. Our interest in the terrestrial biosphere lies in the carbon that is released into the atmosphere or stored in the soil through the land vegetation. The Sheffield Dynamic Global Vegetation Model (SDGVM) simulates the terrestrial vegetation processes (including photosynthesis and respiration) and provides estimates of terrestrial carbon fluxes. The SDGVM is driven by monthly climate data. The monthly data are downscaled to daily data within the SDGVM using a weather generator so that the vegetation processes can be calculated daily. I will show how temporal variability leads to differing carbon flux estimates. We aim to quantify the uncertainty in the carbon flux estimates directly linked to uncertainty and variability in the climate data using probabilistic sensitivity analysis (PSA) methods developed by Oakley and O'Hagan (2004) making use of the GEM-SA software developed by Kennedy (2004) for working with complex models such as the SDGVM. I will show how the form of the climate data makes the use of this software less than straightforward and introduce methodology by which a PSA may be possible. This will involve the characterisation of the uncertainty in the climate in terms of parameters that can be used as input to GEM-SA rather than actual data.
Feb 12	Thu	Lu Zou (Sheffield)	Statistics Seminar
14:00		Multiple Imputations of Bio-Datasets
		Hicks LT7
	Abstract: This presentation will start with a brief introduction to two Bio-datasets involved in my study. One inevitable issue is that many values are missing in both sets. Rather than ignoring them, imputation is considered. This talk will focus on the imputation of continuous variables which are to be used as Biomarkers in two situations: i) normal randomly missing situation and ii) a 'File-matching' situation. Several imputation methods are considered: for single imputation, the K-Nearest Neighbours method (KNN) and the EM-algorithm are studied; for multiple imputations, the Multiple Imputation using Additive Regression, Bootstrapping and Predictive Mean Matching (PMM) and the EM imputation combined with re-sampling methods are investigated. Based on the studies so far, the EM algorithm is relatively more suitable in my case.
Feb 12	Thu	John Jones (Warwick)	Topology Seminar
15:05		Batalin Vilkovisky algebras and string homology
		Hicks Seminar Room J11
	Abstract: String homology was introduced by Moira Chas and Dennis Sullivan in 1999. Their idea was to do intersection theory on the loop space of a finite dimensional manifold. In a subsequent paper, published in 2002, Ralph Cohen and myself gave a different approach to the theory using the general methods of algebraic topology and homotopy theory. One of the outputs of string homology is that the theory shows how to associate an algebraic structure known as a Batalin Vilkovisky algebra to a closed finite dimensional manifold. In this talk I will discuss Batalin Vilkovisky algebras and how they arise in algebraic topology, in particular in string homology, and emphasize two fundamental problems. 1. How does one calculate string homology? 2. What exactly does string homology depend on?
Feb 13	Fri	Eamon Scullion (Sheffield)
13:05
		Lecture Theatre 10
Feb 18	Wed	Alice Courvoisier (Leeds)	Applied Mathematics Colloquium
14:00		The Mean Field Approach to the Transport of Magnetic Fields
		Hicks Lecture Theatre A
	Abstract: The Sun's global magnetic field is believed to be the result of a `large-scale dynamo', whereby inductive motions within the solar convection zone are able to generate and sustain a magnetic field on scales larger than their own. Mathematically, the evolution of the Sun's large-scale magnetic field is conveniently described using mean field electrodynamics, a turbulence closure theory that relies on the parametrisation of small-scale effects by transport coefficients. Among these, the so-called `alpha-effect' is responsible for the growth of the mean magnetic field and will be the focus of my talk. Trying to understand how this coefficient depends on the turbulent motions within the solar plasma is tricky. Instead, we construct simpler models based on 2D motions for which the alpha-effect can be unambiguously determined and we study systematically how the spatial and temporal coherence of the flows influence it. I will start by introducing the alpha-effect from a phenomenological and mathematical point of view before presenting the results of our calculations and discussing their implications.
Feb 18	Wed	Stephane Launois (Kent)	Pure Maths Colloquium
16:00		From total positivity to quantum algebras
		Hicks Seminar Room J11
	Abstract: In recent publications, the same combinatorial description has arisen for three separate objects of interest: non-negative cells in the real grassmannian (Postnikov, Williams); torus orbits of symplectic leaves in the classical grassmannian (Brown, Goodearl and Yakimov); and torus invariant prime ideals in the quantum grassmannian (Lenagan, Rigal and I). The aim of this talk is to present these results and explore the reasons for this coincidence.
Feb 19	Thu	Andrew Stuart (University of Warwick)	Statistics Seminar
14:00		Metropolis-Hastings Methods for Sampling Random Functions
		Hicks LT7
	Abstract: Many applied problems require the practitioner to obtain information from a probability measure on functions. Examples include signal processing, weather prediction, oceanography, nuclear waste management and oil recovery. I will show that, despite the wide variety of physical phenomena underlying these examples, there is a common mathematical structure which can be exploited in a number of ways. I will highlight how this structure can be used to design efficient MCMC methods to sample from the desired probability measure, generalizing random walk and other Metropolis-Hastings methods to the function space setting.
Feb 19	Thu	Andrew Stacey (Trondheim)	Topology Seminar
15:05		Comparative Smootheology
		Hicks Seminar Room J11
	Abstract: "Manifolds are lovely spaces; it's just a pity there aren't enough of them." In my work on loop spaces I have often come across the problem that loop spaces are like ordinary manifolds but not completely alike. One has to be careful when taking ideas and techniques from ordinary differential topology and geometry to spaces like loop spaces. Considerations like this have led a variety of researchers to propose notions of "generalised smooth spaces". Unfortunately, there are a lot of these notions about. In this talk I shall explain why I like "Frolicher spaces" best of all the different versions. I shall also comment a little on other topics, in particular the differences and similarities between the various notions.
Feb 20	Fri	Philippe Caillol (Sheffield)
13:05
		Lecture Theatre 10
Feb 26	Thu	Mike Titterington (Glasgow)	Statistics Seminar
14:00		Approximate inference for latent variable models
		Hicks LT7
	Abstract: Likelihood and Bayesian inference are not straightforward for latent variable models, of which mixture models constitute a special case.. For instance, in the context of the latter approach, conjugate priors are not available. The talk will consider some approximate methods that have been developed mainly in the machine-learning literature and will attempt to investigate their statistical credentials. In particular, so-called variational methods and the Expectation-Propagation method will be discussed. It will be explained that, in the Bayesian context, variational methods tend produce approximate posterior distributions that are located in the right place but are too concentrated, whereas the Expectation-Propagation approach sometimes, but not always, gets the degree of concentration, as measured by posterior variance, right as well.
Feb 26	Thu	Simon Willerton (Sheffield)	Topology Seminar
15:05		Two 2-traces
		Hicks Seminar Room J11
	Abstract: Monoidal bicategories are not scary abstract beasts but crop up concretely in many places in algebra and topology; I will use several examples as the backbone to the talk. In a monoidal bicategory there are two different notions of trace for endomorphisms which in various cases are `dual'. I will illustrate with various pictures and examples.
Feb 27	Fri	Toshi Ogawa (Engineering Science, Osaka University, Japan)
13:05
		Lecture Theatre 10
Mar 2	Mon	Richard Hepworth (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:10		Basics of Curvature
		Hicks Seminar Room J11
Mar 4	Wed	Dr Takashi Sakajo (Hokkaido)	Applied Mathematics Colloquium
14:00		Dynamics of point-vortices in multiply connected domains
		Hicks Lecture Theatre A
	Abstract: The motion of incompressible and inviscid flow is described by the two-dimensional Euler equations. According to Kelvin's theorem, the circulation is conserved along the path of a fluid particle and thus the vorticity neither generates nor disappears during its evolution. Hence in order to solve the Euler equations, we have only to investigate the evolution of the non-zero vorticity domain at the initial moment. Based on this observation, we discretize the initial non-zero vorticity domain with a set of $N$ points, called point vortices, whose strengths are determined by the circulation around these points. Then we track the evolutions of the $N$ point vortices. This discretization method for the Euler equations is known as the vortex method, which reduces the Euler equations to a system of ordinary differential equations for the N point vortices. The present talk gives the equation of motion for $N$ point vortices in a bounded planar multiply connected domain inside the unit circle that contains many circular obstacles. The equation not only describes fundamental interactions between solid obstacles and fluids, but also contributes toward understanding of geophysical flows with many islands and artificial obstacles such as lakes, inland seas and coastal region. As an example, we consider the motion of a vortex dipole that consists of two point vortices with the unit strength of the opposite signs. When the multiply connected domain is symmetric with respect to the real axis, the motion of the vortex dipole is integrable for the initial configuration with the same symmetry. We investigate the integrable system in detail and discuss a non-integrable motion of the vortex dipole without the reflectional symmetry.
Mar 4	Wed	Christian Wuthrich (Nottingham)	Pure Maths Colloquium
16:00		Modular points on elliptic curves
		Hicks Seminar Room J11
Mar 5	Thu	David Leslie (Bristol)	Statistics Seminar
14:00		Posterior weighted reinforcement learning with state uncertainty
		Hicks LT7
	Abstract: Reinforcement learning models are, in essence, online algorithms to estimate the expected reward in each of a set of states by allocating observed rewards to states and calculating averages. Generally it is assumed that a learner can unambiguously identify the state of nature. However in any natural environment the state information is noisy, so that the learner cannot be certain about the current state of nature. Under state uncertainty it is no longer immediately obvious how to perform reinforcement learning, since the observed reward cannot be unambiguously allocated to a particular state of the environment. A new technique, posterior weighted reinforcement learning, is introduced. In this process the reinforcement learning updates are weighted according to the posterior state probabilities, calculated after observation of the reward. We show that this modified algorithm can converge to correct reward estimates, and show the procedure to be a variant of an online expectation-maximisation algorithm, allowing further analysis to be carried out.
Mar 5	Thu	Harry Ullman (Sheffield)	Topology Seminar
15:05		Equivariant generalizations of Millers stable splitting
		Hicks Seminar Room J11
	Abstract: In 1985 Miller proved that Stiefel manifolds, and in particular the unitary group, split stably as a wedge of Thom spaces over Grassmannians. This talk will discuss efforts towards generalizing Miller's results in an equivariant setting including a main conjecture, a survey of results found so far and an explanation as to just why putting $G$ in front of everything in sight isn't the right thing to do.
Mar 6	Fri	Youra Taroyan (Sheffield)
13:05
		Lecture Theatre 10
Mar 9	Mon	Dev Sinha (Oregon)	Topology Seminar
16:10		Cohomology of symmetric groups
		Hicks Seminar Room J11
Mar 10	Tue	Dev Sinha (Oregon)	Topology Seminar
13:10		Hopf invariants
		Hicks Seminar Room J11
Mar 11	Wed	Youra Taroyan (Sheffield)	Applied Mathematics Colloquium
14:00		Alfven instability in a compressible flow
		Hicks Lecture Theatre A
	Abstract: Abstract: Macroscopic instabilities have important energetic and dynamic consequences in space plasmas and laboratory devices. Well known examples include the current pinch, Rayleigh-Taylor and shear flow instabilies which can be studied using the magnetohydrodynamic approach. A brief introduction will be followed by a presentation of a new magnetohydrodynamic instability. It will be demonstrated that linear incompressible Alfvenic disturbances can become exponentially amplified in compressible plasma flows. The instability does not require high flow speeds or shear. The amplification process is based on the mechanism of over-reflection well-known from previous studies of shear flows. A transparent stability criterion can be derived for a simple two-layer model. The instability may arise in both open and closed magnetic structures. An application to a solar coronal loop model with a siphon flow will be presented. Theoretical and observational implications of the Alfven instability will be discussed.
Mar 11	Wed	Robert Marsh (Leeds)	Pure Maths Colloquium
16:00		Cluster structures from 2-Calabi-Yau categories with loops
		Hicks Seminar Room J11
Mar 12	Thu	Gareth Roberts (Warwick)	Statistics Seminar
14:00		Retrospective sampling
		Hicks LT7
	Abstract: This talk will discuss a very simple idea for simulation called retrospective sampling. The method can be applied in the context of many well-used simulation methods such as rejection sampling and MCMC. A number of very simple examples will be described to illustrate the ideas. As time permits, I will give some applications, possibly including exact simulation of diffusion paths and posterior distributions for Dirichlet mixture models.
Mar 12	Thu	Ieke Moerdijk (Sheffield)	Topology Seminar
15:05		Infinity Categories and Infinity Operads I
		Hicks Seminar Room J11
Mar 16	Mon	Ieke Moerdijk (Sheffield)	Topology Seminar
16:00		Infinity Categories and Infinity Operads II
		Hicks Seminar Room J11
Mar 17	Tue	Simon Willerton (Sheffield)
17:10		Measuring metric spaces: short-sightedness and population diversity
		LT6
	Abstract: Metric spaces can be used to represent many disparate things including shapes in space and the differences between species in a population. I will describe one way to measure the size of a metric space arrived at from pure mathematical considerations but discovered independently by ecologists. I will discuss connections with diversity measures and geometry. This is intended to be accessible to all in the School.
Mar 18	Wed	Viacheslav Nikulin (Liverpool/Steklov Mathematical Institute (Moscow))	Pure Maths Colloquium
16:00		Arithmetic groups generated by reflections in hyperbolic spaces.
		Hicks Seminar Room J11
	Abstract: In 1980, 1981 I had shown that the number of maximal hyperbolic arithmetic reflection groups is finite in each dimension n>9, and in 1981 Vinberg had shown that these groups don't exist for n > 29. Only in 2005 Long-Maclachlan-Reid proved finiteness in dimension n=2, and Agol in dimension n=3. The remaining gap, 3 Thus, finally, now we know that the number of these groups is finite in all dimensions together. I plan to outline these results and my further results about effective finiteness (2007). They permit to obtain a finite classification of these groups, in principle. The groups are important in Algebraic Geometry and in the theory of Lorentzian Kac-Moody (Borcherds) Lie algebras.
Mar 19	Thu	Ieke Moerdijk (Sheffield)	Topology Seminar
15:05		Infinity Categories and Infinity Operads III
		Hicks Seminar Room J11
Mar 19	Thu	Jane Hutton (Warwick)	RSS Seminar
16:30		Being an expert witness
		Hicks Room LT2
	Abstract: This talk will consider how and why a statistician might be an expert witness. Practical aspects, such as understanding the difference between civil and criminal cases, the meaning of 'expert' in a legal context, the form of reports and fees will be discussed. My illustrations will mainly be from civil, medical cases. Such cases are generally low profile, and so provide a gentler introduction to being an expert witness that criminal cases. Some differences between English, Irish, South Africa and USA courts will be described. My intention is to encourage the audience to consider acting as experts, as there is a contribution statisticians can make to the judicial system.
Mar 20	Fri	Sergey Zharkov (Sheffield)
13:05
		Lecture Theatre 10
Mar 23	Mon	Richard Hepworth (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:10		Basics of Curvature, Part 2
		Hicks Seminar Room J11
Mar 25	Wed	Alan Hood (St Andrews)	Applied Mathematics Colloquium
14:00		Heating the solar corona by nanoflares triggered by a kink instability
		Hicks Lecture Theatre A
	Abstract: The heating of solar coronal plasma to millions of degrees may be due to the superposition of many small energy-releasing events, known as nanoflares. Nanoflares dissipate magnetic energy through magnetic reconnection. It is proposed that heating is triggered by the onset of an ideal MHD instability, with energy release occurring in the nonlinear phase due to fast magnetic reconnection. Numerical simulations are used to investigate the energy release and the heating process.
Mar 26	Thu	Simon Wilson (Trinity College Dublin)	Statistics Seminar
14:00		Factor Analysis with a Mixture of Gaussian Factors, with Application to Separation of the Cosmic Microwave Background
		Hicks LT7
	Abstract: Blind source separation is a technique in signal processing where the values of 'sources' are inferred from observations that are linear combinations of them. The typical example is separating two voices (the sources) from a stereo audio recording (each microphone picks up a combination of the two speakers' voices). Both the sources and the matrix of linear 'mixing' coefficients may be unknown. In statistical terms, it is an example of factor analysis, the main difference being that the 'factors' here will have some interpretation and there may exist useful prior information on them. $~~$ Here we describe an approach to factor analysis/source separation where the sources are assumed to be Gaussian mixtures, which may be independent or dependent e.g. mixtures of multivariate Gaussians. An MCMC procedure has been developed that implements a fully Bayesian procedure e.g. it computes the posterior distribution of sources, their Gaussian mixture parameters and the matrix of linear coefficients from the data. $~~$ The method is applied to recovery of the cosmic microwave background (CMB), being an example of source separation applied to image data. The CMB is one of many sources of extraterrestrial microwave radiation and we observe a weighted sum of these sources from the Earth at different frequencies. Its accurate reconstruction is of great interest to astronomers and physicists since knowledge of its properties, and in particular its anisotropies, will place strong restrictions on current cosmological theories. From the perspective of a Bayesian solution, this application is interesting as there is considerable prior information about the linear coefficients and the sources. Results from the analysis of data from the WMAP satellite will be presented, where microwave radiation is observed at 5 frequencies and separated into sources, including the CMB. A discussion of the many outstanding issues in this problem is also presented.
Mar 26	Thu	Constanze Roitzheim (Glasgow)	Topology Seminar
15:05		Hochschild cohomology of A-infinity algebras
		Hicks Seminar Room J11
	Abstract: In the 1960s, A-infinity algebras were introduced to study the cohomology of topological spaces with products and are now known to arise widely in various areas of mathematics. Roughly speaking, A-infinity algebras are generalisations of associative algebras. We are going to explain how to extend the definition of Hochschild cohomology from associative algebras to A-infinity algebras and how this will help solving realizability problems in topology.
Mar 26	Thu	Peter Goos (Antwerp)	Statistics Seminar
16:00		The optimal design of conjoint choice experiments
		Hicks LT5
	Abstract: Stated preference data are commonly collected by means of conjoint choice experiments or discrete choice experiments in marketing, health economics or environmental economics. The optimal design of these experiments is a challenging research area because of the nonlinearity of the statistical models used to analyze the data. These models include the conditional logit model, the mixed logit model and the nested logit model. In this talk, I will discuss recent advances in the optimal design for such models as well as some of the challenging computational aspects of the optimal design search.
Mar 27	Fri	Christopher Clack (Sheffield)
13:05
		Lecture Theatre 10
Apr 1	Wed	Steve Cowley (Director of the UKAEA, Culham Laboratory)	Applied Mathematics Colloquium
14:00		Fusion -- the Theoretical Challenge
		Hicks Lecture Theatre A
	Abstract: The international fusion experiment ITER will start operating in the south of France late in the next decade. This historic experiment will generate up to 500 megawatts of fusion power and provide a proof of principle for fusion energy. The theoretical description of fusion plasmas is very challenging and there are many unanswered questions. For example, the plasma is permeated with small scale turbulence that determines the confinement and the evolution. But, a full predictive model of the turbulence is still unavailable. I will outline the challenges and the progress that has been made.
Apr 1	Wed	Miguel Rodriguez-Olmos (Manchester)	Pure Maths Colloquium
16:00		Gauge Equivalence and Conserved Quantities for Lagrangian Systems on Lie Algebroids
		Hicks Seminar Room J11
	Abstract: Lie algebroids generalize several geometric objects such as tangent bundles, Lie algebras or Atiyah sequences. It is possible to give a geometric formalism of Lagrangian mechanics on Lie algebroids that particularizes to the usual Euler-Lagrange, Euler-Poincare, or Wong equations for the above particular cases. In this talk we will introduce this formalism and will study the notions of gauge and dynamical equivalence for Lagrangian systems as well as their relationship with Nöther conserved quantities for the dynamics.
Apr 2	Thu	Philip Jonathan (Shell Technology Centre Thornton)	Statistics Seminar
14:00		Modelling spatial and directional effects in extreme value analysis
		Hicks LT7
	Abstract: The characteristics of extreme waves in storm-dominated regions vary systematically with a number of covariates, including location and storm direction. Reliable estimation of the magnitude of extreme events associated with a given return period requires incorporation of covariate effects within extreme value models. A spatio-directional extremes model will be outlined, based on a non-homogeneous Poisson model of peaks over threshold. At each location, a non-parametric estimate for extreme threshold as a function of storm direction is made. The rate of occurrences of threshold exceedences is modelled as a Poisson process. The size of threshold exceedences is modelled using a generalised Pareto form, the parameters of which vary smoothly in space, and are estimated using a roughness penalised likelihood approach using thin plate splines. The approach will be motivated and illustrated in application to estimation of structural design criteria for the Gulf of Mexico.
Apr 2	Thu	Elizabeth Hanbury (Durham)	Topology Seminar
15:05		Simplicial structures on braid groups and mapping class groups
		Hicks Seminar Room J11
Apr 3	Fri	Jamie Douglas (Sheffield)
13:05
		Lecture Theatre 10
Apr 23	Thu	Goran Peskir (Manchester)	Statistics Seminar
14:00		The British Put-Call Symmetry
		Hicks LT7
	Abstract: I will review recent results/problems arising in the British pricing mechanism. This involves optimal stopping with non-monotone free boundaries.
Apr 23	Thu	Gennady Samorodnitsky (Cornell)	Statistics Seminar
15:30		The 2009 Applied Probability Trust Lecture\\ Large deviations for point processes based on stationary sequences with heavy tails
		Hicks LT7
	Abstract: In many applications involving functional large deviations for partial sums of stationary, but not iid, processes with heavy tails, a curious phenomenon arises: closely grouped together large jumps coalesce together in the limit, leading to loss of information of the order in which these jumps arrive. In particular, many functionals of interest become discontinuous. To overcome this problem we move from the functional large deviations to the point-process-level large deviations. We develop the appropriate topological framework and prove large deviations theorems for point processes based on stationary sequences with heavy tails. We show that these results are useful in many situations where functional large deviations are not.
Apr 29	Wed	Pramod Achar (Louisiana /Cambridge)	Pure Maths Colloquium
16:00		Orbit closures in the enhanced nilpotent cone.
		Hicks Seminar Room J11
	Abstract: Let $\mathcal N$ denote the set of $n \times n$ nilpotent matrices. The ``enhanced nilpotent cone'' is the space $\mathbb C^n \times \mathcal N$. $GL(n)$ acts on $\mathbb C^n$ in an obvious way, and on $\mathcal N$ by conjugation. The orbits of this action are the subject of this talk. From this surprisingly elementary starting point, I will discuss connections to various topics in representation theory, combinatorics, and algebraic geometry, and especially to Syu Kato's work on the ``exotic nilpotent cone'' and affine Hecke algebras. This is joint work with A. Henderson.
Apr 30	Thu	Svetlana Tishkovskaya (Sheffield)	Statistics Seminar
14:00		Optimal Quantisation in Bayesian Estimation
		Hicks LT7
	Abstract: I consider Bayesian estimation of a parameter of a continuous distribution when observation space is quantised. Quantisation, as method of approximating a continuous range of values by a discrete set, arises in many practical situations which include modern methods of digital information processing, data compression, and some procedures of collecting data. It is well known that quantising of observations reduces values of convex information functionals. This information loss can be diminished by selecting the optimal partition. I consider two criteria of optimal quantisation in Bayesian estimation: the criterion of Bayes risk minimum and the criterion of minimum of information loss measured using Shannon information. As alternative to optimal partitioning, which realisation is often computationally demanding, an asymptotically optimal quantisation is also considered.
Apr 30	Thu	Kijti Rodtes (Sheffield)	Topology Seminar
15:05		The connective $k$ theory of a semidihedral group
		Hicks Seminar Room J11
	Abstract: For a finite group G, $ko_*(BG)$ plays a role in Gromov-Lawson-Rosenberg conjecture. We can compute it via $ku^*(BG)$ by using Bockstein spectral sequence and Greenlees spectral sequence. In this talk, we will show how to calculate $ku^*(BG)$ and $ku_*(BG)$ where $G$ is the semidihedral group of order 16.
May 1	Fri	Marialejandra Luna (Sheffield)
13:05
		Lecture Theatre 10
May 6	Wed	Khairia Mira (Sheffield)	Pure Maths Postgraduate Seminar
14:00		The Kunneth formula in connective K-theory
		Hicks Seminar Room J11
May 6	Wed	D Kurtz (Central Lancashire)	Applied Mathematics Colloquium
14:00		Songs of the Stars
		Student Union Auditorium
May 6	Wed	Mike Thompson (Sheffield)	Applied Mathematics Colloquium
15:30		Helioseismology
		Student Union Auditorium
May 6	Wed	Diane Maclagan (Warwick)	Pure Maths Colloquium
16:00		Smooth Multigraded Hilbert schemes.
		Hicks Seminar Room J11
	Abstract: The multigraded Hilbert scheme, introduced by Haiman and Sturmfels, parameterizes all ideals in a polynomial ring with a fixed multigraded Hilbert function with respect to an abelian group grading. I will discuss joint work with Greg Smith proving the conjecture that when the polynomial ring has two variables these Hilbert schemes are always smooth and irreducible. This reduces to combinatorial commutative algebra.
May 6	Wed	Roger Webster (Sheffield)	Applied Mathematics Colloquium
16:30		The tail of Pi
		Student Union Auditorium
May 7	Thu	Kevin Walters (Sheffield)	Statistics Seminar
14:00		Are colonic stem cell data consistent with the immortal model of stem cell division under non-random strand segregation?
		Hicks LT7
	Abstract: Stem cells have the potential to revolutionize modern medicine with their regenerative potential however little is known about tissue stem cell differentiation in-vivo. Technical advances in laboratory methods have started to provide data that allow us to make simple inferences about tissue stem cell behaviour. This talk will focus on a particular model of stem cell differentiation.
May 7	Thu	Hao Zhao (Manchester)	Topology Seminar
15:05		Homotopy exponents of some homogeneous spaces
		Hicks Seminar Room J11
	Abstract: Let p be a prime. Using the methods of homotopy decomposition and spherical fibrations, under some restricted conditions we obtain upper bounds for the $p$-primary homotopy exponents of some homogeneous spaces such as the complex Stiefel manifold, complex Grassmann manifold, $SU(2n)/Sp(n)$, $E_{6}/F_{4}$ and $F_{4}/G_{2}$.
May 8	Fri	Andrew Newton (Sheffield)
13:05
		Lecture Theatre 10
May 13	Wed	Jamie Douglas (Sheffield)	Applied Mathematics Colloquium
14:00		An examination of the linear structure of the CUTIE plasma turbulence code
		Hicks Lecture Theatre A
May 13	Wed	Eli Hawkins (York)	Pure Maths Colloquium
16:00		A Groupoid Approach to Quantization
		Hicks Seminar Room J11
	Abstract: I will describe my approach to quantization of Poisson manifolds using symplectic groupoids. By "quantization", I mean the construction of a noncommutative C*-algebra from a geometrical approximation. This approach unifies several previous examples. It combines the ideas of geometric quantization and groupoid convolution algebras. I will try to explain as many of these concepts as time allows.
May 14	Thu	Assaf Libman (Aberdeen)	Topology Seminar
11:30		The gluing problem and Bredon cohomology
		Hicks Seminar Room J11
May 14	Thu	Erika Hausenblas (Saltzburg)	Statistics Seminar
14:00		Stochastic Partial Differential Equations driven by Poisson Random Measure
		Hicks LT7
	Abstract: I will start with pointing out some examples coming from physics to motivate stochastic partial differential equations (SPDEs). Then I will briefly explain the differences in the dynamics between deterministic partial differential equations and SPDEs. After this motivation I will speak about stochastic integration in Banach spaces and point out the differences with the stochastic integral with respect to the Wiener process. Finally, I give some results concerning SPDEs drive by Poisson random measures.
May 14	Thu	Andras Juhasz (Cambridge)	Topology Seminar
14:30		Classifying minimal genus Seifert surfaces
		Hicks Seminar Room J11
	Abstract: First I will survey two different notions of equivalence for Seifert surfaces. Then I will show how sutured Floer homology helps in the classification of minimal genus Seifert surfaces under both types of equivalence.
May 14	Thu	Michael Farber (Durham)	Topology Seminar
16:15		Topology of random manifolds
		Hicks Seminar Room J11
	Abstract: Betti numbers of configuration spaces of mechanical linkages (known also as polygon spaces) depend on a large number of parameters -- the lengths of the bars of the linkage. Motivated by applications in topological robotics, statistical shape theory and molecular biology, we view these lengths as random variables and study asymptotic values of the average Betti numbers as the number of links n tends to infinity. We establish a surprising fact that for a reasonably ample class of sequences of probability measures the asymptotic values of the average Betti numbers are independent of the choice of the measure.
May 14	Thu	Denise Lievesley (Kings College London)	RSS Seminar
16:30		The Statistician as Public Servant
		Hicks LT2
	Abstract: Denise Lievesley will draw on her experience of working in both statistics and information services in the UK and in the United Nations to highlight the tension between relevance and statistics. But relevant for whom? Relevance should not be defined narrowly but should take account of the very varied communities of users. As statisticians we want what we produce to be used to make a difference in the quality of people's lives which means that our data must be fed into public policy. But how do we ensure that the data and associated interpretation are germane to the development of policies whilst at the same time protecting them from political interference? The challenge is to produce data which are both trusted and trustworthy.
May 15	Fri	Carlos Jaimes (Sheffield)
13:05
		Lecture Theatre 10
May 19	Tue	John Biggins (Sheffield)
17:05		Branching Out
		LT 6 Hicks
	Abstract: I aim to give an overview of the synthesis of two classical probability models (branching processes and random walk) and to indicate connections with several other parts of mathematics.
May 20	Wed	Carsten van de Bruck (Sheffield)	Applied Mathematics Colloquium
14:00		Dark Energy in the Cosmos and the Laboratory
		Hicks Lecture Theatre A
	Abstract: According to observations the expansion of the universe seems to be speeding up, instead of slowing down. To explain this observation, one is either forced to introduce a new energy component (dark energy) with strange properties (such as negative pressure) or to change the laws of gravity. In this talk I will focus on the former possibility and describe theoretical models for dark energy and how to test these with cosmological observations or even in the laboratory.
May 22	Fri	Andrew Gascoyne (Sheffield)
13:05
		Lecture Theatre 10
May 26	Tue	Philip Eve (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Springer varieties
		Hicks Seminar Room J11
May 26	Tue	Tom Sutherland (Sheffield)	Pure Maths Postgraduate Seminar
15:00		A Hall algebra approach to wall crossing
		Hicks Seminar Room J11
May 27	Wed	Eric Friedlander (Northwestern)	Pure Maths Colloquium
14:00		Group cohomology, Weil restriction, and support varieties
		LT6
	Abstract: Let $G$ be a simple algebraic group defined and split over $\mathbf{F}_p$. We may associate to $G$ the finite groups $G(\mathbf{F}_q)$ for any $p$-th power $q$ and also the Lie algebras $g_{\mathbf{F}_q}$ where $g = Lie(G)$. If $M$ is a rational $G$-module, then $M$ can be viewed as a module for each of the $G(\mathbf{F}_q)$ as well as a "$p$-restricted" representation for each of the $g_{\mathbf{F}_q}$. Work of J. Carlson, Z. Lin and D. Nakano relates cohomological invariants associated to $M$ as a $G(\mathbf{F}_p)$-module and as a $g$-representation. In this talk, we describe the Weil restriction functor which converts structures over $\mathbf{F}_q$ to structures over $\mathbf{F}_p$. We apply this functor to the Seitz log map relating unipotent and nilpotent elements in order to formulate and prove various cohomological results for $G(\mathbf{F}_q)$.
May 27	Wed	Alice Robinson (Sheffield)	Applied Mathematics Colloquium
14:00		HF Radar and Wind turbine interaction in Liverpool Bay
		Hicks Lecture Theatre A
	Abstract: HF radar has become accepted over the last 50 years as a key tool in remote sensing of ocean currents and waves. It is favoured for excellent spatial and temporal coverage, and ease of access compared to more traditional buoy's and ADCP's. Data is available in near to real time and is well used by the maritime industry. The Proudman Oceanographic Laboratory operates a 13MHz HF WERA radar in Liverpool Bay. It is by nature sensitive to RFI and clutter which can degrade the accuracy and availability of the current and wave measurements. Liverpool Bay is undergoing extensive wind farm development which will present problems for any radar system due to their large radar cross sections. It is important to understand and mitigate any effects of the wind turbines on data accuracy and availability to achieve maximum performance from the HF radar.
May 27	Wed	Andrew Newton (Sheffield)	Applied Mathematics Colloquium
14:30		Numerical Investigation into sheared MHD turbulence
		Hicks Lecture Theatre A
	Abstract: Shear flows and magnetic fields are ubiquitous in astrophysical plasmas, playing a crucial role in turbulent transport. Here, we present the first numerical results of the suppression of magnetic diffusion by a shear flow in 2D MHD turbulence. For a very strong magnetic field, a new scaling regime of magnetic diffusion quenching by magnetic fields is found, with a stronger dependence on magnetic field strength compared to the previous result [1]. Furthermore, we show the first numerical evidence of enhanced transport due to the interaction between shear flow and magnetic field via resonances,which weakens the magnetic diffusion quenching. Similar results are also presented for momentum transport. These results highlight the importance of shear flows, (Alfven) waves, and resonances in understanding turbulent dissipation of magnetic fields. We discuss important implications of these results in turbulent magnetic reconnection and dynamos. [1] F. Cattaneo and S.I. Vainshtein, Astrophys. J. Lett. 376. L21 (1991)
May 27	Wed	Detlev Hoffmann (Nottingham)	Pure Maths Colloquium
15:00		Bilinear forms and differential forms under field extensions
		LT6
	Abstract: An important problem in algebra is the study of algebraic objects defined over fields and how they behave under field extensions, for example the Brauer group of a field, Galois cohomology groups over fields, Milnor K-theory of a field, or the Witt ring of bilinear forms over a field. Of particular interest is the determination of the kernel of the restriction map when passing to a field extension. We will give an overview over some known results concerning the kernel of the restriction map from the Witt ring of a field to the Witt ring of an extension field. Over fields of characteristic not two, general results are rather sparse. In characteristic two, we have a much more complete picture. In this talk, I will explain the full solution to this problem for extensions that are given by function fields of hypersurfaces over fields of characteristic two. An important tool is the study of the behaviour of differential forms over fields of positive characteristic under field extensions. The result for Witt rings in characteristic two then follows by applying earlier results by Kato, Aravire-Baeza, and Laghribi. This is joint work with Andrew Dolphin.
May 27	Wed	I. Fesenko (Nottingham)	Pure Maths Colloquium
16:30		Understanding conductors of elliptic curves via geometric adelic two-dimensional theory
		LT6
	Abstract: Understanding conductors of elliptic curves via geometric adelic two-dimensional theory Short abstract: The classical way of working with arithmetic aspects of elliptic curves over a global field is to involve (generally noncommutative) Galois extensions of the (one-dimensional) global field. In this classical approach the conductor of elliptic curve remains a mysterious object. Geometrically, elliptic curves over global fields can be viewed via associated two-dimensional models. I will try to explain how the recent theory of two-dimensional adelic spaces and zeta integrals on them gives a real understanding of the conductor (at least, its tame part) of elliptic curves, which is not available in the classical one-dimensional theory.
May 28	Thu	Professor Rick Jardine (University of Western Ontario)	Topology Seminar
15:10		Pointed torsors and Galois groups
		Hicks Seminar Room J11
	Abstract: Suppose that H is an algebraic group which is defined over a field k, and let L be the algebraic closure of k. The canonical stalk for the etale topology on k induces a simplicial set map from the classifying space B(H-tors) of the groupoid of H-torsors (aka. principal H-bundles) to the space BH(L). The homotopy fibres of this map are groupoids of pointed torsors, suitably defined. These fibres can be analyzed with cocycle techniques: their path components are representations of the absolute Galois groupoid of k in H, and each path component is contractible. The arguments for these results are simple, and applications will be displayed.
May 29	Fri	David Robertson (Sheffield)
13:05
		Lecture Theatre 10
Jun 4	Thu	Katy Klauenberg (Sheffield)	Statistics Seminar
14:00		Statistical Modelling for Dating Ice Cores
		Hicks LT7
	Abstract: In ice cores which are drilled through ice sheets in polar regions valuable information about past environment and climate are preserved. A pivotal part of interpreting the information held within the cores is to build ice core chronologies i.e. to relate time to depth. Existing dating methods can be categorised as follows: (1) layer counting using the seasonality in signals, (2) glaciological modelling describing processes such as snow accumulation and plastic deformation of ice, (3) comparison with other dated records, or (4) any combination of these. Conventionally, implementation of these approaches does not use statistical methods. We combine glaciological models with a Bayesian framework. For this purpose, the sources of uncertainty in the glaciological model and the knowledge about these are formalised. Additionally, we include information from layer counting and other dated records (i.e. traces from volcanic eruptions) to constrain the resulting dating. During the talk the setup of this statistical model will be described, the effect of uncertainty in the glaciological model will be demonstrated and the interplay with information from other dating methods will be illustrated. This combined statistical dating approach is applied to date Antarctic ice cores. For the first time the effects of uncertainty implied by the dating method are investigated for ice core chronologies, which provides valueable insights for the applied community.
Jun 4	Thu	Nick Kuhn (Virginia)	Topology Seminar
15:05		Detection numbers in group cohomology
		Hicks Seminar Room J11
	Abstract: Let $H^\ast(BG)$ denote the mod p cohomology of the classifying space of a compact Lie group G (e.g. a finite group). Since Quillen's work around 1970, $H^\ast(BG)$ has been fruitfully studied via restriction to its various elementary abelian p--subgroups $V$. In the early 1990's, Henn, Lannes, and Schwartz generalized Quillen's work. In particular, they define $d_0(G)$ as the smallest d such that the evident restriction map $$H^\ast(BG)\to\Pi_{V\le G} H^\ast(BG)\otimes H^{\ast\le d}(BC_G(V))$$ is monic. I will describe a way to calculate an upper bound for $d_0(G)$ using information that is often easy to compute before one knows much about $H^\ast(BG)$. The bound seems very good in general, and is exact for many groups, e.g. finite groups for which every element of order p is central in a p--Sylow subgroup. The story of why our bound works goes as follows. Firstly, our extensive knowl- edge of $H^\ast(BG)$ as an unstable module over the mod p Steenrod algebra leads us to the study of the primitives in the central essential cohomology of $BG$, viewed as a comodule over the cohomology of its maximal central elementary abelian p-- subgroup. Then we use Hopf algebra tricks, as in work of Duflot, Broto, Henn, and D. Green, to control these primitives. This allows us to connect our problem to properties of the local cohomology of $H^\ast(BG)$ as studied by Benson, Carlson, and Greenlees. Finally, a new theorem of Symonds, establishing Benson's Regularity Conjecture, tells us what we need. Examples will be given. For example, when $p = 2$, $d_0(SU(3, 4)) = 14$, and this is biggest among all finite groups having a 2--Sylow subgroup of order 64 or less.
Jun 10	Wed	Christoffer Karoff (Birmingham)	Applied Mathematics Colloquium
14:00		Flares, oscillations and cycles in the Sun and other stars
		Hicks Lecture Theatre A
	Abstract: We recently presented evidence of a strong correlation between the energy in the high-frequency part of the acoustic spectrum of the Sun and the solar X-ray flux (Karoff and Kjeldsen, 2008). The discovery indicates that flares drive global oscillations in the Sun. If this indication turns out to be true we might be able to use the relation between flares and the energy in the high-frequency part of the acoustic spectrum to detect e.g. flares on the far side of the Sun and flares on other solar-like stars. The last possibility will be tested with observations from the nearly launched Kepler satellite as part of a larger project of sounding stellar cycles with asteroseismology. Asteroseismology can sound stellar cycles by studying periodic changes, in the amplitudes and frequencies of the oscillation modes in the stars, that follow the stellar cycles. By comparing these measurements with conventional ground-based chromospheric activity measurements we might be able to increase our understanding of the relation between the chromospheric changes and the changes in the oscillation modes. Also, asteroseismic measurements of e.g. the depth of the convection zone and internal differential rotation could enable us to answer the question: Are the stellar cycles driven at the top or the base of the convection zone?
Jul 7	Tue	Shabieh Farwa (Sheffield)	Pure Maths Postgraduate Seminar
14:00		"The two squares theorem"
		Hicks Seminar Room J11
Jul 7	Tue	Leigh Shepperson (Sheffield)	Pure Maths Postgraduate Seminar
15:00		TBA
		Hicks Seminar Room J11
	Abstract: TBA
Jul 15	Wed	Rajan Mehta (University of Washington, St Louis)
16:10		From double groupoids to 2-groupoids
		Hicks Seminar Room J11
	Abstract: A double (Lie) groupoid is a groupoid in the category of (Lie) groupoids. A standard example is the fundamental double Lie groupoid of a Lie groupoid. I will describe a functor from the category of double Lie groupoids to the category of simplicial manifolds. In general, the simplicial manifolds that arise in this process are local Lie 2-groupoids. There is a process for turning a local Lie 2-groupoid into a groupoid, but smoothness is lost in general. However, in the above standard example, the resulting groupoid is smooth and agrees with a construction of Moerdijk and Mrcun.
Sep 1	Tue	Tom Leinster (Glasgow (visiting Sheffield))
15:00		Quantifying Biodiversity I
		Hicks Seminar Room J11
	Abstract: There is a lively and chaotic literature on how to quantify the diversity of a biological community. The challenge is to take a big mass of data about a community and distill it down to a single number, measuring its `diversity'. People have been arguing about how to do it for decades.\$$5em] In my talks I hope to shed some light on the matter. This involves various new pieces of mathematics: some newish category theory, a new invariant of metric spaces, and some new aspects of the notion of entropy. The emphasis these get in the talks will depend entirely on the audience; rest assured that I'll explain whatever's necessary. For better or worse, I'll entirely ignore the statistical side. [Some people might feel that one talk is all the appreciation they can handle. For their sake, I'll try to put the material of broadest appeal into the first one.]
Sep 2	Wed	Tom Leinster (Glasgow (visiting Sheffield))
15:00		Quantifying Biodiversity II
		Hicks Seminar Room J11
	Abstract: There is a lively and chaotic literature on how to quantify the diversity of a biological community. The challenge is to take a big mass of data about a community and distill it down to a single number, measuring its `diversity'. People have been arguing about how to do it for decades. In my talks I hope to shed some light on the matter. This involves various new pieces of mathematics: some newish category theory, a new invariant of metric spaces, and some new aspects of the notion of entropy. The emphasis these get in the talks will depend entirely on the audience; rest assured that I'll explain whatever's necessary. For better or worse, I'll entirely ignore the statistical side. [Some people might feel that one talk is all the appreciation they can handle. For their sake, I'll try to put the material of broadest appeal into the first one.]
Sep 3	Thu	Tom Leinster (Glasgow (visiting Sheffield))
15:00		Quantifying Biodiversity III
		Hicks Seminar Room J11
	Abstract: There is a lively and chaotic literature on how to quantify the diversity of a biological community. The challenge is to take a big mass of data about a community and distill it down to a single number, measuring its `diversity'. People have been arguing about how to do it for decades. In my talks I hope to shed some light on the matter. This involves various new pieces of mathematics: some newish category theory, a new invariant of metric spaces, and some new aspects of the notion of entropy. The emphasis these get in the talks will depend entirely on the audience; rest assured that I'll explain whatever's necessary. For better or worse, I'll entirely ignore the statistical side. [Some people might feel that one talk is all the appreciation they can handle. For their sake, I'll try to put the material of broadest appeal into the first one.]
Sep 17	Thu	David Southwood (European Space Agency)	Applied Mathematics Colloquium
14:00		Magnetism and Rotation at Saturn: the puzzles produced by the Cassini space mission
		LT7
	Abstract: The planet Saturn has for long had properties that defied expectations concerning planetary magnetism. A fast rotating gas giant, it was hardly surprising it had a dipolar magnetic field but it was surprising when early spacecraft flybys revealed that the dipole seemed almost perfectly aligned with the rotation axis. More surprises were to come. In the early nineties, measurements of the radio signals with the sensitive Ulysses spacecraft antenna revealed the Saturn kilometric radio signal was pulsing with a rate that varied slowly with time (~few times 0.1% change per year), drawing into doubt the long-assumed link between radio pulsing and deep planetary rotation. Then, just before the arrival of Cassini re-analysis of the Voyager spacecraft magnetic data by a student at Imperial College showed there was a signature present in the Voyager spacecraft magnetic data at the planetary rotation period but one unambiguously associated with a source external to the planet! Each of the magnetic and radio oddities of Saturn was borne out once Cassini was in orbit but that was not the end of the surprises. Early in 2009, members of the Cassini radio team determined that the period of the radio pulsing which originated from the northern hemisphere differed from the period of the signal from the south. Subsequently, it has been firmly determined that the magnetic field measured above the northern Saturnian polar cap appears to be rotating at a rate 0.3% slower than the south. A review will be given of the present knowledge of the Saturn magnetic field and some speculations given on the implications of the results.
Sep 25	Fri	Gary Verth (K.U. Leuven (Belgium))
13:05		Plasma diagnostics with torsional Alfven waves
		Lecture Theatre 9
Sep 29	Tue	Paul Mitchener (Sheffield)	Topology Seminar
14:00		General Descent
		Hicks Seminar Room J11
	Abstract: The term "descent" in coarse geometry usually means the fact that the coarse Baum-Connes conjecture (plus certain mild extra conditions) implies injectivity of the assembly map in the ordinary Baum-Connes conjecture. All of this can be generalised to a general notion of assembly maps; there is a corresponding "coarse isomorphism conjecture", which implies that the assembly map is injective. Thus, coarse techniques can be used to prove injectivity of a variety of assembly maps.
Sep 30	Wed	Dave Roscoe (Sheffield)	Applied Mathematics Colloquium
14:00		The conflict between realism and the scalar potential in electrodynamics
		Hicks Lecture Theatre A
Oct 1	Thu	Jeremy Oakley (Sheffield)	Statistics Seminar
14:00		Eliciting Probability Distributions
		Hicks LT6
	Abstract: Elicitation is the process of extracting expert knowledge about some unknown quantity of interest and representing that knowledge with a suitable probability distribution. It is an important component of Bayesian inference, risk analysis, and decision-making in the presence of uncertainty. In this talk I will give an introduction to the field and discuss some current research interests, including nonparametric elicitation, the trial roulette method, and SHELF: the Sheffield Elicitation Framework.
Oct 2	Fri	Inigo Arregui (Departament de Fisica, Universitat de les Illes Balears, Palma de Mallorca, Spain)
13:05		Magnetohydrodynamic seismology of coronal loops and prominence fine structures
		Lecture Theatre 9
	Abstract: In this talk I will present some recent results from the application of MHD wave seismology inversion techniques to transverse oscillations observed in coronal loops and prominence fine structures. In coronal loops, damping by resonant absorption is considered. First, we will briefly demonstrate how the use of scaling laws is of no use at all for the discrimination between different damping mechanisms. In a seismological context, the combination of observed periods and damping rates with analytical and numerical results for resonantly damped kink waves in non-uniform flux tubes allows us to obtain a restricted 1D solution space that links the internal Alfven speed, the density contrast, and the transverse density structuring, in a fully consistent manner. The resulting Alfven speed is well constrained to a narrow range of values. Similar inversion techniques have recently been applied to oscillating quiescent and active region prominence threads. In quiescent filament threads resonant damping becomes independent of density contrast, for the typical large filament-to-coronal values of this parameter. This allows us to obtain precise estimates for the internal Alfven speed and the transverse inhomogeneity length-scale. Recent results from two-dimensional non-uniform thread models are also presented. They display significantly different results when compared to 1D model results. In an active region prominence, a seismological analysis of oscillating threads observed with Hinode SOT shows that, even if the available data are insufficient to derive well constrained values of the physical variables, a lower limit for the Alfven speed in each of the threads can be established.
Oct 6	Tue	John Greenlees (Sheffield)	Topology Seminar
13:30		Rational torus-equivariant cohomology theories.
		Hicks Seminar Room J11
	Abstract: The talk will describe a model for these cohomology theories for a torus G, and potential applications. The algebraic model A(G) is an abelian category of injective dimension equal to the rank of G, based on the use of idempotents in Burnside rings and the Borel-Hsiang-Quillen localization theorem for passage to torus- fixed points. Its formal structure is rather like that of structured sheaves over an r dimensional variety (this, naturally, guides some of the applications, such as cohomology theories associated to higher dimensional abelian varieties). The talk may describe the strategy of proof in joint work with Shipley, based on rigidity and building up data through an isotropic Hasse-square.
Oct 7	Wed	Rafael Bocklandt (Newcastle)	Pure Maths Colloquium
15:00		Calabi Yau Algebras and quiver polyhedra
		Lecture Theatre 10
	Abstract: Dimer models have been used in string theory to construct path algebras with relations that are 3-dimensional Calabi Yau Algebras. These constructions result in algebras that share some specific properties: they are finitely generated modules over their centers and their representation spaces are toric varieties. In order to describe these algebras we introduce the notion of a toric order and show that all toric orders 3-dimensional Calabi Yau algebras can be constructed from dimer models on a torus. Toric orders are examples of a much broader class of algebras: positively graded category algebras with cancellation. For this broader class the CY-3 condition also implies the existence of a weighted quiver polyhedron, which is an extension of dimer models obtained by replacing the torus with any two-dimensional compact orientable orbifold. We discuss which of these quiver polyhedra give rise to Calabi Yau algebras.
Oct 7	Wed	Prof Michael Berry FRS (Bristol)
16:00		Two by two
		Hicks Seminar Room J11
	Abstract: A tutorial account of families of 2x2 matrices labelled by several parameters will concentrate on the neighbourhood of degeneracies. The emphasis will be on the differences between hermitian and nonhermitian matrices, considered geometric. Physical phenomena in optics and atomic physics where such degeneracies play a crucial role will be described. This introductory talk by Prof Berry will serves to launch the MAGIC courses for 2009/10.
Oct 8	Thu	Nathan Green (Dstl Porton Down)	Statistics Seminar
14:00		Determining the Source of a Hazardous Atmospheric Release
		Hicks LT6
	Abstract: A methodology is explored for making inference about parameters of a hazardous atmospheric release from sensor readings. The key difficulty in performing this inference is that the results must be obtained in a very short timescale (5 min) to make use of the inference for protection. The methodology that has been developed uses some of the components in a sequential Monte Carlo algorithm. However, this inference problem is different from many other sequential Monte Carlo problems, in that there are no state evolution equations, the forward model is highly non-linear and the likelihoods are non-Gaussian. Results for inferences made of atmospheric releases (both real and simulated) of material will be presented, demonstrating that the sampling scheme performs adequately despite constraints of a short time span for calculations. Potential future developments and issues will also be discussed to show areas of future research interest.
Oct 9	Fri	Istvan Ballai (Sheffield)
13:05		Introduction into the theory of nonlinear waves
		Lecture Theatre 9
Oct 12	Mon	Paul Mitchener (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:00		Introduction to $C^\ast$-algebras
		Hicks Seminar Room J11
	Abstract: This talk is intended to be extremely elementary, introducing $C^\ast$-algebras and looking at some fundamental properties. We assume no know knowledge of analysis beyond the definitions of a normed vector space and completeness.
Oct 13	Tue	Shoham Shamir (Sheffield)	Topology Seminar
13:30		Complete intersections in rational homotopy theory
		Hicks Seminar Room J11
	Abstract: In commutative algebra, complete intersection rings are the next best thing after regular rings. The quotient of a graded polynomial ring by a regular ideal is a prime example of a complete intersection ring. Gulliksen showed that a local Noetherian ring is complete intersection if and only if its homology has polynomial growth. Benson and Greenlees recently characterized local complete intersection rings by the existence of a certain structure on their derived category. These definitions have obvious adaptations for rational spaces. For simply connected rational spaces these adapted definitions are shown to be equivalent, yielding a structural characterization of complete intersection rational spaces using spherical fibrations. This is joint work with John Greenlees and Kathryn Hess.
Oct 14	Wed	Edmund Chadwick (Salford)	Applied Mathematics Colloquium
14:00		Oscillatory oseenlets
		LT A
	Abstract: Consider uniform flow past an oscillating body. Assume that the resulting far-field flow consists of both steady and time periodic components. The time periodic components can be decomposed into a Fourier expansion series of time harmonic components. The form of the steady component in terms of the steady oseenlet is well-known. However, the time-harmonic components in terms of oscillatory oseenlet does not yet appear to be in the literature.
Oct 14	Wed	Neil Dummigan (Sheffield)	Pure Maths Colloquium
16:00		Rational points of order 7
		Hicks Seminar Room J11
	Abstract: This is not really what I did on my study leave, but during my study leave I had this 3 page paper published. While the result is truly insignificant, it gives me a good excuse to talk about elliptic curves and modular curves in colloquium style, and saying something about the proof will provide a focus for the discussion.
Oct 15	Thu	M. Eileen Magnello (University College London)	RSS Seminar
16:30		The Development of the Provincial Statistical Societies and the Statistical Society of London
		Hicks Room K14
	Abstract: The statistical societies that emerged in the 1830s were largely a response to the massive social and technological changes that occurred in early- and mid-Victorian Britain. Transportation and communication underpinned these changes: the railways made it possible to travel to the many academic societies across Britain, whilst the penny post, the telegraph and the steam press created a communications revolution, which led to the proliferation of statistical publications. Concomitant with these developments were methodological changes in statistics and the emergence of a new statistical language for the Victorians who were passionate about documenting these social changes in Britain. This paper will examine how the modernisation of Britain led to the growth of a statistical movement in Britain, which, in turn, helped to establish statistical societies and publications in the provinces and London.
Oct 16	Fri	Youra Taroyan (Sheffield)
13:05
		Lecture Theatre 9
Oct 19	Mon	Kirill Mackenzie (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:00		Poisson Manifolds (part 1)
		Hicks Seminar Room J11
	Abstract: Here is a sketch of what I propose for the lectures on Poisson manifolds. + Linear Poisson structures from Lie algebras + Tangent bundles are like Lie algebras ... + Symplectic structures and the Poisson bracket + Reduction of a Hamiltonian action leads to a Poisson manifold + Formalisms for working with Poisson structures: bracket of functions, bracket of 1-forms, Schouten bracket. + The symplectic leaves of a Poisson manifold + The `pre-Kontsevich approach' to quantization: Symplectic realizations. Sketch of integrability. I'm assuming familiarity with manifolds and tangent and cotangent bundles, and differential forms. For Lie algebras and Lie groups nothing at a deep level is required.
Oct 20	Tue	Carl McTague (Cambridge)	Topology Seminar
13:30		The Cayley Plane and the Witten Genus
		Hicks Seminar Room J11
	Abstract: Elliptic cohomology is at the heart of many recent developments in algebraic topology. (Hill-Hopkins-Ravenel for example recently used it to solve the Kervaire invariant problem.) What led to its discovery was Ochanine's observation in the 1980s that there are many more multiplicative genera for spin fiber bundles than for oriented fiber bundles, one for each elliptic curve with a marked point of order 2. Given that multiplicative genera for spin fiber bundles have led to such unexpectedly rich developments, it seems reasonable to investigate multiplicative genera for other types of fiber bundles, in particular O<8> fiber bundles. I will discuss a recently published result of Dessai and a result of my own which in investigating this question place the Witten genus into a geometric framework.
Oct 21	Wed	Tom Sutherland (Sheffield)	Pure Maths Postgraduate Seminar
14:00		An introduction to sheaves.
		Hicks Seminar Room J11
	Abstract: Sheaves have been fundamental objects in algebraic geometry ever since Serre and Grothendieck developed the theory of sheaf cohomology. However their definition goes back to Leray and makes sense not just for algebraic varieties but for any topological space. Roughly a sheaf is an assignment of some local data to a topological space together with a way of gluing such data together. In this sense a sheaf generalises the notion of a vector bundle, which can be defined by its local sections which are then glued together by the transition maps. This passage from local to global is at the heart of theory. This talk will assume no prior knowledge of sheaves nor any acquaintance with algebraic geometry. A familiarity with categorical language would be helpful but not necessary.
Oct 21	Wed	Chutiphon Pukdeboon	Applied Mathematics Colloquium
14:00		Optimal Sliding Mode Controllers for Attitude Tracking of Spacecraft
		LT A
	Abstract: This research studies two optimal sliding mode control laws using integral sliding mode control (ISM) for some spacecraft attitude tracking problems. Integral sliding mode control combining the first order sliding mode and optimal control is applied to quaternion-based spacecraft attitude tracking manoeuvres with external disturbances and an uncertainty inertia matrix. For the optimal control part the state dependent Riccati equation (SDRE) and Control Lyapunov function (CLF) approaches are used to solve the infinite-time nonlinear optimal problem. The second method of Lyapunov is used to show that tracking is achieved globally. An example of multiaxial attitude tracking manoeuvres is presented and simulation results are included to verify the usefulness of these controllers.
Oct 21	Wed	Lawrence Chan (Sheffield)	Applied Mathematics Colloquium
14:30		The relationship between concentration and its dissipation rate in turbulent dispersion
		LTA
	Abstract: To model the probability distribution of concentration in turbulent dispersion it is necessary to make closure assumptions. One aspect of interest in looking for reasonable closure assumptions is the relationship between concentration and its dissipation rate. Here it is assumed that Taylor's frozen turbulence hypothesis can be used to approximate the dissipation rate of concentration using the time derivative of concentration at a fixed point in space. I then use measurements of concentration from line source experiments in wind tunnel grid-turbulence to examine the behaviour of the joint and marginal distributions of concentration and its dissipation rate. A simple stochastic process model is constructed for the concentration time series, from which these distributions are also derived , and then compared with those from the experiments.
Oct 21	Wed	Nick Gurski (Sheffield)	Pure Maths Colloquium
16:00		The Eckmann-Hilton argument
		Hicks Seminar Room J11
	Abstract: Everyone has probably seen a proof that the higher homotopy groups of a space are abelian that consists of a series of pictures in which squares slide around one another. This is one example of the Eckmann-Hilton argument, which is a very simple piece of algebra that allows one to conclude that a group (or more generally, monoid) is abelian. I will explain the algebra involved, give some nice examples from topology, and then show that the situation becomes much more complicated when dealing with examples from category theory.
Oct 22	Thu	Tim Heaton (Sheffield)	Statistics Seminar
14:00		Reconstructing a Wiener process from observations at imprecise times: Bayesian radiocarbon calibration
		Hicks LT6
	Abstract: For accurate radiocarbon dating, it is necessary to identify fluctuations in the level of radioactive carbon 14C present in the atmosphere through time. The processes underlying these variations are not understood and so a data-based calibration curve is required. In this talk we present a novel MCMC approach to the production of the inter- nationally agreed curve and the individual challenges involved. Our methodology models the calibration data as noisy observations of a Wiener process and updates sample paths through use of a Metropolis-within-Gibbs algorithm. Implementation of this algorithm is complicated by certain specific features of the data used, namely that many data points: • relate to the mean of the Wiener process over a period of time rather than at a specific point, • have calendar dates found using methods (e.g. Uranium-Thorium) which are themselves uncertain, • have ordering constraints and correlations in their calendar date uncertainty - for example data are sampled along the same core or have floating calendar dates matched to another sample for which the calendar age is more accurately known. We give an overview of these issues and discuss their implications for the resulting sampler.
Oct 23	Fri	Daniel Reese (Sheffield)
13:05
		Lecture Theatre 9
Oct 26	Mon	Kirill Mackenzie (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:00		Poisson Manifolds (part 2)
		Hicks Seminar Room J11
Oct 27	Tue	Arjun Malhotra (Sheffield)	Topology Seminar
13:30		The Gromov-Lawson-Rosenberg conjecture for some finite groups
		Hicks Seminar Room J11
	Abstract: The Gromov-Lawson-Rosenberg conjecture for a group G says that a compact spin manifold with fundamental group G admits a metric of positive scalar curvature if and only if a certain topological obstruction vanishes. The plan is to discuss the conjecture, and sketch how to prove it for some finite groups.
Oct 28	Wed	Laura Stanley (Sheffield)	Pure Maths Postgraduate Seminar
14:00
		Hicks Seminar Room J11
Oct 28	Wed	Laura Stanley (Sheffield)	Pure Maths Postgraduate Seminar
14:00		An introduction to the Steenrod algebra.
		Hicks Seminar Room J11
	Abstract: This talk will be a general introduction to the Steenrod Algebra, which is an algebra of cohomology operations, one for each prime. Cohomology operations are a gadget which allows us to glean further information out of what the cohomology ring can already give us, leading to a greater understanding of spaces and the maps between them. The Steenrod squares are a prominent example of these, they form a Hopf algebra which will also be explained. I will then give an example of what the Steenrod Algebra can achieve by explaining the Hopf invariant 1 problem. This leads to interesting results such as $R^n$ being a division algebra only when $n=1,2,4$ or 8 and $S^n$ being an H-space only for $n=0,1,3$ or 7.
Oct 28	Wed	Elizabeth Winstanley (Sheffield)	Applied Mathematics Colloquium
14:00		Black holes at the LHC
		LT A
	Abstract: Brane world models in string theory suggest that our universe is a slice, or 'brane', of a higher-dimensional space-time. In this talk we will discuss why one consequence of these models is that copious numbers of mini black holes may be formed by collisions at the Large Hadron Collider (LHC) at CERN. We will describe how these mini black holes are created, and what happens to them once they have been produced. In particular, we discuss why these black holes will not swallow up the entire Earth.
Oct 28	Wed	Lionel Mason (Oxford)	Pure Maths Colloquium
16:00		Integral formulae for the wave equation, Einstein-Weyl spaces, scattering maps and holomorphic discs.
		Hicks Seminar Room J11
	Abstract: My talk will be based on joint work with Claude LeBrun, mostly in arxiv:0806.3761. The dicussion is motivated from a class of integral formulae for solutions to the wave equation in 2+1 dimensions. The question of what spaces admit such integral formulae is addressed and it turns out that the wave equations are most naturally defined on Einstein-Weyl spaces. When subject to a suitable global assumption, these Einstein-Weyl spaces are classified by a scattering map, a smooth diffeomorphism from the two-sphere at past infinity to one at future infinity along null geodesics. The Einstein-Weyl space is then reconstructed from a family holomorphic discs in an auxilliary complex surface with boundary defined by the scattering map. If I have time I will discuss more recent applications to the classification of Zoll surfaces, manifolds all of whose geodesics are closed circles.
Oct 29	Thu	Jianxin Pan (Manchester)	Statistics Seminar
14:00		Modelling of Mean-Covariance Structures for Longitudinal Data
		Hicks LT6
	Abstract: It is well known that when analysing longitudinal data, misspecification of covariance structures may lead to very inefficient or even biased estimators of parameters in the mean structure. Covariance structures, like the mean, can be modelled using linear or nonlinear regression models techniques. Various estimation methods have been recently developed for modelling of mean and covariance structures, simultaneously. In this talk, I will introduce such methods on modelling of mean-covariance structures for longitudinal data, including linear and non-linear regression models, variable selection, semiparametric models, etc. Real examples and simulation studies will be presented for illustration.
Oct 30	Fri	Jaume Terradas (Centre Plasma Astrophysics and Leuven Mathematical Modeling and Computational Science Center, Katholieke Universiteit Leuven)
13:05		Nonlinear instability of kink oscillations due to shear motions
		Lecture Theatre 9
Nov 2	Mon	Paul Mitchener (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:10		C*-algebras, states, and first steps towards C*-algebraic quantisation
		Hicks Seminar Room J11
Nov 4	Wed	Roald Koudenburg (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Introduction to Hyperbolic surfaces and Teichmüller space.
		Hicks Seminar Room J11
	Abstract: Riemann was interested in describing all isomorphism classes of complex structures on a given surface, the so called "Riemann Moduli Problem". He solved the problem for simply connected surfaces: in that case the only possibilities are the disk, the plane and the Riemann sphere. While studying the moduli problem for more complicated Riemann surfaces (where the complex structure is hyperbolic), Teichmüller introduced a refinement of the moduli problem. This led to the Teichmüller space of a surface. In the talk I will tell you what hyperbolic structures on (certain) surfaces are. The moduli space $M(X)$ and the Teichmüller space $T(X)$ of a hyperbolic surface $X$ will be introduced and we'll look at how they are related. The simplest example of a hyperbolic surface is a pair pants $P$ and we'll examine $T(P)$ and $M(P)$. This will give a rough idea of what $T(X)$ will look like in general since every hyperbolic surface can be decomposed into a number of pairs of pants.
Nov 4	Wed	Minhyong Kim (UCL)	Pure Maths Colloquium
16:00		Galois theory and Diophantine geometry.
		Hicks Seminar Room J11
	Abstract: In his manuscripts from the 1980's Grothendieck proposed ideas that have been interpreted variously as embedding the theory of schemes into either -group theory and higher-dimensional generalizations; -or homotopy theory. It was suggested, moreover, that such a framework would have profound implications for the study of Diophantine problems. In this talk, we will discuss mostly the little bit of progress made on this last point using some mildly non-abelian motives associated to hyperbolic curves.
Nov 5	Thu	Stanislav Volkov (Bristol)	Statistics Seminar
14:00		The simple harmonic urn
		Hicks LT6
	Abstract: The simple harmonic urn is a discrete-time stochastic process on Z2 approximating the phase portrait of the harmonic oscillator using very basic transitional probabilities on the lattice, incidentally related to the Eulerian numbers. This urn which we consider can be viewed as a two-colour generalized Polya urn with negative-positive reinforcements, and in a sense it can be viewed as a "marriage" between the Friedman urn and the OK Corral model, where we restart the process each time it hits the horizontal axes by switching the colours of the balls. We show the transience of the process using various couplings with birth and death processes and renewal processes. It turns out that the simple harmonic urn is just barely transient, as a minor modification of the model makes it recurrent. We also show links between this model and oriented percolation, as well as some other interesting processes. This is joint work with Edward Crane, Nicholas Georgiou, Rob Waters and Andrew Wade.
Nov 6	Fri	Viktor Fedun (Sheffield)
13:05
		Lecture Theatre 9
Nov 9	Mon	Paul Mitchener (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:10		C*-algebraic deformation quantisation.
		Hicks Seminar Room J11
Nov 10	Tue	Ieke Moerdijk (Sheffield)	Topology Seminar
13:30		Deformation theory of Lie algebroids, I
		Hicks Seminar Room J11
	Abstract: The notion of Lie algebroid encompasses Lie algebras, foliations, infinitesimal actions, Poisson manifolds and other geometric structures. I will describe a differential graded Lie algebra which controls deformations of Lie algebroids. The corresponding deformation cohomology agree with the classical (Nijenhuis-Richardson) theory for Lie algebras, and captures some known results about deformations of foliations (Heitsch) and Poisson manifolds. The difficulty to overcome lies in the fact that there is no adjoint representation for Lie algebroids; in fact, one way to interpret our results is as the beginnings of a theory of representations-up-to-homotopy for Lie algebroids. (joint work with Crainic, reference: J. Eur. Math. Soc. 2008)
Nov 11	Wed	Leigh Shepperson (Sheffield)	Pure Maths Postgraduate Seminar
14:00		An introduction to Gröbner bases.
		Hicks Seminar Room J11
	Abstract: It is straightforward to divide polynomials of one variable. This means that computing with ideals of single variable polynomials is trivial, as we can use the division algorithm to uniquely represent its elements. However, it is harder in the multivariate case as we cannot `divide' polynomials in the usual sense; moreover when we do, the answer may not be unique. The theory of Gröbner Bases gives us the best setting to perform calculations in the multivariate case. Given a particular ideal of multivariate polynomials, the theory allows us to construct generating sets with extremely nice properties. This talk will introduce the notion of a Gröbner basis and describe Buchberger's algorithm that is used to construct them. We will also give an example to illustrate the method.
Nov 11	Wed	Judith Wolf (POL)	Applied Mathematics Colloquium
14:00		Wave-Current Interaction in Liverpool Bay
		tbd
	Abstract: Waves in shallow water are strongly controlled by the water level as well as the wind forcing and can be refracted by strong current shear. Theory suggests that the mechanisms by which waves and the wind-driven mean flow are generated are closely interconnected in the surface layer through the wind-stress. Also there is evidence that the bottom friction experienced by waves and near-bed currents are mutually enhanced. New theoretical work has been implemented in the POLCOMS-WAM coupled hydrodynamic and wave model system to include the effect of 3D currents, allowing the vertical current shear to affect wave propagation and accounting for 3D radiation stress and Stokes' drift. We investigate the occurrence of typical and extreme wave conditions in Liverpool Bay and the adjacent estuaries and assess which areas may be prone to flooding and erosion due to waves in combination with high water levels. This is a macro-tidal environment prone to storm surges and moderate storm waves with occasional flooding in low-lying areas. Data from the POL Coastal Observatory, including the HF radar system which simultaneously measures waves and currents, have been employed to validate wave, tide and surge models for this area. We have also used the SWAN model in one-way coupled mode in comparison with the POLCOMS-WAM model to investigate the magnitude of interactions between waves, tides and surges. Here we review the physical mechanisms, their effects, and the implications for our understanding of coastal processes, and discuss where further development is still needed in shallow water wave models.
Nov 11	Wed	Paul Martin (Leeds)	Pure Maths Colloquium
16:00		The decomposition matrix of the Brauer algebra over the complex field
		Hicks Seminar Room J11
	Abstract: We describe the solution to this long-open problem in representation theory.
Nov 12	Thu	Vassili Kolokoltsov (Warwick)	Statistics Seminar
14:00		SDEs driven by nonlinear Levy noise with application to the construction of Markov processes with a given generator
		Hicks LT6
Nov 12	Thu	Ieke Moerdijk (Sheffield)
16:10		Deformation theory of Lie algebroids, II
		Hicks Seminar Room J11
Nov 16	Mon	David Jordan (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:10		Poisson Algebras
		Hicks Seminar Room J11
Nov 17	Tue	Andrew Baker (Glasgow)	Topology Seminar
13:30		$E_\infty$ ring spectra related to $BP$
		Hicks Seminar Room J11
	Abstract: I will describe the construction of a commutative $S$-algebra which is tantalisingly close to the Brown-Peterson spectrum at the prime $2$. The ingredients are power operations and calculations using the Adams spectral sequence.
Nov 17	Tue	Eugenia Cheng (Sheffield)
17:00		2-vector spaces: an introduction to higher-dimensional category theory
		tbd
	Abstract: What is a 2-vector space, and how is it different from a 2-dimensional vector space? Why would anyone want to come up with such a notion? And once we have come up with such a notion, how do we know it deserves to be called a``2-vector space"? In this talk we will show how to answer all these questions using category theory. This example highlights one of the ways that category theory can help in mathematics: it helps us give good generalisations of structures that appear in various branches of mathematics including homotopy theory, stacks, topological quantum field theory, type theory, representation theory and concurrency theory. This talk will be introductory; in particular it should not be necessary to be familiar with any category theory, and I will encourage Level 4 undergraduate students to attend. It will help to know what an ordinary vector space is.
Nov 18	Wed	Arjun Malhotra (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Stiefel-Whitney classes
		Hicks Seminar Room J11
	Abstract: For any vector bundle, we can define certain 'characteristic' classes, in the cohomology of the base space. The plan is to describe this general concept briefly, and illustrate how useful they can be by considering Stiefel-Whitney classes in more detail. We give an axiomatic characterization, and then proceed to calculate the Stiefel-Whitney classes of real projective space. We conclude by giving some applications, such as which projective spaces can be parallelizable, and when a manifold is a boundary.
Nov 18	Wed	Colin Steele (Manchester)	Applied Mathematics Colloquium
14:00		Tadpoles, Horseshoes and the Trojan Wars: the restricted 3-body problem in the Solar System
		LT A
	Abstract: The two-body problem in Celestial Mechanics has been solved to give orbits in the form of conic sections (ellipses etc.). The introduction of a third body, however, disallows any algebraic solutions and numerical work is required in order to follow the motion of the objects. The restricted three body problem assumes that one of the three objects is of negligible mass i.e. the third body responds to the gravitational attraction of the first two bodies but does not itself influence the motion of these first two bodies. In the solar system, with there being a wide range of masses of Sun, planets, satellites, minor planets, comets etc, this restricted three-body problem is certainly relevant. Under the restricted three-body problem, the third (light) body can be followed through a wide variety of situations. Without retracting from dynamical solutions, this talk will concentrate on cases close to equilibria and/or involving cycles. Such cases will be modelled including an analysis of the linear stability and a numerical simulation. Particular real cases in the solar system involve minor planets with orbits affected by Jupiter and the motions of some of the inner satellites of Saturn.
Nov 18	Wed	Brendan Owens (Glasgow)	Pure Maths Colloquium
16:00		Knots in 4-dimensional topology.
		Hicks Seminar Room J11
	Abstract: Classical knot theory is the study of embedded circles in 3-dimensional space. The purpose of this talk is to illustrate the rich give-and-take between knot theory and 4-dimensional topology. I will discuss the use of knots in descriptions of 3- and 4-dimensional manifolds. I will also describe how a 4-dimensional point of view of knots gives rise to a group called the knot concordance group, and discuss some recent advances in the study of this group.
Nov 19	Thu	Mark Dixon (ATASS Ltd Exeter)	RSS Seminar
16:30		Statistical Modelling of Sports
		HIcks LT4
	Abstract: Sports events provide a rich source of statistical modelling problems that can be used to trade on betting exchanges such as Betfair. These exchanges work in a very similar manner to standard financial markets, and traders require sophisticated models based upon a detailed knowledge of the sport in question. The aim of these models is to provide an accurate assessment of the probability of different match outcomes that can be compared with the "market view" to determine whether or not to trade and, if so, at what price. In this talk we provide a general overview of the sports betting markets and discuss some of the statistical challenges they provide.
Nov 20	Fri	Christopher Clack (Sheffield)
13:05
		Lecture Theatre 9
Nov 23	Mon	Dave Applebaum (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:10		On mysteries and functors (part 1)
		Hicks Seminar Room J11
	Abstract: Don't expect much category theory (even lower order). The title is based on a quote from Ed Nelson: "First quantisation is a mystery, second quantisation is a functor,"
Nov 24	Tue	James Cranch (Leicester)	Topology Seminar
13:30		Pictures of Distributivity
		Hicks Seminar Room J11
	Abstract: I'll talk a bit about algebraic theories: these are an approach to wrapping the axioms for many algebraic structures into a pleasant categorical package. I'll also say something about the higher-categorical version of algebraic theories which I introduced in my PhD thesis to study questions in topology. Then I'll describe what theories look like whose operations satisfy a distributive law (like the theory of rings, in which multiplication distributes over addition). There will be pictures and hopefully even a physical model of the 3D "distributahedron".
Nov 25	Wed	Alan Zinober (Sheffield)	Applied Mathematics Colloquium
14:00		A New Non-Classical Class of Optimal Variational Problems
		LT A
	Abstract: The Calculus of Variations was developed in the 18th Century and forms a basic foundation of modern optimal (maximising or minimising) variational problems, nowadays often called optimal control. An introduction to the Calculus of Variations with some sample examples will be presented. This will include the Euler-Lagrange and Hamiltonian formulation together with the associated final boundary value conditions. Maple or the numerical shooting method can be used to solve the resulting Two Point Boundary Value Problem (TPBVP), a set of differential equations. A new non-classical class of variational problems has been motivated by recent research on the non-linear revenue problem in the field of economics. This class of problem can be set up as a maximising problem in the Calculus of Variations (CoV) or Optimal Control. However, the state value at the final fixed time, $y(T)$, is a priori\/ unknown and the integrand to be maximised is also a function of the unknown $y(T)$. This is a non-standard CoV problem that has not been studied before. New final value costate boundary conditions will be presented for this CoV problem and some results will be shown.
Nov 25	Wed	Peter Symonds (Manchester)	Pure Maths Colloquium
16:00		Benson's Regularity Conjecture
		Hicks Seminar Room J11
	Abstract: We discuss a proof of Benson's regularity conjecture, that the regularity of the cohomology of a finite group is zero. The regularity is an invariant defined in term of local cohomology and knowing it gives bounds on the degrees of the generators and relations of the ring. The proof is a mixture of algebra and topology.
Nov 25	Wed	Kostas Triantafyllopoulos (Sheffield)	AM/P+S Colloquium
16:00		Bayesian methods for flexible manoeuvring systems in control
		LT A
	Abstract: This talk serves as an Interim Report of the BtG grant on a Flagship project between the Departments of Probability and Statistics, Applied Mathematics and Automatic Control and Systems Engineering. This project investigates the application of Bayesian statistical modelling to a class of problems in control, and in particular to the system modelling and tracking control of a twin rotor multi-input multi-output system (TRMS) in hovering mode. Systematic stochastic modelling of the hovering property of the helicopter/TRMS is vital for a variety of flight missions including load delivery and air-sea rescue. We describe parametric and non-parametric models (forward and inverse), with the aid of which we empirically explore the non-minimum phase phenomenon of the non-linear system. The parametric model is a linear Bayesian time series model which shares some resemblance to the celebrated Kalman filter, and the non-parametric model is a Neural Network (NN) model. We discuss in detail the Bayesian model and provide a comparative analysis with the NN model, in relation to non-minimum phase behaviour. We provide some discussion on future directions of modelling, in particular in the view of (a) establishing non-minimum phase behaviour of the models theoretically and (b) proposing other non-parametric statistical modelling approaches. Finally, we showcase the application of Bayesian statistics in signal processing and in control, something that has not been explored / developed in the literature.
Nov 26	Thu	David Sexton (The Met Office)	Statistics Seminar
14:00		Making probabilistic climate projections for the UK
		Hicks LT6
	Abstract: UKCP09, the latest set of climate projections for the UK were released on June 18th 2009. For the first time the climate projections for the UK are probabilistic, so that it is an appropriate tool for people who are taking a risk-based approach to policy and decision making. I will describe how the probabilities were estimated using a) a combination of a number of climate model ensembles which explore parameter uncertainty in different components of the Earth System b) a set of international climate models other than the Met Office Hadley Centre model and c) a Bayesian framework which combines this climate model output with observations to provide probabilities that are relevant to the real world and therefore relevant to risk-based decision making. I will also outline the main areas of the production system that could benefit from further research into statistical methods and better experimental design.
Nov 27	Fri	Nicolas Leprovost (Sheffield)
13:05
		Lecture Theatre 9
Nov 30	Mon	Dave Applebaum (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:10		Mysteries and functors (part 2)
		Hicks Seminar Room J11
Dec 1	Tue	Nigel Ray (Manchester)	Topology Seminar
13:30		Realisations of the Stanley-Reisner algebra and homotopy uniqueness
		Hicks Seminar Room J11
	Abstract: This talk will be a report on joint work with Dietrich Notbohm (VU Amsterdam). In 1991, for any finite simplicial complex K, Davis and Januszkiewicz defined a family of homotopy equivalent CW-complexes whose integral cohomology rings are isomorphic to the Stanley-Reisner algebra of K. In 2002, Buchstaber and Panov gave an alternative construction, which they showed to be homotopy equivalent to the original examples. It is therefore natural to investigate the extent to which the homotopy type of a space is determined by such a cohomology ring. I shall outline our analysis of this problem i) rationally, and ii) prime by prime, and then attempt to explain how the outcomes may be reassembled using Sullivan's arithmetic square. The entire problem becomes straightforward after a single suspension, and I shall start by discussing this case as a warm-up exercise.
Dec 2	Wed	Chris Brookes (Cambridge)	Pure Maths Colloquium
16:00		Deformation spaces for groups and group algebras
		Hicks Seminar Room J11
	Abstract: My talk will be a survey of assorted work on spaces of group actions on trees and some associated completions and deformations of group algebras. Such a space was defined by Culler and Vogtmann in the study of outer automorphisms of free groups and later linked in with Kontsevich's graphical calculus. At the opposite extreme such spaces have been useful in the representation theory of crossed products by free abelian groups. I am also expecting them to arise in the theory of Iwasawa algebras, (completed) group algebras of p-adic Lie groups.
Dec 3	Thu	David Percy (Salford)	Statistics Seminar
14:00		Predictive elicitation of subjective prior distributions
		Hicks LT6
	Abstract: This seminar tackles the problem of specifying subjective prior distributions for unknown model parameters. We first review strategies for selecting families of priors for common models, including univariate and multivariate probability distributions, generalized linear models and stochastic processes. We then consider methods for evaluating the hyperparameters of these prior distributions. Specifically, we focus on predictive elicitation using quantiles and cumulative probabilities, illustrating the natural beauty and philosophical benefits of this approach. We discuss problems relating to inherent constraints and computational difficulties, and conclude that some compromise is necessary. We illustrate the technique in applications from sport, medicine and industry.
Dec 4	Fri	Rosa Diaz-Sandoval (Sheffield)
13:05
		Lecture Theatre 9
Dec 7	Mon	Elizabeth Winstanley (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:10		Quantisation and Physics
		Hicks Seminar Room J11
Dec 8	Tue	Simon Willerton (Sheffield)	Topology Seminar
13:30		The asymptotic magnitude of surfaces
		Hicks Seminar Room J11
Dec 9	Wed	David Pontin (Dundee)	Applied Mathematics Colloquium
14:00		Magnetic reconnection in three dimensions
		LT A
	Abstract: Magnetic reconnection is of fundamental importance in many plasmas, for example the Solar corona. It plays a role in heating the corona and is thought to be responsible for many dynamic phenomena observed there. The magnetic field in the corona has a highly complex structure that is clearly three-dimensional. Furthermore, recent advances in theory and computational experiments have shown that the nature of reconnection in 3D is fundamentally different from 2D models. Here we discuss the underlying theory of three-dimensional magnetic reconnection. We also review a selection of new 3D reconnection models that illustrate the current state of the art, as well as highlighting the complexity of the process in complicated 3D magnetic fields.
Dec 9	Wed	John Greenlees (Sheffield)	Pure Maths Colloquium
16:00		The Hasse square in Geometry, Algebra, Topology and Arithmetic
		Hicks Seminar Room J11
	Abstract: The classical Hasse principle states that an abelian group M can be recovered from its rationalization and its p-adic completions for all primes p, in the sense that if M is finitely generated, there is a suitable pullback square recovering M. This arithmetic principle applies to modules over many other commutative rings, to sheaves over an elliptic curve and to circle-equivariant cohomology theories. I intend to explain the idea behind this and some classification theorems that follow from it.
Dec 10	Thu	Lesley Morrell (Leeds)	Statistics Seminar
14:00		Modelling the Selfish Herd: Behavioural mechanisms for aggregation in animals
		Hicks LT6
	Abstract: The theory of the selfish herd (WD Hamilton, 1971) has been highly influential to our understanding of animal aggregation. Hamilton proposed that in order to reduce its risk of predation, an individual should approach its nearest neighbour, reducing its risk at the expense of those around it. Despite extensive empirical support, the selfish herd hypothesis has been criticized on theoretical grounds: approaching the nearest neighbour does not result in the observed dense aggregations, and the nearest neighbour in space is not necessarily the one that can be reached fastest. To combat these problems, increasingly complex movement rules have been proposed, successfully producing dense aggregations of individuals, yet various questions remain unanswered. Is one movement rule always the most successful? How to ecological parameters such as the size and density of the group affect rule success? Is the behaviour of the predator important? Should all individuals within a group use the same rule, or should they adjust their behaviour based on where in the group they are, or in response to the behaviour of others? We use simulation models of animal groups to investigate these questions, and demonstrate that there is no rule that performs best under all circumstances: the ecology of the predator and prey are both key in determining how animals should respond to a predation attempt.
Dec 11	Fri	Adam Scaife (MetOffice)
13:05		Gravity waves in the Earth's atmosphere: propagation, dissipation and global scale effects
		Lecture Theatre 9
	Abstract: Starting from linear theory, we will discuss the propagation of small scale gravity waves from their source in the lower, convective layer of the Earth's atmosphere, to their dissipation in the stratosphere and mesosphere above. The role of critical lines and density stratification in wave dissipation will be introduced. These ideas will be used to interpret experiments with global models of the Earth's atmosphere on how gravity waves drive mean circulation and mean temperature structures in the stratosphere and mesosphere. We will also show how gravity waves conspire to drive remarkable low frequency oscillations in the tropical atmosphere.
Dec 16	Wed	Yi Li (Sheffield)	Applied Mathematics Colloquium
14:00		tbd
		LT A
Dec 17	Thu	Ben Youngman (Sheffield)	Statistics Seminar
14:00		Modelling phenomena using different data sources
		Hicks LT6
	Abstract: The building of structures requires that their strength be sufficient to withstand day-to-day wear and tear but also, ideally, all levels of extreme punishment. Yet in practice economical grounds require that some trade-off between strength and susceptibility to damage be made to avoid costs spiralling. As it is logical to expect that the largest events will be most damaging, there is therefore motivation to estimate the distribution of extremes by, for example, estimating the probability of exceeding a certain high level. This is a typical problem in extremal analyses. More recently this problem has been extended by seeking estimates of extremal distributions over space, which is the topic of this talk, though here matters will be further complicated by spatio-temporally sparse data. To try to combat this, data obtained via different methods, yet in theory quantifying the same phenomenon, will be modelled simultaneously. Extreme value theory will be drawn upon to tackle this problem. This talk begins with an introduction to the topic and progresses by applying some ideas discussed.
Dec 17	Thu	Afzalina Azmee (Sheffield)	Statistics Seminar
14:00		Two-stage testing in three-arm non-inferiority trials
		Hicks LT6
	Abstract: The aim of a non-inferiority trial is to show that the new experimental treatment is not worse than the reference treatment by more than a certain, pre-defined margin. We consider the design of a 3-arm non-inferiority trial, where the inclusion of a placebo group is permissible. The widely used 3-arm non-inferiority procedure was authoritatively first described by Pigeot et al. (2003), which involved establishing superiority of reference against placebo in the first stage before testing non-inferiority of experimental against reference in the second stage. If this preliminary test fails, the second-stage test has to be abandoned. In such an eventuality, we believe the whole study will be wasted as nothing new could be learnt about the new experimental treatment. Therefore, instead of showing superiority in the first stage, we propose that the reference treatment has to be significantly different than placebo as a pre-requisite before using Fieller's confidence interval to assess non-inferiority. This procedure leads to no peculiar intervals (i.e. exclusive or imaginary) and offers easy interpretation regarding the efficacy of experimental and reference treatments.
Jan 1	Fri	Alice Courvoisier (Leeds)	Applied Mathematics Colloquium
14:00		The Mean Field Approach to the Transport of Magnetic Fields
		Hicks Lecture Theatre A
Jan 20	Wed	Urs Schreiber (Utrecht)	Topology Seminar
16:00		Path-structured oo-toposes
		Hicks Seminar Room J11
	Abstract: The description of differential String-structures, a central ingredient in certain geometrically defined quantum field theories, requires a nonabelian generalization of differential generalized cohomology. This can be constructed in terms of smooth path $\infty$-groupoids of smooth $\infty$-stacks. I describe these and indicate how they give rise to Chern characters in deRham cohomology on $\infty$-stacks.
Jan 26	Tue	Urs Schrieber (Utrecht)	Topology Seminar
16:00		Path-structured $\infty$-toposes, part 2
		Hicks Seminar Room J11
	Abstract: The description of differential String-structures, a central ingredient in certain geometrically defined quantum field theories, requires a nonabelian generalization of differential generalized cohomology. This can be constructed in terms of smooth path $\infty$-groupoids of smooth $\infty$-stacks. I describe these and indicate how they give rise to Chern characters in deRham cohomology on $\infty$-stacks.
Jan 28	Thu	David Wishart (St Andrews)	RSS Seminar
16:30		The Flavour of Whisky: A statistical and hedonistic appraisal, with Robert Burns
		Hicks Room K14
Feb 9	Tue	Nick Gurski (Sheffield)	Topology Seminar
15:00		Homotopy theory for 2-categories
		Hicks Seminar Room J11
	Abstract: I will discuss a general technique for getting a model category structure (in fact, a Cat-enriched model category structure) on a 2-category. The weak equivalences will be the internal equivalences in your 2-category, and the fibrations will be the internal isofibrations. Both of these kinds of morphisms are quite easy to define, and proving the model category axioms requires using some very basic 2-dimensional limits and colimits. Given time, I will say something about how one can then lift these model structures to produce some much more interesting examples.
Feb 10	Wed	Mitchell Berger (Exeter)	Applied Mathematics Colloquium
14:00		Applications of Braid Theory
		LTA
	Abstract: Two great puzzles in solar astrophysics concern the source of coronal heating and the distribution of solar flares. The atmosphere of the sun is heated to one million degrees or more, possibly by swarms of tiny flares. These tiny flares could be consequences of the braiding of magnetic field lines. Reconnection between braided threads of magnetic flux can release energy stored in the braid. The larger flares exhibit a power law energy distribution. Several authors have suggested that a self-organization process in the solar magnetic field could lead to such a distribution. Here we show how reconnection of braided lines can organize the small scale structure of the field, leading to power law energy release. An application of braids to mixing theory will also be discussed.
Feb 11	Thu	Jonathan Jordan (Sheffield)	Statistics Seminar
14:00		Geometric preferential attachment graphs
		Hicks K14
	Abstract: Preferential attachment (or "scale-free") random graphs, in which a growing network develops by new vertices attaching preferentially to existing vertices which already have a high degree, were proposed, originally by Barabási and Albert, as models for networks appearing in a wide range of contexts (including biological, technological and social) in which examination of data often reveals an approximately power law distribution of vertex degrees. It was rigorously shown by Bollobás at al that preferential attachment graphs did indeed have this property. In many of the contexts in which random graph models are used it makes sense for the vertices to have some location in space. The original preferential attachment model has no spatial element, and in this talk I will describe a model which combines a preferential attachment element with a spatial element. I will describe results which show that under certain conditions on the spatial element the power law degree property is retained. I intend that most of the talk should be accessible to an applied audience, though there will be a few slides discussing my proof method.
Feb 12	Fri	Viktor Fedun (Sheffield)
13:05		3D numerical simulations of a MHD waves in solar atmosphere
		Lecture Theatre 10
Feb 16	Tue	Martin Andler (University of Versailles St Quentin)	Pure Maths Colloquium
16:00		Kontsevich quantization
		Hicks Seminar Room J11
Feb 17	Wed	Philip Eve (Sheffield)	Pure Maths Postgraduate Seminar
12:00		A friendly introduction to spectral sequences
		Hicks Seminar Room J11
	Abstract: Spectral sequences are a computational tool of use in algebra and topology. In this talk we will introduce spectral sequences, giving an informal explanation at first before progressing to a more rigorous definition. We will explain what is meant by a "Serre spectral sequence", and apply the idea in order to determine the cohomology of the unitary group U(n). If time permits, we will finish by looking briefly at a couple of other ways in which spectral sequences arise: the Eilenberg-Moore SS and the (Leray-)Mayer-Vietoris SS.
Feb 17	Wed	Martin Whittle (SheffieldSheffield)	Applied Mathematics Colloquium
14:00		Dissipative Particle Dynamics Simulation of Colloids
		LTA
	Abstract: Clearing legacy radioactive sludge from cooling ponds is a priority for the nuclear industry in its current renaissance. To develop and optimise the necessary machinery it is relying heavily on simulation to model flow and part of this programme involves the incorporation of mesoscopic simulations directed at the rheology of colloids. Here we look at one such approach using Dissipative Particle Dynamics (DPD). DPD was developed in the 1990's and is one of a steadily increasing number of mesoscopic simulation techniques that has been used to model complex fluids and flows in microchannels. Here we discuss methods of modelling colloids using DPD and compare the results of simulations with some other approaches. Although DPD has an inbuilt thermostat this becomes ineffective at high shear rates and we will explore some methods of applying auxiliary thermostatting for non-equilibrium simulations. The results display several classic features of colloidal rheology including evidence of pseudo-plasticity at high volume fraction. Nevertheless, despite the advantages of simplicity, the model still presents a number of challenges that will be discussed.
Feb 18	Thu	Vincent Macaulay (Glasgow)	Statistics Seminar
14:00		Inference about past human migration episodes from modern DNA data
		Hicks K14
	Abstract: One view of human prehistory is of a set of punctuated migration events across space and time, associated with settlement, resettlement and discrete phases of immigration. It is pertinent to ask whether the variability that exists in the DNA sequences of samples of people living now, something which can be relatively easily measured, can be used to fit and test such models. Population genetics theory already makes predictions of patterns of genetic variation under certain very simple models of prehistoric demography. In this presentation I will describe an alternative, but still quite simple, model designed to capture more aspects of human prehistory of interest to the archaeologist, show how it can be rephrased as a mixture model, and illustrate the kinds of inferences that can be made on a real data set, taking a Bayesian approach.
Feb 19	Fri	Jamie Douglas (Sheffield)
13:05
		Lecture Theatre 10
Feb 22	Mon	Tom Sutherland (Sheffield)	Non-commutative Geometry, Analysis and Groups
16:10		Deformation quantisation
		Hicks Seminar Room J11
	Abstract: Deformation quantisation (or phase-space quantisation) comes from the idea of constructing a representation of quantum mechanics by deforming the commutative product in the algebra of functions on a Poisson manifold to a non-commutative so-called star-product. It first appeared in the work of Dirac, and over the years many different authors have proved that deformation quantisations exist for successively broader classes of manifolds. The case of a general Poisson manifold was finally proved by Kontsevich who showed that it was implied by his Formality Conjecture. This talk will focus on giving an outline of his proof.
Feb 23	Tue	Dirk Schuetz (Durham)	Topology Seminar
15:00		Sigma invariants, finiteness properties and closed 1-forms
		Hicks Seminar Room J11
	Abstract: Sigma invariants, defined by Bieri-Neumann-Strebel-Renz, of a group G capture, among other things, finiteness properties of kernels of homomorphisms of G into the reals. As with finiteness properties, there exist homological and homotopical versions of these invariants, and due to the groundbreaking work of Bestvina and Brady it is known that they are different in general. We further investigate the differences between homological and homotopical invariants and study its impact on the existence of nonsingular closed 1-forms on closed manifolds of high dimension.
Feb 24	Wed	Khairia Mira (Sheffield)	Pure Maths Postgraduate Seminar
13:00		Classifying spaces
		Hicks LT4 (D floor)
	Abstract: If we have a topological group G, the question is : is there a space X such that the fundamental group of X is isomorphic to G and the higher homotopy groups for it are trivial?. The Milnor construction gives us the answer, which is: there is and it is called the classifying space for G. The construction gives us the formula of the principal G-bundle over the classifying space, which called the universal G-bundle. In this talk we will introduce the definition of the classifying space of a topological group G, and we will explain the existence theorem for it. After that we will give some examples to find the classifying space for some topological groups, and finaly, if time permits, we will give just the statments for some propositions to present some properties of the classifying space.
Feb 25	Thu	Mark Broom (Sussex)	Statistics Seminar
14:00		Models of evolution on structured populations with asymmetry
		Hicks I19
	Abstract: We investigate two examples of models of populations with structure, involving asymmetry. These are different in character, with the common theme that both the structure and the asymmetry have an important influence on population outcomes. The first part of the talk concerns the study of evolutionary dynamics on populations with some non-homogeneous structure, a topic in which there is a rapidly growing interest. We investigate the case of non-directed equally weighted graphs and find solutions for the fixation probability of a single mutant in two classes of simple graphs. This process is a Markov chain and we prove several mathematical results. For example we prove that for all but a restricted set of graphs, (almost) all states are accessible from the possible initial states. To find the fixation probability of a line graph we relate this to a two-dimensional random walk which is not spatially homogeneous. We investigate our solutions numerically and find that for mutants with fitness greater than the resident, the existence of an asymmetric population structure helps the spread of the mutants. Thus it may be that models assuming well-mixed populations consistently underestimate the rate of evolutionary change. In the second part we consider a model of kleptoparasitism, the stealing of food from one animal by another. The handling process of food items can take some time and the value of such items can vary depending upon how much handling an item has received. Furthermore this information may be known to the handler but not the potential challenger, so there is an asymmetry between the information possessed by the two competitors. We use game-theoretic methods to investigate the consequences of this asymmetry for continuously consumed food items, depending upon various natural parameters. A variety of solutions are found, and there are complex situations where three possible solutions can occur for the same set of parameters. It is also possible to have situations which involve members of the population exhibiting different behaviours from each other. We find that the asymmetry of information often appears to favour the challenger, despite the fact that it possesses less information than the challenged individual.
Feb 26	Fri	Marialejandra Luna-Cardozo (Sheffield)
13:05
		Lecture Theatre 10
Mar 2	Tue	Neil Strickland (Sheffield)	Topology Seminar
15:00		Tambara functors
		Hicks Seminar Room J11
	Abstract: Let $R$ be a strictly commutative ring spectrum with an action of a finite group $G$; then the homotopy group $\pi_0(R)$ fits into an algebraic structure known as a Tambara functor. We will discuss the algebraic theory of Tambara functors and their relationship with Witt rings, which have a number of different applications in stable homotopy theory.
Mar 3	Wed	Marina Skender (Leuven)	Applied Mathematics Colloquium
14:00		Quasi-equlibrium current sheet and the onset of impulsive bursty reconnection
		LT A
	Abstract: A two-dimensional reconnecting current sheet is studied numerically in the MHD approach. Different simulation setups are employed in order to follow the evolution of the formed current sheet in diverse configurations: Two types of initial equilibria, Harris and force-free, two types of boundary conditions, periodic and open, with uniform and non-uniform grid set, respectively. All the simulated cases are found to exhibit qualitatively the same behavior in which a current sheet evolves slowly through a series of quasi-equilibria; eventually it fragments and enters a phase of fast impulsive bursty reconnection. In order to gain more insight on the nature and characteristics of the instability taking place, physical characteristics of the simulated current sheet are related to its geometrical properties. The aspect ratio of the current sheet is observed to increase slowly in time up to a maximum value at which it fragments. Additional turbulence introduced to the system is shown to exhibit the same qualitative steps, but with the sooner onset of the fragmentation and at smaller aspect ratio.
Mar 3	Wed	Andrey Lazarev (Leicester)	Pure Maths Colloquium
16:00		Maurer-Cartan moduli and twistings
		Hicks Seminar Room J11
	Abstract: The notion of a Maurer-Cartan (MC) element in a differential graded Lie algebra is an abstraction of the notion of a flat connection on a vector bundle. MC elements and their moduli spaces appear in disparate areas of mathematics; usually in the context of deformations of various types of objects (complex-analytic structures, connections, associative and Lie algebras and their homotopy invariant versions etc.) I will give a modern overview of MC theory from the point of view of L-infinity algebras and describe how one can twist structures by an MC element. As an example of the general technology I will describe a canonical L-infinity map from an A-infinity algebra to its Hochschild complex and, if time permits, outline an application to graph cohomology. This is joint work with J. Chuang.
Mar 4	Thu	Jonty Rougier (Bristol)	Statistics Seminar
14:00		Uncertainty and Risk in Natural Hazards
		Hicks K14
	Abstract: In natural hazards (volcanoes, earthquakes, floods etc) it is useful for modelling purposes to make a distinction between aleatory and epistemic uncertainty, where the former represents the inherent or natural uncertainty of the hazard, and the latter represents everything else. Natural hazards scientists are often reluctant to quantify epistemic uncertainty with probability, due in a large part to its subjective nature. But this challenge should be weighed against the additional problems that non-quantified uncertainty create for the risk manager and the policymaker. This talk explores these issues in the light of the recent NERC scoping study on natural hazards uncertainty and risk.
Mar 5	Fri	Andrew Newton (Sheffield)
13:05
		Lecture Theatre 10
Mar 8	Mon	Karl Schwede (Michigan)
16:00		Singularities of polynomials in characteristic 0 and characteristic p
	Abstract: I will discuss the singularities of the zero-locus of a complex valued polynomial equation. A particular focus will be payed to comparing different singularities. I will discuss two different approaches to this question, both analytic (characteristic zero) and algebraic (positive characteristic).
Mar 9	Tue	Karl Schwede (Michigan)
11:00		Counting log canonical centers and compatibly Frobenius split subvarieties
		Hicks Seminar Room J11
	Abstract: Log canonical centers and compatibly Frobenius split subvarieties are two very closely related objects that were each defined in very different contexts in the last 25 years. Log canonical centers appeared first in the minimal model program as places where one can perform induction on dimension, and Frobenius split subvarieties first appeared in the study of Schubert varieties. I will talk about various properties that both these objects share leading up to some recent joint work with Kevin Tucker where we give a sharp bound on the number of both such objects that can appear in an algebraic variety. In the case of log canonical centers, this work partially generalizes work of Helmke.
Mar 9	Tue	Michael Joachim (Muenster)	Topology Seminar
15:00		Equivariant cohomotopy for infinite discrete groups
		Hicks Seminar Room J11
Mar 10	Wed	Karl Schwede (Michigan)
10:00		Test ideals in non-Q-Gorenstein rings
	Abstract: Given an $F$-finite reduced ring R of positive characteristic $p > 0$, one can denote the associated big test ideal $\tau_b(R)$. This is the ideal generated by all test elements for all tight closure operations in all modules. If $R$ is reduced generically from a normal Q-Gorenstein ring $R_0$ of characteristic zero, then the big test ideal $\tau_b(R)$ coincides with the multiplier ideal of $R$ (also reduced from characteristic zero). However, if $\tau_b(R)$ is not Q-Gorenstein, then the multiplier ideal is not (typically) defined. One way around this issue is to define the multiplier ideal $J(R_0, \Delta_0)$ for pairs $(R_0,\Delta_0)$ where $\Delta_0$ is a Q-divisor on $Spec R_0$ such that $K_{R_0} + \Delta$ is Q-Cartier. On the other hand, inspired by the characteristic zero theory, S. Takagi defined the test ideal in positive characteristic for pairs $(R, \Delta$) where $\Delta$ is an effective $Q$-divisor on Spec $R$. In this talk, we will discuss the following result. $\tau_b(R) = \sum_{\Delta} \tau(R, \Delta)$ where the sum is over \Delta such that $K_R + \Delta$ is Q-Cartier. This affirmatively answers a question asked by several people including Blickle, Lazarsfeld, K. Lee, and K. Smith. It also is closely related to recent work of de Fernex and Hacon in characteristic zero.
Mar 10	Wed	Ian Grojnowski (Cambridge)	Pure Maths Colloquium
16:00		Almost local differential operators
		Hicks Seminar Room J11
	Abstract: One of the most fundamental theorems in representation theory is the Beilinson-Bernstein theorem, which describes the representations of a Lie algebra such as sl_n in much simpler terms---as sheaves of modules for differential operators on a smooth algebraic variety. I will describe this theorem, and some work in progress to generalise it to describe non-commutative deformations of enveloping algebras in terms of 'almost local differential operators'.
Mar 11	Thu	John Aston (Warwick)	Statistics Seminar
14:00		Using Functional Principal Component Analysis and Mixed Effect Models to Analyse Spoken Language
		Hicks I19
	Abstract: Fundamental frequency (F0, broadly ``pitch'') is an integral part of spoken human language; however, a comprehensive quantitative model for F0 can be a challenge to formulate due to the large number of effects and interactions between effects that lie behind the human voice's production of F0, and the very nature of the data being a contour rather than a point. A semi-parametric functional response model for F0 will be formulated by incorporating linear mixed effects models through the functional principal component scores. This model is applied to the problem of modelling F0 in the tone languages such as Mandarin and Qiang (a dialect from China), languages in which relative pitch information is part of each word's dictionary entry.
Mar 12	Fri	Carlos Jaimes (Sheffield)
13:05
		Lecture Theatre 10
Mar 16	Tue	Eugenia Cheng (Sheffield)	Topology Seminar
15:00		Iterated distributive laws via the Gray tensor product
		Hicks Seminar Room J11
	Abstract: Monads give us a way of expressing algebraic structure, and distributive laws between monads give us a way of combining two types of algebraic structure. The basic example combines the free monoid monad (for multiplication) and the free Abelian group monad (for addition) via the usual distributive law, giving us the free ring monad. We give a framework for combining $n$ monads on the same category via distributive laws satisfying Yang-Baxter equations, showing that this way of distributing algebraic structure behaves somewhat like braids. While it is possible to prove this using a very dull induction, one might wonder why on earth the Yang-Baxter equations popped up here. So I prefer to present a proof that emphasises the geometry of the situation, using the Gray tensor product for 2-categories.
Mar 17	Wed	Shabieh Farwa (Sheffield)	Pure Maths Postgraduate Seminar
13:10		The Weil Conjectures
		Hicks LT4 (D floor)
	Abstract: Given a smooth projective variety over a finite field, one can consider the number of points of this variety over field extensions of the base field. The Weil Conjectures (now actually a theorem) are a closed description of the generating function (The Zeta Function) of these numbers. The purpose of the talk is to give the introduction to this important theorem. We will discuss how to count the number of points on Elliptic Curves over the finite fields,( something that's of high importance in modern cryptography), by proving the Weil Conjectures for the Elliptic Curves and giving explanation of all relating concepts by examples.
Mar 17	Wed	Michael Proctor	Applied Mathematics Colloquium
14:00		Fully consistent mean field MHD
		tbd
	Abstract: We consider the linear stability of two-dimensional nonlinear magnetohydrodynamic basic states to long-wavelength three-dimensional perturbations. Following the work of Hughes and Proctor the 2D basic states are obtained from a specific forcing function in the presence of an initially uniform mean field of strength B. By extending to the nonlinear regime the kinematic analysis of Roberts, we show that it is possible to predict the growth rate of these perturbations by applying mean field theory to both the momentum and the induction equations. If B = 0, these equations decouple and large-scale magnetic and velocity perturbations may grow via the kinematic effect and the AKA instability respectively. However, if the imposed field is non-zero, the momentum and induction equations are coupled by the Lorentz force; in this case, we show that four transport tensors are now necessary to determine the growth rate of the perturbations. We illustrate these situations by numerical examples; in particular, we show that a mean field description of the nonlinear regime based solely on a quenched coefficient is incorrect.
Mar 17	Wed	Kobi Kremnitzer (Oxford)	Pure Maths Colloquium
16:00		Algebraic groups over the field with one element and crystal bases
		Hicks Seminar Room J11
	Abstract: Relative algebraic geometry can be done over a symmetric monoidal category. This gives a way of doing algebraic geometry over the field with one element. One can use Kashiwara's crystal bases to define reductive groups and Schubert varieties over the field with one element. These are related to toric degenerations of Schubert varieties. This is joint work with Nick Royzenblum.
Mar 18	Thu	Norman Fenton (Queen Mary)	Statistics Seminar
14:00		Uncertainty, Risk and Decision Making
		Hicks K14
	Abstract: Current approaches to uncertain reasoning and risk assessment are often fundamentally flawed. Motivated by real examples from the law and medicine (including a murder trial and a medical negligence trial in which I was an expert witness), I will explain how such flawed reasoning can be avoided by adopting a Bayesian approach. I will introduce the notion of subjective probability and Bayes theorem and argue that this is the only rational approach for handling uncertainty. The problem with this approach is how to scale it up to complex risk assessment problems involving many causally related factors. I will introduce the notion of Bayesian nets and show how they address this problem. I will demonstrate how we have used Bayesian nets in a range of real applications including in legal arguments, medical risk assessment, and software risk assessment.
Mar 19	Fri	Andrew Gascoyne (Sheffield)
13:05
		Lecture Theatre 10
Apr 13	Tue	Emmanuel Farjoun (Jerusalem)	Topology Seminar
15:05		Homotopy Normal maps of Monoids
		Hicks Seminar Room J11
Apr 14	Wed	Reidun Twarock (York)
14:00		Viruses and geometry : New insights into virus architecture and function via affine extended symmetry groups
		Lecture Theatre A
	Abstract: Simple viruses consist of a genome (RNA or DNA) surrounded by a protective protein container. For a significant number of viruses, these containers exhibit icosahedral symmetry. The locations of the proteins in these containers can therefore be predicted in terms of surface lattices that are invariant under icosahedral symmetry as shown in Caspar and Klug's seminal work on virus architecture from the 1960s. In this talk I will show that there exists a deeper level of geometric organisation that orchestrates the full three-dimensional structures of simple virus particles, providing for the first time predictive information on shapes and dimensions of the individual viral components. The principle of this organisation is encoded in a finite library of three-dimensional point arrays that are a consequence of our recent classification of affine extensions of the icosahedral symmetry group. I will demonstrate with a range of viruses that our theory is capable of predicting a wide spectrum of distinct viral features and their relative sizes in striking detail. These include the edges of protein subunits, the double-shelled genomic RNA structure in MS2, and the dodecahedral RNA cage in Pariacoto virus. Several applications of this fundamental geometric principle of virus architecture are discussed, including virus assembly, viral evolutions and the prediction of structural transitions important for infection.
Apr 14	Wed	Paul Mitchener (Sheffield)	Pure Maths Colloquium
16:00		C*-algebras, C*-categories, and functors.
		Hicks Seminar Room J11
	Abstract: There are a number of situations in mathematics where a C*-algebra is associated to a geometric object. Often, this association is not functorial. In this talk we look at a generalisation of C*-algebras called C*-categories, and show how, in many situations, a C*-algebra can be replaced by an equivalent C*-category- and in the C*-category setting, the association we obtain is functorial.
Apr 15	Thu	Dave Benson (Aberdeen)
14:00		Jordan Blocks and vector bundles
		Hicks Seminar Room J11
Apr 15	Thu	John McColl (Glasgow)	Statistics Seminar
14:00		Assessment and Feedback in Statistics Courses
		Hicks K14
	Abstract: Giving useful feedback to students about their work ought to be an integral part of the teaching, learning and assessment process, so that learners know where they went wrong and what they can do to improve in the future. In the National Student Survey, student ratings of assessment and feedback are generally less favourable than those for other aspects of their experience, suggesting that this is an area in which UK Higher Education needs to improve. Up till now, there has been little discussion about how best to produce effective feedback for the different assessment methods used in modern Statistics courses. This talk will summarise the characteristics of effective feedback, as described in the research literature, and will indicate how these guidelines can be applied to the assessment of analysis-of-data tasks in Statistics courses. We will then present results from a small study of students in one Statistics course at the University of Glasgow in two conditions, one where feedback was given 'as usual' and the other where feedback was given in accordance with the principles of effective feedback. Finally, we will introduce a freely available, web-based quiz system which has been designed to give tailored feedback to multiple choice questions in a Statistics setting.
Apr 16	Fri	Richard Morton (Sheffield)
13:05
		Lecture Theatre 10
Apr 20	Tue	John Calabrese (Sheffield)	Pure Maths Postgraduate Seminar
13:00		Connections on bundles
		Hicks Seminar Room J11
	Abstract: There are several ways to define connections on fibre bundles. Michael Spivak once wrote: "I personally feel that the next person to propose a new definition of a connection should be summarily executed." In this talk we'll have a look at Ehresmann connections. Such a thing is (roughly) a choice of `horizontal' or `flat' directions on the total space of the bundle. If everything goes well, we'll conclude by specialising to the case of vector bundles, where we can restrict to a more algebraic notion of connection (sometimes called a Koszul connection).
Apr 21	Wed	Tatiana Talipova (Nizhny Novgorod, Russia )	Applied Mathematics Colloquium
14:00		Avalanche and Landslide Dynamics
		LT A
	Abstract: The Savage-Hutter model is applied to describe the gravity driven shallow-water flows in inclined channels of parabolic-like shapes modeling the avalanches moved in the mountain valleys or the landslide motions in underwater canyons. The Coulomb (sliding) friction term is included in model. The Riemann invariants are found for this hyperbolic system. Several analytical solutions described the nonlinear dynamics of avalanche are obtained: Riemann wave, dam-break problem, self-similar solutions and the Carrier-Greenspan-like solutions. Some of them extend the known solution for inclined plate (1D geometry). They can be used to test the 2D numerical models of debris volcano avalanches, mountain flanks and landslides in submarine continental slopes.
Apr 21	Wed	Joe Chuang (City University, London)	Pure Maths Colloquium
16:00		Surfaces and acyclic algebras.
		Hicks Seminar Room J11
	Abstract: Finite-dimensional algebras with trace forms give rise to topological invariants of Riemann surfaces. I will describe joint work with Andrey Lazarev on a variation due to Kontsevich that produces better invariants.
Apr 22	Thu	Piotr Fryzlewicz (London School of Economics)	Statistics Seminar
14:00		Thick-pen transformation for time series
		Hicks K14
	Abstract: Traditional visualisation of time series data often consists of plotting the time series values against time and "connecting the dots". We propose an alternative, multiscale visualisation technique, motivated by the scale-space approach in computer vision. In brief, our method also "connects the dots", but uses a range of pens of varying thicknesses for this purpose. The resulting multiscale map, termed the Thick-Pen Transform (TPT) corresponds to viewing the time series from a range of distances. We formally prove that the TPT is a discriminatory statistic for two Gaussian time series with distinct correlation structures. Further, we show interesting possible applications of the TPT to measuring cross-dependence in multivariate time series, and to testing for stationarity. In particular, we derive the asymptotic distribution of our test statistic, and argue that the test is applicable to both linear and nonlinear processes under low moment assumptions. Various other aspects of the methodology, including other possible applications, are also discussed.
Apr 23	Fri	Abhishek Srivastava (Aryabhatta Research Institute of Observational Sciences (ARIES), Manora Peak, Nainital, India.)
13:05		On Probing the Solar Atmosphere by Observed MHD Waves
		Lecture Theatre 10
	Abstract: The observed MHD wave harmonics in a large-scale (e.g., loops) and small-scale (e.g., bright points, network cavities) magnetic structures of the solar atmosphere, are being very important recent days to probe the crucial plasma conditions of these solar structures to understand their dynamics and heating. While, the observations of propagating MHD waves in various solar structures are also significant to probe their medium in which these waves propagate. Under the new light of my recent observational findings, I present some trends of the local plasma diagnostics based on the observed MHD waves in various solar structures, and also discuss their implications and future aspects.
Apr 27	Tue	Gery Debongnie (Manchester)	Topology Seminar
15:00		On the rational homotopy type of subspace arrangements
		Hicks Seminar Room J11
	Abstract: We shall explore different properties of the complement spaces of subspace arrangements, from the viewpoint of rational homotopy theory. A rational model will be described, from which we deduce several results. For example, we give a complete description of coordinate subspace arrangements whose complement space is a product of spheres.
Apr 28	Wed	Francesca Ticconi (DLR - German Aerospace Center)	Applied Mathematics Colloquium
14:00		SAR Polarimetry
		LT A
	Abstract: The direction of the electric field vector, describing an ellipse in a plane transverse to propagation, plays an essential role in the interaction of electromagnetic waves with material bodies and the propagation medium. This polarisation transformation behaviour is denoted as "Polarimetry" in radar and synthetic aperture radar (SAR) sensing and imaging. A fully polarimetric radar transmits two orthogonal polarisations and receives the backscattered wave on the same two polarisations. This results in four received channels where both the amplitude and relative phase are measured. The measured signals in these four channels represent all the information needed to measure the polarimetric scattering properties of the target. Such information is necessary for the estimation of soil moisture and surface roughness parameters, since a major problem in this estimation is the separation of soil moisture and surface roughness contributions to the backscattered radar signal. A set of methods known as target decomposition theorems have been developed for the interpretation of polarimetric SAR data and two different approaches will be shown based respectively on a physical-based model decomposition and on the eigenvector-based target decomposition. For the soil moisture content retrieval, an inversion model, based on this latter decomposition, has been applied on L-band airborne SAR data and the result of the inversion will be shown.
Apr 28	Wed	Liam O'Carroll (Edinburgh)	Pure Maths Colloquium
16:00		Ideals of Herzog-Northcott type
		Hicks Seminar Room J11
	Abstract: Juergen Herzog, in a by now classic paper, gave minimal generating set for the vanishing ideal of the affine space curve $% k[t^{n_{1}},t^{n_{2}},t^{n_{3}}]$ under the restriction that the $n_{i}$ form a relatively prime triple of positive integers. Necessarily this ideal is prime, and is either a complete intersection or an almost complete intersection with generators the $2\times 2$-minors of the matrix \begin{equation*} \left( \begin{array}{ccc} x^{a_{1}} & y^{a_{2}} & z^{a_{3}} \\ y^{b_{2}} & z^{b_{3}} & x^{b_{1}} \end{array} \right) \end{equation*} where the $a_{i}$ and $b_{j}$ are positive integers. We used these ideals quite recently to answer in the negative a twenty year old problem about the Uniform Artin-Rees property on the prime spectrum of an excellent ring. In this talk we discuss the properties of this ideal in general. We first show that it is a Northcott ideal (in the sense of Vasconcelos). This enables us to display immediately its properties connected to liaison and the fact that it is unmixed. Next we revisit work of Herzog, Bresinsky and Valla connected with the property of being a set-theoretic complete intersection. Finally we focus on the case of the polynomial ring $k[x,y,z].$ We show that the ideal is prime only in the case treated by Herzog, that it is usually radical, and we use the theory of multiplicities to estimate the number of its components. Some extensions of aspects of this work will be sketched.
Apr 29	Thu	Andrew Wade (Strathclyde)	Statistics Seminar
14:00		Non-homogeneous random walks with asymptotically zero drifts
		Hicks K14
	Abstract: For this talk a random walk is a discrete-time time-homogeneous Markov process on d-dimensional Euclidean space. If such a random walk is spatially homogeneous, its position can be expressed as a sum of independent identically distributed random vectors. Such homogeneous random walks are classical and the literature devoted to their study extensive, particularly when the state-space is the d-dimensional integer lattice. The most subtle case is when the mean drift (i.e., average increment) of the walk is zero. The assumption of spatial homogeneity, while simplifying the mathematical analysis, is not always realistic for applications. Thus it is desirable to study non-homogeneous random walks. As soon as the spatial homogeneity assumption is relaxed, the situation becomes much more complicated. Even in the zero-drift case, a non-homogeneous random walk can behave completely differently to a zero-drift homogeneous random walk, and can be transient in two dimensions, for instance. Such potentially wild behaviour means that results for non-homogeneous random walks often have to be stated under rather restrictive conditions, and techniques from the study of homogeneous random walks are difficult to apply. I will give an introduction to some of the known results on non-homogeneous random walks with asymptotically zero mean-drift, that is, the magnitude of the drift at a point tends to 0 as the distance of that point from the origin tends to infinity. It turns out that this is the natural regime in which to look for important phase transitions in asymptotic behaviour. This includes work by Lamperti in the 1960s on recurrence/transience behaviour. I will also discuss recent joint work with Iain MacPhee and Mikhail Menshikov (Durham) concerned with angular asymptotics, i.e., exit-from-cones problems. We show that, in contrast to recurrence/transience behaviour, the angular properties of non-homogeneous random walks are remarkably well-behaved in some sense in the asymptotically zero drift regime.
Apr 29	Thu	Sara Hughes (ViiV Healthcare)	RSS Seminar
16:30		Missing data: It is better to prepare and prevent than to repair and repent
		Hicks K14
	Abstract: Does your study team know what the critical data is for analysis? Does your team know what most damages the trial's statistical power? Does your team know what level of missing data cannot be repaired? Considerable research has been done in recent years to develop sophisticated statistical methods for handling missing data and dropouts in the analysis of clinical trial data. However, there has not been sufficient emphasis by either statisticians or other study team members on proactively setting out at the study initiation stage to assess the impact of missing data and investigate ways in which to reduce dropouts. Doing this has the potential to considerably improve the clarity and quality of study results and also increase efficiency. This talk will present an example from HIV where Statistics and Clinical Operations collaborated to try and reduce non-treatment-related dropouts. The first step was to perform a pooled analysis of past HIV trials investigating which patient subgroups are more likely to drop out unnecessarily. The second step was to educate study personnel at all levels about the patient types more likely to dropout, and the impact this has on data quality and sample sizes required. The final step was to then work with each group to create a proactive plan regarding focused retention efforts, identifying ways to increase retention relevant to the patients most at risk.
Apr 30	Fri	Xenophon Moussas (Faculty of Physics, National and Kapodistrian University of Athens)
13:05
		Lecture Theatre 10
May 4	Tue	Thomas Cottrell (Sheffield)	Pure Maths Postgraduate Seminar
13:00		An introduction to multicategories.
		Hicks Seminar Room J11
	Abstract: In a category, each morphism has a single source object and a single target object. A multicategory is a generalised version of a category, in which each morphism has as its source a finite string of objects. Many mathematical structures are particularly interesting in the one-object case; for instance, a one-object category is a monoid. Multicategories are no different; a one-object multicategory is known as an operad. However, the study of multicategories arose in logic, whereas the study of operads arose in topology. It was not for about 30 years that anyone realised that operads are a special case of multicategories. This talk serves as an introduction to both multicategories and operads, giving examples and applications of both.
May 4	Tue	Martin Lindsay (Lancaster)	Non-commutative Geometry, Analysis and Groups
16:00		Quantum Stochastic Integrals and Semimartingales (Yorkshire Functional Analysis Group meeting)
		Lecture Theatre 6
May 5	Wed	Richard Morton (Sheffield)	Applied Mathematics Colloquium
14:00		Oscillations in solar plasma with variable background
		LT A
	Abstract: The solar atmospheric plasma is an extremely dynamic medium threaded by a complex magnetic field that is constantly subject to heating and cooling processes. The magnetic field provides the foundations for a wide variety of plasma fine structure in the solar atmosphere, e.g. coronal loops, coronal holes, prominences. Each of these features in the solar atmosphere can support an array of magneto-hydrodynamic (MHD) oscillatory modes. We present here a first study of the propagation of MHD waves in a magnetised plasma environment that is cooling due to radiation. Previous investigations have concentrated on the affect of radiation on the perturbations only. An approximate radiation function that has the form of Newtonian cooling is used for the sake of simplicity. We find that the cooling of the plasma leads to a time dependent frequency of MHD waves (or oscillations) and causes both damping and amplification of these periodic phenomena. This result could have important implications for various aspects of magneto-seismology in the solar atmosphere.
May 5	Wed	Yuri Drozd (Insitute of Mathematics, Kiev)	Pure Maths Colloquium
16:00		Auslander curves of nodal projective configurations and related tilting.
		Hicks Seminar Room J11
	Abstract: To any nodal rational projective curve we associate a non-commutative curve called its ``Auslander curve.'' We study its homological properties and construct a tilting sheaf, which establishes an equivalence of the derived category of coherent sheaves over such a curve and that of modules over a finite dimensional algebra. We also study the embedding of the category of coherent sheaves over the initial nodal curve into the category of coherent sheaves over its Auslander curve.
May 6	Thu	Andy Wood (Nottingham)	Statistics Seminar
14:00		Fractals, self-similarity and the estimation of fractal dimension: a statistical perspective.
		Hicks K14
	Abstract: The first part of the talk will give an elementary introduction to fractals, and will include discussion of what they are, some of the various ways in which they can arise and why they are of interest. Relevant concepts such as self-similarity will also be explained. The second part of the talk will briefly discuss statistical estimation of the dimension of a random fractal generated as a realisation of a suitable continuous-time stochastic process, which is observed on a finite grid. The estimation of fractal dimension is of theoretical and practical interest in a number of contexts. The asymptotic framework relevant here is "infill" asymptotics, and the limit theory for fractal dimension estimators in this setting can be quite non-standard.
May 7	Fri	Amy Scott (Sheffield)
13:05
		Lecture Theatre 10
May 11	Tue	Timothy Eardley (Sheffield)	Pure Maths Postgraduate Seminar
13:00		An introduction to $p$-adic numbers.
		Hicks Seminar Room J11
	Abstract: The p-adic numbers, Q_p, were first introduced by Hensel in 1897 in an attempt to utilise the techniques of power series for number theory. However, these ideas have lead to p-adic analysis, an area of interest in its own right, as well as to applications in many other areas including to Local Class Field Theory. In this talk we will first motivate their introduction and detail some of their more unusual properties. Then we shall look at questions of square roots and roots of unity in Q_p, before finally looking at an application to Local Class Field Theory.
May 11	Tue	Andrei Akhvlediani (Oxford)	Topology Seminar
15:00		On the categorical meaning of Gromov and Hausdorff distances.
		Hicks Seminar Room J11
	Abstract: By interpreting the distance $d(x,y)$ as $\hom(x,y)$, Lawvere considered metric spaces as categories enriched in the extended positive reals. This viewpoint led to the adoption of tools of enriched category theory in the study of metric spaces; its usefulness is evident already in the work of Leinster and Willerton on the magnitude of metric spaces. In this talk we will use enriched category theory to analyse the Gromov distance, which is a metric on the class of isometry classes of compact metric spaces, and its precursor - the Hausdorff metric. We exhibit the Hausdorff metric as part of a monad and define Gromov distance in terms of so-called $V$-modules. The categorical viewpoint allows us to pursue those distances in great generality and reveals some of their algebraic properties. Some familiarity with category theory will be helpful, but not essential.
May 12	Wed	Vladimir Vladimirov (York)	Applied Mathematics Colloquium
14:00
		LT A
May 12	Wed	Shaun Stevens (UEA)	Pure Maths Colloquium
16:00		Towards explicit L-packets for Sp(4).
		Hicks Seminar Room J11
	Abstract: The local Langlands conjectures predict a natural surjection from the set of equivalence classes of irreducible smooth complex representations of a p-adic classical group G to the continuous representations of the Weil-Deligne group in the Langlands dual group of G. The fibres of this map are the L-packets of the title. This map is known to exist for Sp(4), from work of Gan--Takeda, and now in general, from work of Arthur to appear. However, this still leaves the question of understanding the L-packets explicitly. As well as explaining this background in more detail, I will report on work in progress with Corinne Blondel and Guy Henniart giving an approach to finding these L-packets explicitly, using Bushnell--Kutzko's theory of types and work of Moeglin.
May 13	Thu	Ivan Panin (Steklov Institute)
14:00		On the relation of symplectic algebraic cobordism to Schlichting's KO-theory
		Hicks Seminar Room J11
May 13	Thu	Philip O'Neill (Nottingham)	Statistics Seminar
14:00		Stochastic models and data analysis for healthcare associated infections
		K14
	Abstract: Antibiotic resistant pathogens such as MRSA and VRE are of considerable importance in healthcare settings in terms of both clinical and economic impact. In this talk we describe analyses of highly detailed datasets taken from hospital studies looking at, among other things, the effectiveness of control measures and the effect of undetected carriage. The methods involve formulating appropriate stochastic transmission models whose parameters are then estimated using MCMC methods.
May 18	Tue	Kirill Mackenzie (Sheffield)	Topology Seminar
16:00		Lie bialgebroids
		Hicks Seminar Room J11
	Abstract: Lie bialgebroids were introduced by the speaker and Xu Ping in 1994. This will be a very unhistorical tour d'horizon, with much benefit of hindsight. A Poisson bracket on a manifold M is usually defined as an R-Lie algebra structure on the algebra of smooth functions, which is also a derivation in each variable. This induces a bracket on the 1-forms which behaves very much like the bracket of vector fields. These two bracket structures -- on TM and T^*M (or rather, on the modules of sections of TM and T^*M) -- resemble the situation in a Lie bialgebra. Lie bialgebras arose in Drinfel'd's work in the 1980s, in part as semiclassical limits of quantum groups. There is now an extensive literature. Lie bialgebroids were originally seen as a unifying concept, allowing Lie bialgebras and general Poisson manifolds to be treated simultaneously. They turned out to provide examples of differential Gerstenhaber algebras, Courant algebroids, and Dirac structures. In a different direction, they arise in the theory of double Lie groupoids. A vague acquaintance with Poisson algebras or Poisson manifolds is desirable, though basics will be recalled. My notes from the Quantization seminar are http://kchmackenzie.staff.shef.ac.uk/shef-only/poisson-09-10-26.pdf and contain far more than is needed for this talk.
May 20	Thu	Kate Ren (Sheffield)	Statistics Seminar
14:00		Incorporating Prior Information into Clinical Trial Designs
		Hicks I19
May 20	Thu	Peter Gregory (Sheffield)	Statistics Seminar
14:00		Looking for a simple solution to a simple problem: Bayesian modelling of positively skewed data
		Hicks I19
	Abstract: The motivation for this research was a medical cost data set from a clinical trial. If the proposed new intervention were to be accepted by a Regulatory Body then a Health Care Provider has to budget for future treatments for some members of the rest of the population. In this Bayesian analysis we want to determine the expected value for one unobserved member of this population from its posterior predictive distribution by firstly establishing the parametric data model that best captures the positive skew characteristics of the costs. We then develop a novel approach to modelling the priors that enable an expert's prior beliefs to be elicited while permitting a limited analytical study of the model. These techniques have been applied to recent medical data sets to establish their comparative efficiency when compared with classical estimators.
May 20	Thu	Jonty Rougier (Bristol)	Statistics Seminar
15:30		Complex systems: Accounting for model limitations
		Hicks I19
	Abstract: Many complex systems, notably environmental systems like climate, are highly structured, and numerical models, known as simulators, play an important role in prediction and control. It is crucial to account for limitations in simulators, since these can be substantial, and can vary substantially from one simulator to another. These limitations can be categorised in terms of input uncertainty, parametric uncertainty, and structural uncertainty. The talk explains this framework, and the particular challenge of accounting for simulator limitations in dynamical systems, using illustrations from a low-order model for glacial cycles.
May 25	Tue	Richard Hepworth (Copenhagen)	Topology Seminar
15:05		Groups, Discs and Cacti
		Hicks Seminar Room J11
	Abstract: The "framed little discs operad" is a topological gadget that acts on the double loop space of any based space X. The "cactus operad" is a gadget of the same kind, which this time (almost) acts on the free loops in a manifold M. The two operads are known to be homotopy equivalent. The purpose of the talk is to elaborate on the relationship between cacti and framed discs. First we will introduce a new action of cacti on the space of based loops in a topological group, and then we will show that it is equivalent to the action of framed discs on double loopspaces. Along the way we will give a new equivalence between cacti and framed discs.
May 27	Thu	Graeme Sarson (Newcastle)	Statistics Seminar
14:00		Forward models of prehistoric population dynamics
		Hicks K14
Jun 2	Wed	Misha Ruderman (Sheffield)
14:00		Transverse oscillations of coronal loops
		LTA
	Abstract: On 14 July 1998 TRACE observed transverse oscillations of a coronal loop generated by an external disturbance most probably caused by a solar flare. These oscillations were interpreted as standing fast kink waves in a magnetic flux tube. Firstly, in this talk we embark on the discussion of the theory of waves and oscillations in a homogeneous straight magnetic cylinder with the particular emphasis on fast kink waves. Next, we consider the effects of stratification, loop expansion, loop curvature, non-circular cross-section, loop shape and magnetic twist. An important property of observed transverse coronal loop oscillations is their fast damping. We briefly review the different mechanisms suggested for explaining the rapid damping phenomenon. After that we concentrate on damping due to resonant absorption. We describe the latest analytical results obtained with the use of thin transition layer approximation, and then compare these results with numerical findings obtained for arbitrary density variation inside the flux tube. The implication of the theoretical results for coronal seismology is briefly discussed. We describe the estimates of magnetic field magnitude obtained from the observed fundamental frequency of oscillations, and the estimates of the coronal scale height obtained using the simultaneous observations of the fundamental frequency and the frequency of the first overtone of kink oscillations. In the last part of the talk we summarize the most outstanding and acute problems in the theory of the coronal loop transverse oscillations.
Jun 22	Tue	Iakovos Androulidakis (Gottingen)	Non-commutative Geometry, Analysis and Groups
16:00		Pseudodifferential calculus for singular foliations
		LT 6
	Abstract: Regular foliations have been studied for many decades but their leaf spaces are in general very pathological topological spaces. One of the aims of Connes' noncommutative geometry has been to study such leaf spaces in terms of their holonomy groupoids. In joint work with G. Skandalis (Paris 7) we have begun to extend these methods to singular foliations. These are widespread: group actions and Poisson manifolds, for example, give rise to singular foliations. The holonomy groupoid of a singular foliation (M,F) is an even more ill-behaved object, nevertheless in earlier work we showed how to construct the associated C*-algebra. In this lecture, we will give an overview of this construction, and discuss how it can be used to give a longitudinal pseudodifferential calculus for such leaf spaces and develop an index theory.
Jun 30	Wed	Saniago Zarzuela (University of Barcelona)	Pure Maths Colloquium
16:00		Apery and micro-invariants of a one-dimensional Cohen-Macaulay rings and invariants of its tangent cone
		Hicks Seminar Room J11
	Abstract: Given a one-dimensional Cohen-Macaulay local ring we study and compare several families of invariants related with its tangent cone. When $A$ is equicharacteristic, Juan Elias introduced in $2001$ the set of micro-invariants of $A$ in terms of its first neighborhood ring. On the other hand, if $A$ is a one-dimensional complete equicharacteristic and residually rational domain, Valentina Barucci and Ralf Fröberg defined in $2006$ a set of invariants in terms of the Apery set of the value semigroup of $A$, and showed that both sets of invariants coincide if the tangent cone $G(A)$ is Cohen-Macaulay. We give a new interpretation for these sets of invariants that allow to extend them to any one-dimensional Cohen-Macaulay local ring. We compare these sets with the family of invariants recently introduced by Teresa Cortadellas and the speaker for the tangent cone of a one-dimensional Cohen-Macaulay local ring and give explicit formulas relating them. We show that, in fact, they coincide if and only if the tangent cone $G(A)$ is Cohen-Macaulay. Some explicit computations will also be given, particularly for the case of semigroup rings.
Sep 28	Tue	Paul Mitchener (Sheffield)	Topology Seminar
13:45		KK-theory spectra and assembly
		Hicks Seminar Room J11
	Abstract: The plan is to introduce assembly maps in various settings (including both algebraic and analytic K-theory) and general classification results involving assembly maps. The analytic assembly map is classically defined in terms of KK-theory, and needs some work to express in a way where the classification machinery can be used. I will explain this process. As time permits, I will also show how the homotopy algebraic K-theory assembly map, which is usually defined with the general machinery, can be expressed in terms of the bivariant algebraic KK-theory developed by Cortinas and Thom. This is useful for computations.
Sep 29	Wed	Saul Schleimer (Warwick)	Pure Maths Colloquium
16:00		Algorithmic topology
		Hicks Seminar Room J11
	Abstract: The three-sphere recognition problem dates to Poincare's pioneering work in ``analysis situs''. The unknot recognition problem is even older and in some sense predates topology itself. I will give an elementary introduction to the work of Haken and Rubinstein on these problems, ending with a discussion of their computation complexity.
Sep 30	Thu	Kostas Triantafyllopoulos (Sheffield)	Statistics Seminar
14:00		Multivariate stochastic volatility modelling using Wishart autoregressive processes
		Lecture Theatre 6
	Abstract: This talk will discuss some of the research I conducted while in study leave. In particular a new multivariate stochastic volatility estimation procedure for financial time series will be developed. A Wishart autoregressive process is considered for the volatility precision covariance matrix, for the estimation of which a two stage procedure is adopted. In the first stage conditional inference on the autoregressive parameters is developed and the second stage develops unconditional inference, based on a Newton-Raphson iterative algorithm. The proposed methodology, suitable for medium dimensional data, bridges the gap between closed-form estimation and simulation-based estimation algorithms in stochastic volatility modelling. Two examples, consisting of foreign exchange rates data and of data from the common constituents of the Dow Jones 30 Industrial Average index, illustrate the proposed methodology; for both examples we discuss asset allocation using as performance indicator mean-variance portfolio optimization. In this talk we will discuss Wishart processes, which may be of interest in their own right or targeting other than financial applications.
Oct 5	Tue	Boris Botvinnik (Oregon)	Topology Seminar
14:00		The moduli space of generalized Morse functions
		Hicks Seminar Room J11
Oct 6	Wed	Steve Donkin (York)	Pure Maths Colloquium
16:00		Geometry and representation theory
		Hicks Seminar Room J11
	Abstract: A survey of the relationship between the geometry of varieties associated to algebraic groups and representation theory of the group - mostly historical but, in particular mentioning the solution of Hilbert's 14th problem (in invariant theory of reductive groups) but coming up to date with some concrete calculations of cohomology groups of line bundles via representation theory.
Oct 7	Thu	Andrew Baker (Glasgow)	Topology Seminar
15:05		Galois theory for Lubin-Tate cochains on classifying spaces
		Hicks Seminar Room J11
	Abstract: I'll discuss some results on Galois theory of the extension of Lubin-Tate cochain spectra $$E^{BG} = F(BG_+,E) \to F(EG_+,E) \equiv E,$$ where $E$ is a Lubin-Tate spectrum and $G$ is a finite group. In contrast to the case of $F(BG_+,HF_p)$, it turns out that this is always a faithful extension, but not always Galois.
Oct 8	Fri	Brad Hindman (JILA, University of Colorado, Boulder, CO 80309-0440, USA)
13:05		Using eigenfunction phases to measure deep meridional circulation
		Lecture Theatre 5
	Abstract: A steady meridional flow makes only a second-order shift to the Sun's p-mode frequencies while producing a first-order distortion in the p-mode eigenfunctions. In particular, the flow induces latitudinal variation in the eigenfunction's phase. We suggest a technique to extract the meridional flow by detailed measurement of this phase variation. Using a simple toy model we estimate and illustrate the viability of detecting and measuring meridional flow deep in the convection zone using the suggested procedure.
Oct 12	Tue	Richard Hepworth (Copenhagen)	Topology Seminar
14:00		Higher categories and configuration spaces
		Hicks Seminar Room J11
	Abstract: Joyal introduced categories $\Theta_n$ in order to define a theory of `weak n-categories'. These $\Theta_n$ also appear in Rezk's recent approach to the same question. This talk will report on joint work with David Ayala, where we show how the $\Theta_n$ encode combinatorial models for configuration spaces of points in $\mathbb{R}^n$. If time permits then I will describe some ambitions regarding Lurie's topological chiral homology.
Oct 13	Wed	Jamie Douglas (Sheffield)	Applied Mathematics Colloquium
14:00		Linear eigenspectra in tokamak fusion plasmas
		tbd
	Abstract: Nuclear fusion has become one of the "hot" topics in recent years, with the likes of Prof. Stephen Hawking and Prof. Brian Cox offering their own perspective on the issue (see below). Although many of the applied mathematical and theoretical physics aspects of maintaining a fusion plasma are well understood, some aspects of linear theory remain unexplored. Using the CUTIE tokamak fusion plasma simulation code developed at the Culham Science Centre, which has successfully reproduced many nonlinear features of tokamak plasmas, we are now investigating the linear properties of these plasmas. This seminar will cover an introduction to nuclear fusion, tokamak reactors and the CUTIE code, before outlining some of the linear modes we have investigated using a linear version of the CUTIE code which employs two new techniques for finding linear modes: the resolvent eigenvalue technique which reveals the entire linear spectrum; and the nonlinearisation technique for finding the dominant linear mode. \par Prof. Stephen Hawking, quoted in the Guardian newspaper 11th September 2010: "Nuclear fusion...would provide an inexhaustible supply of energy without pollution or global warming. Many badly needed goals, like fusion and cancer cures, would be achieved much sooner if we invested more." \par Prof. Brian Cox quoted in the same article: "The provision of clean energy is of overwhelming importance. What frustrates me is that we know how to do [fusion] as physicists, and how it works. It is an engineering solution that is within our grasp. I think the most important practical problem, which may be more of an engineering challenge than a scientific one, is to build economically viable nuclear fusion power stations. If we haven't dealt with our world's increasing appetite for energy by the end of this century, I think we will be in very deep trouble indeed."
Oct 13	Wed	Ed Segal (Imperial College, London)	Pure Maths Colloquium
16:00		Landau-Ginzburg models in algebraic geometry
		Hicks Seminar Room J11
	Abstract: A lot of progress in algebraic geometry has been made from the discovery that the derived category of sheaves on a variety describes the branes in a particular topological field theory associated to that variety. I'll try and explain roughly what all of these words mean, and then describe how a more general field theory leads to a generalization of the derived category. I'll then tell you some of the things you can do with this generalization, and in particular how it links to the matrix factorizations studied in algebraic singularity theory.
Oct 15	Fri	Rekha Jain (Sheffield)
13:05		Axisymmetric Scattering (and Absorption) of p Modes by a Thin Magnetic Flux Tube
		Lecture Theatre 9
	Abstract: The buffeting action of the solar acoustic waves (p-modes) excites MHD tube waves. The propagation of these tube waves along the length of the tube creates a back reaction on the field-free fluid surrounding the tube, generating outgoing scattered wave field. I will present a calculation of the far-field scattering matrix for the special case of axisymmetric, vertically oriented, thin, magnetic flux tube. Our ultimate goal is to model the absorption and scattering of acoustic waves by magnetic plages. However, the first step in this future line of inquiry is the calculation of the scattering matrices (both near- and far-field) for a stratified single magnetic flux tube. The work presented will be one piece of many required to accomplish this goal.
Oct 19	Tue	Eugenia Cheng (Sheffield)	Pure Maths Postgraduate Seminar
12:00		Introduction to operads and loop spaces
		Hicks Seminar Room J11
	Abstract: One of the basic ways of producing algebra from topology is the fundamental group, whose elements are homotopy classes of loops. However, if we wish to avoid quotienting out by homotopy we need a more subtle construction to deal with the fact that concatenation of loops is not associative. Operads provide a convenient way of keeping track of the resulting algebra which is only associative ``up to homotopy''. In this talk we will introduce operads as a way of handling operations of different arities. We will explain how operads can be used to recognise when a given space ``is'' a loop space, that is, the space of loops of another space. Finally we will discuss how operads can be regarded as algebraic theories of a specific kind which does not admit the theory of groups. As loop spaces are ``groups up to homotopy'' this means that operads cannot be used to define the whole theory of loop spaces.
Oct 19	Tue	Kijti Rodtes (Sheffield)	Topology Seminar
14:00		Real connective K theory of finite groups
		Hicks Seminar Room J11
	Abstract: Real connective K theory of finite groups, $ko_{*}(BG)$, plays a big role in the Gromov-Lawson-Rosenberg (GLR) conjecture. To calculate it, we can proceed in several ways, e.g., by using the Atiyah-Hirzbruch spectral sequence, by the Adams spectral sequence or by the Greenlees spectral sequence (GSS). However, it is evident that the lattermost way, GSS, is very powerful and suitable for tackling the GLR conjecture. In this talk, we will show how to compute real connective K theory by using Bruner-Greenlees methods.
Oct 20	Wed	Peter Haynes (Cambridge)	Applied Mathematics Colloquium
14:00		What controls the rate of mixing of passive scalars in smooth flows?
		LTA
	Abstract: Stirring and mixing of chemical and biological species is an important in atmospheric and oceanic flows and in many other contexts. Some aspects of stirring and mixing can be captured by 'Lagrangian stretching theories' which essentially consider evolution in small fluid elements in which the flow may be approximated as a linear function of space coordinates, but time varying. This is a great simplification to solving the full advection-diffusion equation and potentially gives a practical approach to calculation. It also motivates an examination of whether 'Lagrangian stretching theories' are always correct. Solution of a suitable idealised problem shows that Lagrangian stretching theories make correct predictions (for an initial value problem) if the advection diffusion operator, which always has a continuous spectrum in the limit of vanishing diffusivity, has no discrete eigenvalues.
Oct 20	Wed	Neil Ghani (Strathclyde)	Pure Maths Colloquium
16:00		Induction principles, all the time (...or how I fell in love with fibrations)
		Hicks Seminar Room J11
	Abstract: We all learned about induction for proving properties of natural numbers at school. But what about other data types such as lists -- do they have induction principles? And what exactly are properties and can we use induction for different notions of properties. Finally, if we work in categories other than the category of sets, do we still have induction principles? In this talk I'll show that, indeed, we can have induction principles parameterised by the category we work in, the data type we are interested in and the notion of property under consideration. These results arise from a very beautiful picture of induction if one will willing to consider the topic within a fibrational setting.
Oct 21	Thu	Lauren Rodgers (Forensic Science Service)	Statistics Seminar
14:00		A continuous model for deconvoluting DNA mixtures
		Lecture Theatre 6
	Abstract: There are numerous problems encountered in the interpretation and evaluation of DNA profiles, particularly when there is more than one contributor. The current statistical methods are based on binary models and make limited use of the quantitative information contained in the profile. We have developed a continuous model which can probabilistically take account of allelic dropout, allelic stutter and the amplification efficiency of allele given molecular weight. This presentation will include: on overview of DNA profiling; a description of our proposed continuous model; and some illustrative calculations with DNA mixtures.
Oct 22	Fri	Giuseppe Colantuono (Italy)
13:05		Effect of stratification and background flow on the frequency of bounded Rossby modes with topography
		Lecture Theatre 9
Oct 26	Tue	Timothy Eardley (Sheffield)	Pure Maths Postgraduate Seminar
12:00		Elliptic curves with complex multiplication
		Hicks Seminar Room J11
	Abstract: Elliptic curves are naturally an algebraic geometric object, but despite this there are many number theoretic questions they can provide answers for. The eventual aim of this talk is to discuss one of these remarkable uses: that certain elliptic curves over the complex plane can be used to generate the maximal abelian unramified extension of a quadratic imaginary number field. However, first we will start from scratch by introducing elliptic curves in the most the most natural way, describing them by Weierstrass equations and indicating their group structure. We will then discuss the group endomorphisms in order to state our main result, hinted at above.
Oct 26	Tue	David Barnes (Sheffield)	Topology Seminar
14:00		Monoidality of Exotic Models
		Hicks Seminar Room J11
	Abstract: The category of $K_{(p)}$-local spectra is an important approximation to the stable homotopy category that is somewhat easier to study. When p=2 this category is rigid, that is, all of the higher homotopy information of $K_{(2)}$-local spectra is contained in the triangulated structure of the homotopy category. For $p=3$ this is not true, as well as $K_{(3)}$-local spectra there is the exotic model of Franke. The homotopy category of this exotic model has the same triangulated structure as $K_{(3)}$-local spectra, but arises from a different homotopy theory. This talk will report on joint work with Constanze Roitzheim, where we show how to define a monoidal product for this exotic model, relate it to the smash product of $K_{(3)}$-local spectra and then compute the Picard group of the exotic model.
Oct 27	Wed	Tobias Berger (Sheffield)	Pure Maths Colloquium
16:00		Special values of $L$-functions
		Hicks Seminar Room J11
	Abstract: Since Euler we know that the value of the Riemann zeta function at non-positive integers is a rational number. Do these values have any meaning? The Bloch-Kato conjectures answer this question more generally for values of so-called L-functions. I will give an introduction to the conjectures and explain a strategy first employed by Ribet that continues to yield new results towards them.
Oct 28	Thu	Richard Boys (Newcastle)	Statistics Seminar
14:00		Linking systems biology models to data
		Lecture Theatre 6
	Abstract: This talk considers the assessment and refinement of a dynamic stochastic process model of the cellular response to DNA damage. The proposed model is a complex nonlinear continuous time latent stochastic process. It is compared to time course data on the levels of two key proteins involved in this response, captured at the level of individual cells in a human cancer cell line. The primary goal of is to "calibrate" the model by finding parameters of the model (kinetic rate constants) that are most consistent with the experimental data. Significant amounts of prior information are available for the model parameters. It is therefore most natural to consider a Bayesian analysis of the problem, using sophisticated MCMC methods to overcome the formidable computational challenges.
Oct 29	Fri	Jamie Douglas (Sheffield)
13:05		Linear eigenspectra in tokamak plasmas: advanced theory
		Lecture Theatre 9
	Abstract: Following from the recent Applied Maths seminar on the same topic, we delve deeper into the theory of the underlying plasma physics and numerical methods used in solving the linear systems governing tokamak plasmas. Under investigation are: the presence of Alfven waves and tearing modes in resistive MHD systems; the introduction of nontrivial mean density gradients leading to drift waves and drift instabilities; ion sounds waves in the four field model of Hazeltine [Phys. Fluids 28, 1985]; and extensions including the effects of ion temperature and toroidal curvature. The resolvent eigenvalue method for revealing linear spectra and the nonlinearisation method for finding the dominant mode are expounded in more detail.
Nov 2	Tue	Nadia Gheith (Sheffield)	Pure Maths Postgraduate Seminar
12:00		Introduction to Coarse Geometry and Coarse Invariants
		Hicks Seminar Room J11
	Abstract: We introduce the notion of coarse geometry, which is the study of the very large scale properties of metric spaces. This is in contrast to topology, which studies small scale properties. We begin by defining coarse maps between spaces, and coarse equivalence, with some examples. We then define geodesics and geodesic rays in order to define the "ends" of spaces, which is a first example of a coarse invariant. Finally we will show how to associate a proper geodesic space to any group, enabling us to define ends of groups. We will give a classification theorem for finitely-generated groups, and illustrate it with some easily visualised examples.
Nov 2	Tue	Sarah Whitehouse (Sheffield)	Topology Seminar
14:00		Central cohomology operations and $K$-theory
		Hicks Seminar Room J11
	Abstract: In various contexts $K$-theory operations can be shown to map to operations of other cohomology theories, in such a way that the image of this map is precisely the centre of the target ring. I will discuss some results of this sort, both old and new, including joint work with Imma GÁlvez and M-J Strong.
Nov 3	Wed	Joel Weller (Sheffield)	Applied Mathematics Colloquium
14:00		Cosmological inflation with a Dirac-Born-Infeld field
		LTA
	Abstract: Our understanding of the cosmos is underpinned by precision observations on very large and very small scales, and theoretical models must not only be well-motivated but also consistent with the wealth of data available. The inflationary paradigm, in which the universe experiences a period of rapid expansion early in its history, stands as a crowning example of this principle, in that it leaves observable traces in the distribution of structure on large scales and the cosmic microwave background (CMB) radiation that can be explained in terms of the microscopic quantum fluctuations of the field(s) driving inflation. The availability of high precision observational data in cosmology means that it is possible to go beyond the simple descriptions of cosmic inflation in which the expansion is driven by a single scalar field. One set of models of particular interest involve the Dirac-Born-Infeld (DBI) action, arising in string cosmology, in which the dynamics of the field are affected by a speed limit in a manner akin to special relativity. In this talk, I will discuss how the problems faced by the standard hot big bang model are resolved by introducing an inflationary period, and describe the mathematical treatment of the standard and DBI scenarios.
Nov 3	Wed	Misha Belolipetsky (Durham)	Pure Maths Colloquium
16:00		On volumes of arithmetic quotients of hyperbolic $n$-space
		Hicks Seminar Room J11
Nov 4	Thu	Eugenia Cheng (Sheffield)	Category Theory
16:10		A multisimplicial approach to higher-dimensional categories (I)
		Hicks Seminar Room J11
	Abstract: We will begin a series on the multisimplicial nerve definition of n-category by Simpson/Tamsamani. We will start by talking about nerves of ordinary categories/groupoids, and the non-algebraic notion of fundamental groupoid that this gives.
Nov 5	Fri	Viktor Fedun (Sheffield)
13:05
		Lecture Theatre 9
Nov 9	Tue	Bob Bruner (Wayne State )	Topology Seminar
14:00		Ossa's theorem, Pic(A(1)) and generalizations
		Hicks Seminar Room J11
	Abstract: Ossa's calculation of the complex connective K-theory of classifying spaces of elementary abelian groups depends upon the idempotence of a particular module over the exterior algebra on two generators. For the real connective K-theory, the algebra is more subtle. We give a particularly simple way to understand it, and relate the results to two localizations of the category of A(1)-modules and their Pic groups. I will end with comments and conjectures about higher analogs.
Nov 10	Wed	Ashley Willis (Sheffield)	Applied Mathematics Colloquium
14:00		Charting the phase-space of transitional fluid flow
		LTA
	Abstract: In 1883, Reynolds observed a transition from laminar to turbulent flow in a pipe. Although more than 125 years have passed, fundamental questions on the nature of this transition remain. All evidence to date suggests that laminar pipe flow (Hagen Poiseuille flow) is linearly stable, but it has only been proved rigorously for special cases. At the modest flow rates examined by Reynolds, it is now clear the finite amplitude disturbances to the laminar are required to trigger the transition to turbulence. Recently, a host of finite-amplitude solutions for pipe flow has been discovered (Faisst & Eckhart 2004; Pringle, Duguet & Kerswell 2008). While a few have been shown to be embedded within the 'laminar-turbulent boundary', the role of the vast majority of solutions is yet to be determined. In this talk, evidence for the appearance of travelling waves during transition is presented, plus a method for projection of the underlying dynamics.
Nov 11	Thu	Various Local Statisticians (GSS, Sheffield, Leeds )	RSS Seminar
10:30		White Rose Statistics
		Jury's Inn, Sheffield, S1 4QW
	Abstract: The Sheffield and Leeds/Bradford local groups of the RSS and the Sheffield Government Statistical Service will be hosting a day of talks focussing on a range of work being undertaken in the region. The day will include a one-hour seminar by Jil Matheson and a series of fifteen minute talks in 3 parallel sessions, with titles including - Methodology for estimating the stock of UK businesses; Data Disclosure - what can we do to protect our data?; Financial and volumetric scenario models to underpin policy; Developments in FE statistics; Using ONS Productivity data to evaluate training programmes; The DWP Customer Map: who our customers are How DWP data is used - improvements to migration statistics; Transparency: responding to the challenge within Education; Attainment outcomes of looked after children - matched data; Longitudinal Study of Young People in England; Developing new statistical sources through data matching; Using NHS audit data for research; Top ten rules for obscuring the message with poor data display; Experiences of a statistician on a NICE appraisal committee
Nov 11	Thu	Jil Matheson (National Statistician & Chief Executive of the UK Statistics Authority)	RSS Seminar
14:00		White Rose Statistics
		Jury's Inn, Sheffield, S1 4QW
Nov 12	Fri	Michael Balikhin (m.balikhin@googlemail.com)
13:05
		Lecture Theatre 9
Nov 16	Tue	Philip Eve (Sheffield)	Pure Maths Postgraduate Seminar
12:00
		Hicks Seminar Room J11
Nov 17	Wed	Edmund Ryan (Sheffield)	Applied Mathematics Colloquium
14:00		Improving estimates of atmosphere-land carbon flux by assimilating satellite observations of biomass
		LTA
	Abstract: There are large uncertainties in estimates of the atmosphere-land exchange of carbon by natural processes (photosynthesis and respiration). Accurate estimates are crucial for better understanding of the global carbon cycle and climate modelling. Traditonally the models we use to get these estimates are tested for their ability to reproduce real-life processes by comparing model output with observations. However, a more useful way of using the observations, which takes into account the observational error, is to assimilate the observations into the model. This is called Data Assimilation or DA. We can use DA to estimate the states of the system or to estimate some or all of the parameters to the model. While DA has been generally performed on small models, some recent work is using it on the larger ones for example JULES (Joint Uk Land Surface Simulator) which is the land part to the climate model used by the met office. However, up till now, DA has been mainly carried out using ground observations. In this PhD, I am exploring the value of using satellite observations instead, due to the major advantages such observations have over ground based ones (ie more frequent observations and more observations on the spatial scale).
Nov 17	Wed	Geordie Williamson (Oxford)	Pure Maths Colloquium
16:00		Categorification in representation theory
		Hicks Seminar Room J11
	Abstract: I will try to give an overview of the big machine called "categorification" with emphasis on applications in representation theory. Over the last thirty years it has been observed that interesting algebras (group algebras, Hecke algebras, enveloping algebras) act on Grothendieck groups of categories arising in representation theory. If one asks what structures act on the categories themselves one is led to consider categorifications of these algebras. It turns out that these categorifications often have a very rigid structure and lead to new insights in representation theory.
Nov 18	Thu	Piotr Fryzlewicz (London School of Economics)	Statistics Seminar
14:00		Haar-Fisz methodology for interpretable estimation of large, sparse, time-varying volatility matrices
		Lecture Theatre 6
	Abstract: The emergence of the recent financial crisis, during which many markets underwent changes in their statistical structure over a short period of time, illustrates the importance of non-stationary modelling in financial time series. We start this talk by advocating a simple non-stationary multivariate model for financial returns. One task of critical importance to a financial analyst is accurate estimation of the volatility matrix, and in our model, this will be a time-varying quantity. Our estimation method is based on Haar wavelet thresholding, supplemented with the essential variance-stabilising Fisz transform (hence the name Haar-Fisz). Thanks to the use of Haar wavelets, our estimator: (a) has a natural in-built sparsity, i.e. local cross-market correlations are naturally estimated as zero wherever possible, which enhances the invertibility of the estimated matrix; (b) adequately captures sudden regime changes; (c) is theoretically tractable, also in the pointwise sense; (d) is rapidly computable, which is important if the matrix is large. In addition, we take advantage of the non-linearity of wavelet thresholding to propose two distinct version of the estimator, one of which is based on the polarisation identity. We use real-data examples to illustrate our methodology.
Nov 19	Fri	Andrew Gascoyne (Sheffield)
13:05
		Lecture Theatre 9
Nov 23	Tue	Thomas Cottrell (Sheffield)	Pure Maths Postgraduate Seminar
12:00		Simplicial sets and the nerve construction
		Hicks Seminar Room J11
	Abstract: Every category has an underlying graph, which contains the underlying data of the category, but gives no information about the composition, identities and axioms of the category. A simplicial set is a more expressive structure that is able to capture this extra information. Every (small) category has an underlying simplicial set, called its nerve. Furthermore, maps between these nerves correspond exactly to functors between categories. I will begin this talk by discussing order-preserving maps between finite totally-ordered sets, and this will lead to two definitions of simplicial set: one a categorical definition, the other an explicit combinatorial construction. I will then give the construction for the nerve of a category, and explain how to characterise those simplicial sets that arise as nerves. This gives rise to an alternative definition of category, and this definition can be generalised to higher dimensions, which is one of our motivations for thinking of categories in this way.
Nov 23	Tue	Eugenia Cheng (Sheffield)	Topology Seminar
14:00		Distributive laws for Lawvere theories
		Hicks Seminar Room J11
	Abstract: Lawvere Theories and monads are two ways of handling algebraic theories. They are related but subtly different; one way in which they differ is that models for a given Lawvere Theory can automatically be taken in many different base categories, whereas monads have a fixed base category. Distributive laws give a way of combining two algebraic structures expressed as monads, so one might naturally ask whether something analogous can be done for Lawvere Theories. In this talk I will give a way of doing this, using a reformulation of Lawvere Theories that is of interest in its own right. I will also discuss an illuminatingly wrong way of doing it. I will not assume any prior knowledge of Lawvere Theories, so the first part of the talk will serve as an introduction to these things.
Nov 24	Wed	Nils Mole (Sheffield)	Applied Mathematics Colloquium
14:00		Modelling the moments of the expected mass fraction for a line source in decaying grid turbulence
		LTA
	Abstract: To assess hazards resulting from dispersing clouds or plumes of toxic or flammable gases, one would like to know the probability density function (pdf) of concentration, including its dependence on space and time. The expected mass fraction (EMF) provides a space-integrated equivalent of the pdf. Here I develop a model for the moments of the EMF, which I apply to the particular case of a plume dispersing from a steady line source in decaying grid turbulence. The results will be compared with measurements from some laboratory experiments in wind and water tunnels.
Nov 24	Wed	Behrang Noohi (King's College, London)	Pure Maths Colloquium
16:00		Topological stacks, and some applications
		Hicks Seminar Room J11
	Abstract: We give a non-technical introduction to differentiable/topological stacks and discuss some old and new results. Along the way we provide plenty of examples and give some concrete applications of these results.
Nov 25	Thu	Samuel Touchard (Sheffield)	Statistics Seminar
14:00		Forecasting pollution levels using Dynamic Linear Models
		Lecture Theatre 6
	Abstract: In this talk, I will try to forecast the pollution levels of 5 five pollutants, from 8 years data. The model I used is a Dynamic Linear Model (DLM), a regression model where the parameter vector is no longer assumed constant over time. Also, 3 covariates (humidity, temperature, wind speed) will be used to get a better estimation. After introducing the issue of pollution, I will describe the model, in the univariate case first, and in the multivariate case afterwards. Then, I will apply this model to the data, do some comments about the results, how it would be possible to improve it, and give some ideas for further work.
Nov 26	Fri	Richard Morton (Sheffield)
13:05		Sausage Oscillations in Magnetic Pores
		Lecture Theatre 9
	Abstract: A large number of waves and oscillations observed throughout the solar atmosphere are thought to occur due to driving mechanisms in the solar interior and solar photosphere, e.g. p-modes, granular buffeting. It is important to assess how the wave energy generated in the solar interior/photosphere is transported and dissipated in the higher layers of the solar atmosphere, as the wave energy is thought to be one of the main mechanisms responsible for the heating and the dynamics observed in the transition region and corona. Recent advances in ground-based instruments and analysis techniques has paved the way for high spatial resolution and high cadence observations of the lower solar atmosphere. It is now possible to study wave phenomena occurring in some of the smallest known magnetic features, e.g. magnetic bright points. We present here high cadence observations of the sausage oscillations occurring in magnetic pores. We are able to identify the oscillations using a relatively new analysis technique (with respect to solar applications) known as Empirical Mode Decomposition (EMD).
Nov 28	Sun	Jacob Rasmussen (Cambridge)	Topology Seminar
15:00
		Hicks Seminar Room J11
Nov 28	Sun	Jacob Rasmussen (Cambridge)	Topology Seminar
15:00
		Hicks Seminar Room J11
Nov 30	Tue	Nick Gurski (Sheffield)	Topology Seminar
14:00		Two-dimensional braids
		Hicks Seminar Room J11
	Abstract: Braids occur naturally in topology, category theory, and other fields like representation theory, and the basic theory of the braid groups could be considered classical. On the other hand, "two-dimensional braids" are much newer objects of study that seem to arise from far more complicated algebra. In this talk I will introduce the study of two-dimensional braids using category theory, topology, and geometry, and will explain how the interactions between these various fields helps to show that the algebra of two-dimensional braids is actually simpler than it first appears.
Dec 1	Wed	Katrin Leschke (Leicester)	Pure Maths Colloquium
16:00		Transformations of constant mean curvature surfaces
		Hicks Seminar Room J11
	Abstract: In classical surface theory, transformations have been used to locally construct surfaces out of given simple ones by replacing a PDE which describes a certain surface class by an ODE or a simpler PDE which describes the transformation. In my talk, I will explain two transformations of constant mean curvature surfaces: the simple factor dressing is linked to a harmonicity condition, whereas the Darboux transformation uses that the surface is isothermic. In the case of constant mean curvature surface these two transformations are the same; in particular, these transformations also give global information, e.g., points of the spectral curve of a constant mean curvature torus are given by simple factor dressing of the torus.
Dec 2	Thu	Andrew Parnell (University College Dublin)	Statistics Seminar
14:00		Faster joint posterior modelling through marginal posterior mixtures
		Lecture Theatre 6
	Abstract: We discuss the issue of creating a joint posterior distribution for a set of parameters when only marginal posteriors are available (or are reasonable to compute). More specifically, for data '$x$ and parameters $\theta$ in $R^n$, we require $\pi(\theta|x)$ from the marginal data posterior $\pi(\theta_i|x_i)$. Through a simple adjustment of Bayes' theorem we can use $\pi(\theta_i|x_i)$ to inform the joint posterior, provided $\pi(\theta_i)$ and $\pi(\theta)$ (the marginal and joint priors, respectively) are, in some sense, compatible. \par The technique can be further enhanced by treating $\pi(\theta_i|x_i)$ as a mixture of distributions conjugate to the joint prior. In most cases, it is trivial to approximate any marginal posterior distribution as such a mixture. When the joint prior is Gaussian, the resulting posterior can then be obtained extremely quickly via any one of a number of standard Bayesian computational techniques. \par We apply this technique to two problems in palaeoclimatology (both described in Haslett et al 2006). The first involves long-tailed random walk smoothing of temporal climate histories ($c(t)$) created from pollen sediment cores where pollen is sampled at $n$ layers $y_i$, $i=1, . . . , n$. The marginal posteriors $\pi(c_i|y_i)$ are easily obtained by other means, whereas the random walk gives flat marginal prior distributions $\pi(c_i)$. We obtain the joint prior $\pi(c|y)$ in a twostage process without resorting to more burdensome computational methods. The second problem involves spatial forward modelling of pollen changes given modern climate data (also known as response surface modelling; Huntley et al 1993). Here, the marginal posteriors are Gaussian surfaces with few hyperparameters; they are relatively quick to create. The joint posterior surface then becomes a mixture of Gaussian processes. Again, the two-stage process dramatically decreases the computational burden, and allows for parallelisation. The models we propose have much in common with Rue et al (2009) and Holmstrom and Erasto (2002). The technique seems widely applicable across the field of statistical modelling. We explore some of the extensions which may allow for higher dimensional models or more complex prior distributions.
Dec 3	Fri	Ashley Willis (Sheffield)
13:05
		Lecture Theatre 9
Dec 7	Tue	Shabieh Farwa (Sheffield)	Pure Maths Postgraduate Seminar
12:00		The Riemann-Roch Theorem
		Hicks Seminar Room J11
	Abstract: Given a curve C over a field K, the meromorphic functions on the curve are the ratios of holomorphic functions, and they form a vector space. Knowing the dimension of this vector space is of great importance in complex analysis and algebraic geometry. The Riemann-Roch Theorem is a tool for the computation of the dimension of this space. In this talk, first of all I will explain the importance of this theorem by the example of correction of errors occurring during the transmission of data. I will then state the theorem without proof. The theorem uses the notions of "canonical divisor", "degree of a divisor" and "genus of a curve"; I will explain these terms with some examples, and state some important properties of them. Finally I will illustrate how the Riemann-Roch Theorem applies to the projective line, which has particular importance in error-correction for data stored on CDs and DVDs.
Dec 7	Tue	John Hunton (Leicester )	Topology Seminar
14:00		What is an attractive shape?
		Hicks Seminar Room J11
	Abstract: Suppose we have a differentiable manifold M with a self diffeomorphism yielding an expanding, hyperbolic attractor A. What can we say about the topology of A? In the case that A is of codimension 1 in M, we show that A can be modeled as a moduli space of an aperiodic tiliing and, conversely, we obtain conditions for when a tiling space can be embedded nicely in a manifold. These results give insights into the shape of such attractors, and new topological invariants for tilings, finer than the usual cohomological tools used in the subject.
Dec 8	Wed	Kirill Mackenzie (TBC) (Sheffield)	Pure Maths Colloquium
16:00
		Hicks Seminar Room J11
Dec 9	Thu	Alison Etheridge (Oxford)	Statistics Seminar
14:00		Modelling evolution in a spatial continuum: the spatial $\Lambda$-Fleming-Viot process
		Lecture Theatre 6
	Abstract: One of the outstanding successes of mathematical population genetics is Kingman's coalescent. This provides a simple and elegant description of the genealogical trees relating individuals in a sample of neutral genes from a panmictic population, that is, one in which every individual is equally likely to mate with every other and all individuals experience the same conditions. But real populations are not like this. Spurred on by the recent flood of DNA sequence data, an enormous industry has developed that seeks to extend Kingman's coalescent to incorporate things like variable population size, natural selection and spatial and genetic structure. But a satisfactory approach to populations evolving in a spatial continuum has proved elusive. In recent joint work with Nick Barton, IST Austria, we introduced a framework for modelling the evolution of populations distributed in a spatial continuum. This leads to a new class of measure-valued processes which we will describe and, as time permits, explore in this talk.
Dec 10	Fri	David Robertson (Sheffield)
13:05
		Lecture Theatre 9
Dec 14	Tue	Nige Ray (Manchester)	Topology Seminar
14:00		Toric methods in cobordism theory
		Hicks Seminar Room J11
	Abstract: I shall recall certain basic aspects of real and complex cobordism theory, and explain how toric and quasitoric manifolds have enriched the theory since 1986, albeit unwittingly at first. I shall also describe a conjecture concerning stably $SU$-structures. Finally, I shall discuss the universal toric genus for equivariant cobordism, and consider its values on omnioriented quasitoric manifolds. Most of this work is joint with Victor Buchstaber and Taras Panov, or due to Alastair Darby.
Dec 15	Wed	Ian Craig (Waikoto, New Zealand)
14:05		Exact models for magnetic reconnection in coronal plasmas
		LT A
	Abstract: An introduction to magnetic reconnection in coronal plasmas is given. Some exact analytic solutions are presented that describe recent 'fan' and 'spine' reconnection models.
Dec 15	Wed	Tom Fisher (Cambridge)	Pure Maths Colloquium
16:00		Families of $n$-congruent elliptic curves
		Hicks Seminar Room J11
	Abstract: Elliptic curves $E$ and $F$ are $n$-congruent if their $n$-torsion subgroups are isomorphic as Galois modules via an isomorphism respecting the Weil pairing. Rubin and Silverberg gave formulae for the families of elliptic curves $n$-congruent to a given elliptic curve for $n=2,3,4,5$. Formulae in the case $n=7$ are given by Halberstadt and Kraus. I will describe an invariant-theoretic approach to obtaining these formulae and use it to extend to the cases $n=9$ and $n=11$. There are corresponding formulae when the isomorphism of $n$-torsion subgroups does not respect the Weil pairing.
Dec 16	Thu	Grant Bigg (Sheffield)	Statistics Seminar
14:00		Using icebergs as a tool in geoscience: how did the needle get into the haystack?
		Lecture Theatre 6
	Abstract: Since the sinking of the Titanic in 1912, icebergs have possessed a powerful aura for polar navigation. However, they are not only a threat to shipping but tell us about climate change, and the sediments dropped from them are key indicators of past climate fluctuations around the globe. In this talk the science of icebergs is explored, paying particular attention to where it intersects with sometimes difficult statistical issues. The power of statistical-dynamical modelling of icebergs to reveal new and interesting facts about past and present climate change is shown. The statistical analysis of remote sensing images is seen to be a powerful tool for aiding navigation as the Arctic sea routes are opened up. And finally, the use of systems control theory will be seen to offer the possibility of a new view of the evolution of the Greenland ice sheet over the last century.
Jan 1	Sat	Ian (Waikato)	Applied Mathematics Colloquium
14:00		Exact models for magnetic reconnection in coronal plasmas
		tbd
	Abstract: An introduction to magnetic reconnection in coronal plasmas is given. Some exact analytic solutions are presented that describe recent 'fan' and 'spine' reconnection models.
Jan 1	Sat	Ata S Sharma (Sheffield)	Applied Mathematics Colloquium
14:00		Predicting structure in turbulence
		tbd
	Abstract: *Predicting structure in turbulence * How to find a simple model that predicts the important structural and statistical features of turbulence is a central unsolved problem in classical physics. Most commonly found flows are turbulent, for instance flow of air over an aeroplane wing or water past a ship's hull, flow of oil through an trans-continental pipeline, or the movement of the atmosphere. All these flows experience chaotic three-dimensional motion, but nonetheless show persistent, repeating structure. This talk will cover significant new advances, involving the application of systems-theoretic ideas to the equations governing turbulence, which predict these structures. The computationally cheap approach explains and predicts structures and velocity statistics that have previously been identified only in experiments or by direct numerical simulation. Short Biography: After graduating as a physicist from UCL, Dr Sharma completed his doctoral thesis in control engineering at Imperial College, London on the modelling and control of tokamak nuclear fusion reactors. Following two years in industry, he returned to academia as a postdoc to work on fluid flow control, and was then awarded an Imperial College Junior Research Fellowship in that area. Dr Sharma joined ACSE as a lecturer in July.
Jan 26	Wed	Phil Livermore (Leeds)	Applied Mathematics Colloquium
14:00		Inviscid dynamos: evolving a magnetic field subject to a continuum of constraints
		LT A
	Abstract: The geomagnetic field is generated in Earth's liquid core by a dynamo process, a complex nonlinear system described by a collection of partial differential equations. In the last few decades, running numerical models of the geodynamo has become fairly widespread, although these are so complex and run with parameters so many orders of magnitude different from Earth's core that there remains large gap between the current state of the art and models that are defensibly realistic. Since 1963 it has been known how to model the slow time evolution of the geodynamo system with zero viscosity, arguably one of the the simplest realistic descriptions of the system. However, this limit has associated a continuum of constraints that the magnetic field must satisfy, a stumbling block that has hindered progress on this front for 48 years. In this talk, I shall summarise recent work that allows, on the adoption of a suitable numerical method, this continuum of constraints to collapse to a finite number and therefore admits the possibility of numerical models that evolve whilst simultaneously satisfying these constraints. I will describe some basic time evolution models that exploit these developments.
Feb 2	Wed	Sandra Chapman (Warwick)	Applied Mathematics Colloquium
14:00		Quantifying and understanding the statistical properties of turbulence -- what we have learned from the solar wind
		LTA
	Abstract: The solar wind exhibits fluctuations over a broad range of timescales characteristic of magnetohydrodynamic (MHD) turbulence evolving in the presence of structures of coronal origin. In- situ spacecraft observations of plasma parameters are at minute (or below) resolution for intervals spanning the solar cycle and provide a large number of samples for statistical studies. The magnetic field power spectrum typically has an inertial range of turbulence over several orders of magnitude with approximately Kolmogorov power law and at lower frequencies, an approximately '1/f' energy containing range believed to be of direct coronal origin and at higher frequencies, a kinetic range of turbulence. With a magnetic Reynolds number estimated to be of order 10^5 the solar wind provides a unique 'laboratory' for the study of MHD turbulence, and dissipation processes. Recent results however also suggest that in the ecliptic, signatures of scaling which are of direct coronal origin are embedded in the inertial range of turbulence of the solar wind, and as a consequence these show solar cycle and latitudinal dependence. At high latitudes, in uninterrupted streams of fast solar wind flow, and with recent high cadence observations of coronal structures there is the opportunity to study evolving finite range turbulence which can also inform our understanding of turbulence in boundary layers. This talk will survey quantitative statistical methods that can be used to distinguish these distinct physical processes in the solar wind and offer connections to a wider class of nonlinear systems approaches.
Feb 9	Wed	Jesse Andries (Monash)	Applied Mathematics Colloquium
14:00		Some theoretical considerations on magnetohydrodynamical waves in shear flows
		LT A
	Abstract: The theoretical foundation of the study of linear MHD waves and instabilities in stationary equilibria, is much less developed than its counterpart in static equilibria. For static equilibria a sound theory is based on the eigenmodes of a self-adjoint force operator, which can be equivalently expressed by a variational principle (Rayleigh-Ritz) for the quadratic potential energy functional. Such an approach seems impossible for stationary equilibria. While some relations between the eigenfrequencies and a number of quadratic functionals have long been known (Frieman and Rotenberg, 1960), those do not straightforwardly allow to construct a corresponding variational principle. Attempts so far involved the generalisation to a bilinear functional (where the energy interpretation is absent), and the associated doubling of the dimensionality of the variational space, or the assumption of some symmetry in the equilibrium. We will discuss the central problem and show that, contrary to what is often believed and claimed, many results do generalise to stationary media (shear flows). In particular, we focus on the clear interpretation of the energy functionals as they appear in a generalised variation principle that we formulated recently (Andries 2010, Physics of Plasmas, 17, 2106).
Feb 9	Wed	Sanju Velani (York)	Pure Maths Colloquium
16:00		Diophantine approximation: the Lebesgue and Hausdorff theories.
		Hicks Seminar Room J11
Feb 10	Thu	Kevin McConway (Open University)	RSS Seminar
16:30		Statistics and the Media
		Hicks Room LTA
	Abstract: When it comes to statistics, statisticians often think of the media and journalists as a hotbed of confusion, distortion and, well, damned lies. These beliefs are not entirely baseless - there is some appalling nonsense out there - but there is good statistical journalism too. The talk draws on the speaker's experience as a statistician of working with print and broadcast journalists, and in particular in collaborating on the BBC Radio 4 series "More or Less". It will discuss and give examples of what can go wrong and what can go right. Good journalists are better communicators than are most statisticians; if we want to get our ideas and research findings into the public consciousness, we need to learn from journalism and we need to learn how to work with journalists and the media. Can that be done without compromising our principles?
Feb 15	Tue	Nadia Gheith (Sheffield)	Pure Maths Postgraduate Seminar
12:00		Model categories
		Hicks Seminar Room J11
	Abstract: A model category is a technical structure that helps us to understand homotopy theory abstractly. The aim is to use the techniques of homotopy theory to study objects other than topological spaces, such as chain complexes, categories, or coarse spaces. In order to do this, we specify categorical structure that makes homotopy theory possible. In this talk we will begin by discussing some interesting properties of the category of topological spaces, as this is where homotopy theory is originally defined. We will use these to motivate the definition of model category, and sketch several examples of model category structures. Finally we will briefly discuss the example of coarse spaces, which is work in progress.
Feb 15	Tue	Harry Ullman (Sheffield)	Topology Seminar
15:00		The equivariant stable homotopy theory of isometries
		Hicks Seminar Room J11
	Abstract: Non-equivariantly, a space of linear isometries admits a stable splitting. In an equivariant setting, however, this does not generally happen. Instead, one can naturally build an equivariant stable tower with interesting topological properties similar to those exhibited by the non-equivariant splitting. We discuss this construction, while also mentioning obstructions to producing an equivariant splitting. Finally, we mention work-in-progress on retrieving a stable splitting from the tower in the special case where an equivariant splitting is possible.
Feb 16	Wed	Eduard Kontar (Glasgow)	Applied Mathematics Colloquium
14:00
		LTA
Feb 16	Wed	Michael Cowling (New South Wales)	Pure Maths Colloquium
16:00		Powers of Random Matrices
		Hicks Seminar Room J11
	Abstract: This talk is about random matrices. If we select an $n \times n$ orthogonal matrix $X$ ``at random'', using the uniform distribution on the orthogonal group $\mathrm{O}(n)$, then the powers of $X$ are not uniformly distributed in $\mathrm{O}(n)$. However, as $n$ increases, the distribution of $X^n$ stabilizes. We prove this, consider generalizations to matrices in other compact Lie groups, and make some remarks about random matrices in other Lie groups.
Feb 17	Thu	Mark Strong (University of Sheffield)	Statistics Seminar
14:00		Managing Structural Uncertainty in Health Economic Decision Models
		Lecture Theatre 6
	Abstract: It was George Box who famously wrote 'Essentially, all models are wrong'. Given our limited understanding of the highly complex world in which we live this statement seems entirely reasonable. Why then, in the context of health economic decision modelling, do we often act as if our models are right even if we know that they are wrong? Imagine we have built a deterministic mathematical model to predict the costs and health effects of a new treatment, in comparison with an existing treatment. The model will be used by NICE to inform the decision as to whether to recommend the new treatment for use in the NHS. The inputs to the model are uncertain, and we quantify the effect of this input uncertainty on the model output using Monte Carlo methods. We may even quantify the value of obtaining more information. We present our results to NICE as a fait accompli. But, if we believe George Box then surely we should consider that our model output, and our uncertainty analysis, and our estimates of the value of information are all 'wrong' because they are generated by a model that is 'wrong'! The challenge is to quantify how wrong. This seminar will explore the problem of structural uncertainty in health economic decision models, along with some suggested approaches to managing this uncertainty.
Feb 17	Thu	Siti Rahayu (University of Sheffield)	Statistics Seminar
14:30		Interpretation Methods of Multivariate Control Chart's Signal
		Lecture Theatre 6
	Abstract: Multivariate control charts have been the most popular tool among the quality control/process control researchers when it comes to multivariate processes monitoring. The impact of correlation among process variables on multivariate process performance, the problem of multiplicity in hypotheses testing and the difficulties in monitoring a large number of univariate control charts simultaneously can be solved readily by implementing a multivariate control chart. The only drawback of using a multivariate control chart is that once the out-of-control signal is triggered, the interpretation of the signal is potentially difficult. There are a number of interpretation methods have been proposed by researchers but so far all the methods give inconsistent results. Some of the interpretation methods will be introduced and the strength and the weaknesses will be discussed. A new approach will be introduced as another option for interpreting a multivariate control chart signal.
Feb 22	Tue	Magdalena Kedziorek (Sheffield)	Pure Maths Postgraduate Seminar
12:00		Mackey functors
		Hicks Seminar Room J11
	Abstract: Mackey functors were introduced in the 70's as a tool to study representations of finite groups via representations of their subgroups. In this talk we will present the notion of a Mackey functor together with the examples of the representation ring of a finite group G, and the Burnside Ring. We will finish by stating two "induction theorems" which tell us when we can use Mackey functors to understand the representations of G via a reasonably small family of its subgroups. The Artin theorem will use cyclic subgroups and the Brauer theorem will use elementary subgroups.
Feb 22	Tue	Simon Willerton (Sheffield)	Topology Seminar
15:00
		Hicks Seminar Room J11
Feb 25	Fri	James McLaughlin (School of Computing, Engineering and Information Sciences, Northumbria University,)
13:05		Nonlinear fast magnetoacoustic wave propagation in the neighbourhood of a 2D magnetic X-point: oscillatory reconnection
		Lecture Theatre 9
	Abstract: he work of McLaughlin et al. (2009) provides a link between two traditionally separate areas of solar physics: MHD wave theory and reconnection, and is one of the first demonstrations of reconnection naturally driven by MHD wave propagation. I shall introduce the topic, discuss the results of McLaughlin et al. (2009) and set the work in the larger context and general interest of wave-driven reconnection and reconnection generating wave-motions.
Mar 1	Tue	Laura Stanley (Sheffield)	Topology Seminar
15:00		Upper Triangular Technology for odd primary K-Theory
		Hicks Seminar Room J11
	Abstract: First published in 2002, Vic Snaith proved an isomorphism between a group of automorphisms of certain smash products of 2-complete connective K-Theory spectra and a group of infinite upper triangular matrices with entries in the 2-adic numbers. This would allow these infinite matrices to be used as a tool for studying maps of K-Theory spectra. Later, Snaith and his PhD student Jonathan Barker showed which matrix the Adams operation $\psi^3$ corresponds to under the isomorphism. In this talk I will present the results of my thesis which are the corresponding odd primary analogues of both of these results, give an idea of how to prove them and indicate how the method generalises to tell us things about p-local K-Theory operations.
Mar 2	Wed	Erwin Verwichte (Warwick)	Applied Mathematics Colloquium
14:00		Observations of MHD wave activity in the solar corona
		LTA
	Abstract: The advent of extreme-ultraviolet and x-ray imagers and spectrometers in the last decade has brought overwhelming observational evidence of magnetohydrodynamic wave activity in the solar corona. Such waves carry in their signatures valuable information about the structures along which they travel and has given birth to the field of coronal seismology that aims to extract this information. In this seminar I will highlight some of the key discoveries and discuss the nature of these waves, taking examples from established and new instruments such as TRACE, Hinode and SDO.
Mar 2	Wed	Mark Kambites (Manchester)	Pure Maths Colloquium
16:00		Monoids Acting by Isometric Embeddings
		Hicks Seminar Room J11
	Abstract: I will report on some recent joint work with Robert Gray, which aims to extend geometric methods from group theory to semigroups and monoids. The talk will start with an introduction to geometric group theory, and should be accessible to a general mathematical audience.
Mar 3	Thu	Ajay Jasra (Imperial College)	Statistics Seminar
14:00		On the stability of a class of sequential Monte Carlo methods in High Dimensions
		Lecture Theatre 6
	Abstract: We investigate the stability of a Sequential Monte Carlo (SMC) method applied to the problem of sampling from a single target density on R for large d. It is well known, using a single importance sampling step, one produces an approximation for the target distribution that deteriorates as the dimension d increases, unless the number of MC samples N increases at an exponential rate in d. This degeneracy can be avoided by introducing a sequence of artificial targets, starting from a `simple' target density and moving to the one of interest and using an SMC method to sample from the sequence. Using this class of SMC methods with a fixed number of samples, one can produce an approximation for which the effective sample size (ESS) converges to a random variable \varepsilon_N as d -> \infty, such that 1<\varepsilon_{N}
Mar 4	Fri	Khalil Alghafri (Sheffield)
13:05
		F20
Mar 4	Fri	Catelin Badea (Lille)
14:30		What is Operator Theory Good For?
		Hicks Lecture Theatre 1
	Abstract: The purpose of these talks is to survey recent results displaying the efficiency of spectral theory in solving various problems. We shall discuss some topics in applied mathematics (von Neumann's and Dykstra's algorithms) and in pure mathematics. The latter will include problems in harmonic analysis (behaviour of the Fourier-Stieltjes coefficients of measures, thin sets), topological dynamics (sets of recurrence, topological transitivity) and ergodic theory (van der Corput sets).
Mar 5	Sat	Nicolas Monod (Lausanne)
10:00		Fixed Point Theorems and Derivations
		Hicks Lecture Theatre 1
	Abstract: A new fixed point theorem is presented, applying to Banach spaces such as L1 or duals of C*-algebras. Applications include the optimal answer to the "derivation problem" for group algebras which originated in the 1960s. (Joint work with Bader and Gelander.)
Mar 5	Sat	Nicolas Monod (Lausanne)
11:30		Littlewood and Large Forests
		Hicks Lecture Theatre 1
	Abstract: Littlewood and large forests: Motivated by a classical result of Sz.-Nagy in functional analysis, Dixmier asked in 1950 which group representations can be made unitary. This question is still open, but I will report on some progress obtained with Epstein and Ozawa. We approach the question with ideas borrowed from XIXth century electricity theory as well as from contemporary percolation theory. As a result, we obtain notably non-unitarizable representations for Burnside groups and a new characterization of amenability. (The talk will be expository.)
Mar 8	Tue	Thomas Athorne (Sheffield)	Pure Maths Postgraduate Seminar
12:10		Topos Theory: an ahistorial introduction
		Hicks Seminar Room J11
	Abstract: Historically, the notion of topos emerged from some extremely difficult, technical work done in Algebraic Geometry by Grothendieck and others. It was only years later that Lawvere and Tierney noticed the connection to logic; in fact, a topos is a category with all the necessary logical structure to interpret mathematics. In this talk, I will introduce the notion of topos as if it were designed for this purpose---I will motivate it as a generalised category of sets. I will give the definition, explain some of the nice properties it gives, and focus at the end of the talk on detailed descriptions of a few concrete examples.
Mar 8	Tue	James Cranch (Leicester)	Topology Seminar
15:00		The structure of cofibre sequences
		Hicks Seminar Room J11
	Abstract: I'll start by reminding people how the classical duality theorems for manifolds have evolved to follow various technological revolutions in algebraic topology, and then I'll speculate about how they might evolve in the near future. I'll explain how a modern understanding of Lefschetz duality -- the duality theory for manifolds with boundary -- would seem to require (among other things) an understanding of some interesting structure on cofibre sequences. Then I'll demonstrate what I've worked out about that structure.
Mar 9	Wed	David Jordan (Sheffield)	Pure Maths Colloquium
16:00		Recurrence sequences, Poisson brackets and noncommutative algebras
		Hicks Seminar Room J11
	Abstract: The underlying theme of the talk is the relationship, via quantization and semiclassical limits, between Poisson algebras and parametrized families of noncommutative algebras. I intend to discuss this through a case study beginning with a nonlinear recurrence sequence arising in work of Fordy and Marsh on periodic quiver mutation. Understanding the recurrence leads to a Poisson bracket on a rational function field, with a Poisson automorphism modelling the recurrence, and to an affine Poisson subalgebra that establishes complete integrability for the automorphism. This leads in turn to my current desert island ring, a noncommutative deformation of this Poisson subalgebra. Although the recurrence is nonlinear it can be linearized in a simple way and this idea carries forward throughout the rest of the talk.
Mar 10	Thu	Chris Stride (Sheffield)	RSS Seminar
16:30		Cheating in Football; team culture, player behaviour, or question of circumstance?
		LT 3
	Abstract: Cheating is defined as ``to act fraudulently, to deceive, swindle, or flout rules designed to maintain conditions of fairness''. This study examined cheating in the context of association football, collecting data from the 2010 Football World Cup (WC2010) on the incidence of 17 cheating behaviours. Multilevel generalised linear models were then used to examine whether such behaviours are solely a demonstration of the perpetrator's beliefs and values, or whether they can be seen as a manifestation of team cultures or the situations that players find themselves in. If you are intrigued by the above or would simply like to watch some video clips of footballers behaving badly, then pop along to this seminar!
Mar 11	Fri	Peter Whyper (University of Sheffield)
13:05
		Lecture Theatre 9
Mar 15	Tue	Siu Por Lam	Topology Seminar
15:00		Equivariant K theory and equivariant Real K-theory of some spaces
		Hicks Seminar Room J11
Mar 16	Wed	Ineke de Moortel (St Andrews)	Applied Mathematics Colloquium
14:00		Coupled Kink and Alfvén Mode Propagation in the Solar Corona
		LTA
	Abstract: Observations have revealed ubiquitous transverse velocity perturbation waves propagating in the solar corona. We perform 3D numerical simulations of broadband footpoint-driven transverse waves propagating in a low β plasma. When density structuring is present, mode coupling in inhomogeneous regions leads to very efficient coupling of the kink mode to the Alfvén mode. The frequency-dependent decay of the propagating kink wave is observed as energy is transferred to the local Alfvén mode. For all density structures considered, modest changes in density were capable of efficiently converting energy from the driving footpoint motion to localised Alfvén modes. Hence, transverse footpoint motions at the base of the corona will transfer energy to Alfvén modes in the corona.
Mar 16	Wed	Kirill Mackenzie (Sheffield)	Pure Maths Colloquium
16:00		Morphisms of Lie algebroids
		Hicks Seminar Room J11
	Abstract: The title is dull, but the material is not. Given a mathematical structure it is usually straightforward to define a good notion of morphism. In the case of Lie algebroids, this only happened about 25 years after their introduction, and when a definition was given, it was widely disliked. The main purpose of the talk is to display the range of differential geometric phenomena which are covered by the concept: Maurer-Cartan forms, symplectic realizations, Poisson sigma models, as well as the more obvious ones.
Mar 17	Thu	Martijn Pistorius (Imperial College)	Statistics Seminar
14:00		MAXIMAL INCREMENTS OF RANDOM WALKS AND LEVY PROCESSES
		Lecture Theatre 6
	Abstract: A random walk reflected at its minimum is equal to the random walk minus its running minimum. The reflected process plays a role in various applications. It is related to the method of cumulative sums (CUSUM) used in mathematical statistics, and has been employed in various areas in applied probability, such as queueing theory, mathematical finance and mathematical genetics. For a random walk which step-size distribution has finite negative mean and satisfies Cramer's condition, we show that the current value, the rescaled maximum and the overshoot are asymptotically independent, and identify explicitly the limit-distribution of the overshoot. We obtain analogous results for the corresponding statistics of a Levy process. As corollary we obtain a factorization of the exponential distribution. This is joint work with A Mijatovic.
Mar 17	Thu	Malwina Luczak (LSE)
17:00		Markov chain models of complex systems
		Hicks LT 3
	Abstract: Markov chains provide a useful paradigm for modelling complex systems from various application areas. Rigorous analysis of their evolution can provide insights into the real situations they model. In this lecture, I will describe one Markov chain model from each of the following fields: computer science, statistical mechanics and mathematical biology. In each case, I will give some details of what is known about the model's behaviour.
Mar 18	Fri	Andrew Gascoyne (Sheffield)
13:05
		Lecture Theatre 9
Mar 21	Mon	Philipp Wruck (Hamburg)	Topology Seminar
14:05		Geometrical Aspects of Topological Invariants
		Hicks Seminar Room J11
Mar 22	Tue	Frank Neumann (Leicester)	Topology Seminar
15:00		Weil conjectures for the moduli stack of vector bundles on an algebraic curve
		Hicks Seminar Room J11
	Abstract: In 1949 Weil conjectured deep connections between the topology and arithmetic of algebraic varieties over a field in characteristic p. These conjectures led to the development of l-adic etale cohomology as an analog of singular rational cohomology in topology by Grothendieck and his school and culminated in the proof of the Weil conjectures by Deligne in the 70s. After giving a brief introduction into the classical Weil conjectures for algebraic varieties and into moduli problems, I will outline how an analog of these Weil conjectures for the moduli stack of vector bundles on a given algebraic curve can be formulated and proved. The result basically tells "how many" vector bundles (up to isomorphisms) there are over an algebraic curve in characteristic p.
Mar 23	Wed	Christian Beck (Queen Mary, UL)	Applied Mathematics Colloquium
14:00		Superstatistical techniques for complex systems with time scale separation
		tbd
	Abstract: Many complex driven nonequilibrium systems are effectively described by a superposition of several statistics on different time scales, in short a `superstatistics'. Superstatistical techniques have recently been successfully applied to a variety of complex systems, for example turbulence (Lagrangian, Eulerian, environmental), hydroclimatic fluctuations, pattern formation, mathematical finance, traffic delay statistics, random matrix theory, networks, scattering processes in high energy physics, as well as medical and biological applications. In this talk I will first give a general overview of this concept and its recent applications, and then discuss three examples is somewhat more detail: Train delay statistics on the British railway network, accelerations of tracer particles in turbulent flows, and cancer survival statistics.
Mar 23	Wed	Eugenie Hunsicker (Loughborough)	Pure Maths Colloquium
16:00		Geometric topology for singular manifolds
		Hicks Seminar Room J11
	Abstract: The classical theorems of Geometric Topology relate geometric, topological and analytic invariants of a compact manifold. These include the Gauss-Bonnet Theorem, the Hodge Theorem, the Hirzebruch Signature Theorem and the Atiyah-Singer Index Theorem. These theorems are interesting and important, because they allow information to travel among the areas of geometry, topology and global analysis. After the proof of the Index Theorem in the 70's, there was interest in extending these remarkable results to classes of manifolds with some sorts of singularities. However, the natural direct generalisations are not correct. In this talk, I will start by reviewing the central results in the compact setting. Then I will outline some of the developments in topology and in global analysis that have given us the language in which to express relationships between analysis and topology in the singular setting. Finally, I will give an overview of the progress so far on this general project.
Mar 24	Thu	Tusheng Zhang (University of Manchester)	Statistics Seminar
14:00
		Lecture Theatre 6
Mar 24	Thu	Professor Sir Roger Penrose OM FRS (Oxford)
17:30		Are we able to see through the Big Bang, into another World?
		Richard Roberts Auditorium
	Abstract: The proposal of Conformal Cyclic Cosmology (abbreviated CCC) asserts that what we presently regard as the entire history of our universe, from its Big-Bang origin to its indefinitely expanding future (but without inflation), is but one aeon in an unending succession of similar such aeons, where the infinite future of each matches to the big bang of the next via an infinite change of scale. CCC predicts that supermassive black-hole encounters in the aeon prior to ours would be observable to us as families of concentric rings of unusual temperature structure in the cosmic microwave background. Recent analysis of data from the WMAP satellite has been argued to provide confirmation of this signal, allowing us to "see through" our Big Bang to such events occuring in the aeon prior to ours. The present status of this controversial proposal will be discussed.
Mar 25	Fri	Balazs Pinter (University of Aberystwyth)
13:05
		Lecture Theatre 9
Mar 28	Mon	Sming Tsai
16:00		Observational signatures of SUSY dark matter
		Hicks LT9
Mar 29	Tue	Victoria Quigley (Sheffield)	Pure Maths Postgraduate Seminar
12:10		An introduction to $C^*$-algebras and the Gelfand-Naimark theorem
		Hicks Seminar Room J11
	Abstract: The study of $C^*$-algebras in pure mathematics began in the 1940s, in a paper of Gelfand and Naimark. The idea is that given a compact Hausdorff space, the collection of continuous functions on it can naturally be given an algebraic structure. The notion of $C^*$-algebra encapsulates this structure and, crucially, enables us to generalise it to a non-commutative version. $C^*$-algebras arise in many areas, including the theory of operators on Hilbert spaces, locally compact topological spaces and non-commutative geometry, as well as in theoretical physics. In this talk we will begin by introducing $C^*$-algebras, focusing on those which are both commutative and unital. We will then sketch the proof of an important theorem by Gelfand and Naimark which classifies all such $C^*$-algebras. In doing so, we touch upon a few topics of interest in the area of functional analysis, including spectral theory and the Gelfand transform.
Mar 29	Tue	Constanze Roitzheim (Glasgow)	Topology Seminar
15:00		Simplicial, stable and local framings
		Hicks Seminar Room J11
	Abstract: One key objective in stable homotopy theory is finding Quillen functors between model categories. These are functors respecting homotopy structures. Framings provide a way to construct and classify Quillen functors from simplicial sets to any given model category. There is also a more structured set-up where one studies Quillen functors from spectra to a stable model category. We will investigate how this is compatible with Bousfield localisations and how it can be used to study the deeper structure of the stable homotopy category.
Mar 30	Wed	Sasha Borovik (Manchester)	Pure Maths Colloquium
16:00		Protomathematics, metamathematics, and hidden structures of elementary school mathematics
		Hicks Seminar Room J11
	Abstract: The subject area of my talk can be classified as psychology of mathematical abilities, but approached from a mathematician's point of view. I will discuss some hidden structures of elementary school mathematics (frequently quite sophisticated and non-elementary) and conjectural cognitive mechanisms which allow some of so-called "mathematically able" children to feel the presence of these structures.
Apr 1	Fri	Beniamin Orza (Sheffield)
13:05
		Lecture Theatre 9
Apr 4	Mon	Carl Kent (Sheffield)
16:00		Petrov classification of spacetimes
		G08
Apr 6	Wed	Vladimir Bavula (Sheffield)	Pure Maths Colloquium
16:00		An analogue of the Conjecture of Dixmier is true for the algebra of polynomial integro-differential operators
		Hicks Seminar Room J11
	Abstract: In 1968, Dixmier posed six problems/conjectures for the algebra of polynomial differential operators, i.e. the Weyl algebra. In 1975, Joseph solved the third and sixth problems and, in 2005, I solved the fifth problem and gave a positive solution to the fourth problem but only for the homogeneous differential operators. The remaining three problems are still open. The first problem/conjecture of Dixmier (which is equivalent to the Jacobian Conjecture as was shown in 2005-07 by Tsuchimito, Belov and Kontsevich) claims that the Weyl algebra 'behaves' like a finite field extension. In more detail, the first problem/conjecture of Dixmier asks: is it true that an algebra endomorphism of the Weyl algebra an automorphism? In 2010, I proved that this question has an affirmative answer for the algebra of polynomial integro-differential operators. In my talk I explain the main ideas, the structure of the proof and recent progress on the first problem/conjecture of Dixmier.
Apr 7	Thu	Adrian Bowman (University of Glasgow)	Statistics Seminar
13:30		Flexible regression models for environmental applications
		Lecture Theatre 6
	Abstract: Additive, and more general nonparametric, approaches to modelling extend standard regression methods by allowing very flexible, but smooth, relationships between variables of interest. The role of these models in environmental applications, where there is a need to model complex forms of spatial and temporal trends, as well as spatial and temporal correlation, will be discussed. Technical aspects of the talk will include computational strategies for spatiotemporal smoothing and ways of extending standard inferential methods. The data structures considered will include river networks as well as more standard spatial domains. Applications will include the modelling of SO2 pollution over Europe, water quality in the River Tweed and rainfall-flow response in the river Dee.
Apr 7	Thu	Oztas Ayhan (Middle East Technical University, Turkey)	Statistics Seminar
15:00		Memory recall errors and their relation to survey response
		Lecture Theatre 5
	Abstract: This talk covers a study which compares self--reports during an interview with staff and students who attended a University health centre, with the records of visits to the same health centre over the previous 12 months. Design of the study reflects the effects of importance of the event, duration since the event, frequency of the occurrence of the event, measurement scale of the event, and bounded and unbounded recalling. In order to assess the extent of recall error, responses to retrospective questions on health centre visits are compared with administrative records. Statistical models are proposed for short and long term human memory recall error effects on responses.
Apr 8	Fri	Abhi Srivastava (Aryabhatta Research Institute of Observational Sciences (ARIES), Manora Peak, Nainital, India)
13:05
		Lecture Theatre 9
Apr 11	Mon	Ben Shepherd and Matt Hewitt
16:00		Report back from NPPD 2011 conference in Glasgow
		See schedule
Apr 18	Mon	Elizabeth Winstanley (Sheffield)
16:00		Report back from Bologna meeting
		G08
May 3	Tue	Neil Strickland (Sheffield)	Topology Seminar
15:00
		Hicks Seminar Room J11
May 4	Wed	James Douglas (Sheffield)	Applied Mathematics Colloquium
14:00		Linear stability analysis of non ideal tokamak plasma fluid models
		LT A
	Abstract: As the price of energy increases in an age of austerity, it is proper to invest in alternate energy sources. A tokamak is a magnetic confinement fusion device which seeks to maintain a burning plasma at temperatures comparable to the core of the Sun, thus harnessing the energy released during fusion reactions. Although many of the applied mathematical and theoretical physics aspects of maintaining a fusion plasma are well understood, some aspects of linear theory remain unexplored. Using the CUTIE tokamak fusion plasma simulation code developed at the Culham Science Centre, which has successfully reproduced many nonlinear features of tokamak plasmas, a thorough investigation of the linear properties of these plasmas is presented. This investigation includes reduced models, such as RMHD, and pertinent extensions covering the role of advective flows and toroidal curvature on linear stability. An introduction to nuclear fusion, tokamak reactors and the CUTIE code is discussed, before outlining some of the linear modes we have investigated using a linear version of the CUTIE code. This linear code employs two powerful new techniques for finding linear modes: the resolvent eigenvalue technique which reveals the entire linear spectrum; and the nonlinearisation technique for finding the dominant linear mode.
May 5	Thu	Jim Smith (University of Warwick)	Statistics Seminar
14:00		Controlling A Remote Bayesian from being irrational Abstract
		Lecture Theatre 6
	Abstract: UK military commanders have a degree of devolved decision authority delegated from command and control (C2) regulators, and they are trained and expected to act rationally and accountably. Therefore from a Bayesian perspective they should be subjective expected utility maximizers. In fact they largely appear to be so. However when current tactical objectives conflict with broader campaign objective there is a strong risk that fielded commanders will lose rationality and coherence. By systematically analysing the geometry of their expected utilities, arising from a utility function with two attributes, we demonstrate in this paper that even when a remote C2 regulator can predict only the likely broad shape of her agents' marginal utility functions it is still often possible for her to identify robustly those settings where the commander is at risk of making inappropriate decisions.
May 6	Fri	JingSong He (Department of Mathematics, Ningbo University, P.R. China)
13:05		Rogue wave solution for the NLS and DNLS type equations
		Lecture Theatre 9
	Abstract: In this talk, the variable coefficient nonlinear Schrodinger equation(VCNLSE), deriva- tive nonlinear Schrodinger equation(DNLSE) and variable coefficient derivative non- linear Schrodinger equation(VCDNLSE) are discussed. The rogue wave solution of VCNLSE, DNLSE and VCDNLSE are given. The DNLSE is solved by Darboux transformation. The solutions of VCNLSE (VCDNLSE) are given from known solutions of NLSE(DNLSE) by a transformation developed by us recently. Several figures for these solutions are plotted to understand intuitionally its dynamical evolution. This is a joint work with Prof. Yishen Li, Lihong Wang and my students (Youying Wang and Shuwei Xu).
May 9	Mon	Carsten van de Bruck (Sheffield)
16:00		Chameleons in cosmology
		See schedule
May 10	Tue	David Spiegelhalter (Cambridge)
17:00		Living with risk and uncertainty - we're all going to die (sometime)
May 11	Wed	Iñigo Arregui (Universitat de les Illes Balears, Palma de Mallorca)
14:00		Prominence thread oscillations: seismology and dynamics of transverse kink waves
		LT A
	Abstract: Quiescent prominences are large clouds of plasma suspended against gravity in the solar atmosphere, by forces thought to be of magnetic origin. High resolution observations show that prominences consist of fine threads. Transverse oscillations in prominence threads and their temporal damping are a common feature in a number of recent observations obtained by, e.g., the Swedish Solar Telescope (SST) in La Palma. Consider cylindrically symmetric magnetic flux tubes in the zero plasma beta approximation. Physical models for prominence threads can then be constructed by specifying particular density distributions. By analyzing the oscillatory properties of transverse kink waves in rather general two-dimensional density models, we provide insight to both seismology of transversely oscillating structures and to the physics of resonantly damped kink modes. Concerning the inversion of physical parameters using transverse kink waves, we find that the details of longitudinal density structuring have a significant impact on the inferred values of the Alfvén speed in those structures, while they are almost irrelevant when determining their transverse density structuring. On the subject of the physics of resonantly damped kink modes, we show the potential of combining the information from the spatial distribution of eigenfunctions together with energy arguments to better understand the energy transfer between kink waves of global character and oscillations at small spatial scales around the resonance. A detailed examination of the time-averaged Poynting flux in a two-dimensional region around the resonance shows how and where energy is fed into the resonance and the way it is thereafter distributed along the magnetic field lines. The use of the governing equations in the form of energy conservation laws and the computation of the different terms informs us about the spatial distribution of relevant quantities, such as the kinetic and magnetic energies, the generated current densities, and the associated resistive heating. The method and results here reported are also applicable to coronal loops and their transverse oscillations.
May 11	Wed	Inigo Arregui (Universitat de les Illes Balears, Palma de Mallorca, Spain)	Applied Mathematics Colloquium
14:00		Prominence thread oscillations: seismology and dynamics of transverse kink waves
		LT A
	Abstract: Quiescent prominences are large clouds of plasma suspended against gravity in the solar atmosphere, by forces thought to be of magnetic origin. High resolution observations show that prominences consist of fine threads. Transverse oscillations in prominence threads and their temporal damping are a common feature in a number of recent observations obtained by, e.g., the Swedish Solar Telescope (SST) in La Palma. Consider cylindrically symmetric magnetic flux tubes in the zero plasma beta approximation. Physical models for prominence threads can then be constructed by specifying particular density distributions. By analyzing the oscillatory properties of transverse kink waves in rather general two-dimensional density models, we provide insight to both seismology of transversely oscillating structures and to the physics of resonantly damped kink modes. Concerning the inversion of physical parameters using transverse kink waves, we find that the details of longitudinal density structuring have a significant impact on the inferred values of the Alfvén speed in those structures, while they are almost irrelevant when determining their transverse density structuring. On the subject of the physics of resonantly damped kink modes, we show the potential of combining the information from the spatial distribution of eigenfunctions together with energy arguments to better understand the energy transfer between kink waves of global character and oscillations at small spatial scales around the resonance. A detailed examination of the time-averaged Poynting flux in a two-dimensional region around the resonance shows how and where energy is fed into the resonance and the way it is thereafter distributed along the magnetic field lines. The use of the governing equations in the form of energy conservation laws and the computation of the different terms informs us about the spatial distribution of relevant quantities, such as the kinetic and magnetic energies, the generated current densities, and the associated resistive heating. The method and results here reported are also applicable to coronal loops and their transverse oscillations.
May 12	Thu	Inigo Arregui (Departament de Física, Universitat de les Illes Balears, Palma de Mallorca, Spain)
13:05		Bayesian magnetohydrodynamic seismology of coronal loops
		Lecture Theatre 9
	Abstract: Current magnetohydrodynamic seismology inversion techniques using both theoretical and observed wave properties in coronal structures show a number of limitations, such as the obtention of infinite number of solutions that equally well reproduce observed wave properties. We perform a bayesian parameter inference in the context of resonantly damped transverse coronal loop oscillations that aims to overcome these limitations. The forward problem is solved in terms of parametric results for kink waves in one-dimensional flux tubes in the thin tube and thin boundary approximations. This reduces the problem to solving two analytic algebraic equations for the period and damping of kink oscillations. For the inverse problem, we adopt a bayesian approach to infer the most probable values of the relevant parameters, for given observed periods and damping times, and to extract their confidence levels. The posterior probability distribution functions are obtained by means of Markov Chain Montecarlo simulations, incorporating observed uncertainties in a consistent manner. We find well localized solutions in the posterior probability distribution functions for two of the three parameters of interest, namely the Alfvén travel time and the transverse inhomogeneity length-scale. The obtained estimates are consistent with previous classic inversion results, but the method enables us to additionally constrain the transverse inhomogeneity length-scale and to estimate real error bars for each parameter. These results can serve to improve our current estimates of unknown physical parameters in coronal structures and to test the assumed theoretical model(s).
May 12	Thu	Lee Fawsett (University of Newcastle)	Statistics Seminar
14:00
		Lecture Theatre 6
May 12	Thu	Alison Macfarlane (City)	RSS Seminar
16:30		Where not to be born in the 1860s: How Florence Nightingale and her contemporaries used maternity statistics
		LT3
	Abstract: In 1862, Florence Nightingale responded to concerns about lack of training facilities for midwives in England, by establishing a midwifery training ward in King's College Hospital in central London. Because of the high mortality among women who gave birth there, she closed it in 1867. To investigate the causes of the high mortality, she and her unacknowledged co-worker, John Sutherland, compared maternal mortality statistics at King's with those for other institutions and populations nationally and internationally. 2010 marked the centenary of the death of Florence Nightingale, who was accustomed to visiting Tapton House, the home of her great aunt, Mary Shore, in the west of the city.
May 16	Mon	Victor Ambrus (Sheffield)
16:00		Spinors in curved space
		See schedule
May 18	Wed	Ben Shepherd (Sheffield)	Applied Mathematics Colloquium
14:00		Holographic Superconductivity
		LT A
	Abstract: Superconductors are materials which have zero electrical resistance below a certain critical temperature. However, there is no theory in condensed matter physics to describe the best superconductors, i.e. those with the highest critical temperature. The AdS/CFT correspondence provides a way to investigate these high temperature superconductors, in which we consider a higher dimensional gravitational theory with a black hole in anti de Sitter (AdS) space. The theory describing our superconductor is then given by the boundary of AdS. After introducing superconductivity and the AdS/CFT correspondence, we will show that a planar black hole with an SU(N) gauge field gives the correct properties associated with high temperature superconductors.
May 19	Thu	Mathew Penrose (University of Bath)	Statistics Seminar
14:00		Limit Theorems in Stochastic Geometry with Applications
		Lecture Theatre 6
	Abstract: For an empirical point process governed by a probability density function in d-space, consider functionals obtained by summing over each point some function which is locally determined. General laws of large numbers and central limit theorems for such functionals are known. We discuss such results, their extensions to point processes in manifolds, associated local limit theorems, and applications to particular functionals such as multidimensional spacings statistics, dimension estimators and entropy estimators.
May 20	Fri	Pedro Gonzales-Morales (University of Sheffield)
13:05
		Lecture Theatre 9
May 23	Mon	Greg Sculthorpe/Joel Weller/Susan Vu/Elizabeth Winstanley
16:00		Report back from UKCOSMO meeting and BHVIII conference
		See schedule
May 27	Fri	Rosa Diaz-Sandoval (Sheffield)
13:05
		Lecture Theatre 9
Jun 1	Wed	Bernhard Keller (Paris 7)	Pure Maths Colloquium
16:00		Quiver mutation and quantum dilogarithm identities
		Hicks Seminar Room J11
	Abstract: Quiver mutation is an elementary operation on quivers which appeared in physics in Seiberg duality in the 1990s and in mathematics in Fomin-Zelevinsky's definition of cluster algebras in 2002. In this talk, I will show how, by comparing sequences of quiver mutations, one can construct identities between products of quantum dilogarithm series. These identities generalize Faddeev-Kashaev-Volkov's classical identity and the identities obtained recently by Reineke. Morally, the new identities follow from Kontsevich-Soibelman's theory of refined Donaldson-Thomas invariants. They can be proved rigorously using the theory linking cluster algebras to quiver representations.
Jun 2	Thu	Professor Chris Budd (Bath)
17:30
Jun 6	Mon	Joel Weller (Sheffield)
16:00		MOND
		See schedule
Jun 8	Wed	Georg Struth (Sheffield)	Applied Mathematics Colloquium
14:00		Algebraic Methods for Developing and Analysing Computing Systems
		LT A
	Abstract: Programs without bugs is one of the grand ideals of computer science. It has stimulated decades of research, resulted in a number of Turing Awards, and has significant, and increasing, societal and economic relevance. It is widely accepted that mathematical methods are essential for analysing computing systems, and that new methods need to be developed to deal with their discrete, often nondeterministic nature. In turn, it has been claimed that these methods are increasingly relevant to other disciplines, such as physics, biology or economics. In this talk I will introduce variants of semirings, iteration algebras and relation algebras as fundamental structures of computing which are applicable to a variety of program analysis tasks. I will show how such algebraic methods can be used for proving theorems about programs that appear, for instance, in compiler optimisation, and how they provide frameworks in which the correctness of programs can be analysed. I will demonstrate that automated theorem provers and counterexample generators are instrumental both for program analysis and the development of algebraic methods. I will show how decision procedures and representation theorems for (fragments) of these algebras further support program analysis tasks. If time permits I will report on ongoing work on algebraic methods for concurrent and probabilistic systems, and mention some mathematically interesting open questions in these areas.
Jun 13	Mon	Ben Shepherd
16:00		AdS/CFT correspondence
		See schedule
Jun 20	Mon	Elizabeth Winstanley (Sheffield)
16:00		Kerr black holes
		See schedule
Jun 27	Mon	Elizabeth Winstanley (Sheffield)
16:00		Asymptotically Lifshitz space-times
		See schedule
Sep 21	Wed	Sam Dolan (University of Southampton)
14:30		Self-force calculations for black hole inspirals
		See schedule
	Abstract: Advances in numerical relativity (NR) since 2005 have led to rapid progress in the modelling of black hole inspirals. Yet an important frontier awaits: the large mass-ratio regime. For example, in the final year before merger, an Extreme Mass-Ratio Inspiral (EMRI) will undergo 10^5 orbits in the strong-field regime. EMRIs may be analysed via black hole perturbation theory, by assuming the small body follows a trajectory on the background spacetime of the large black hole, and that the trajectory is perturbed away from a geodesic of the background by a `self-force'. Practical methods for computing self-force effects at first order in the mass ratio are now well-established. In this short review, I will focus on four emerging themes in the self-force programme: (i) comparison of gauge-invariant results from gravitational self-force (GSF) calculations with other methodologies (e.g. Post-Newtonian, EOB and NR); (ii) ongoing development of numerical schemes for highly accurate calculations of GSF on Kerr spacetime; (iii) aspirations to achieve accurate, self-consistent long-term orbital evolutions of EMRIs using GSF calculations; (iv) understanding of qualitatively new phenomena, such as resonances [arXiv:1009.4923], which have practical implications for data analysis strategies.
Sep 26	Mon	Paul Mitchener (Sheffield)	Topology Seminar
15:00		Analytic K-theory vs. Algebraic K-theory
		Hicks Seminar Room J11
	Abstract: In this talk we show how algebraic K-theory can be presented in a "topological" way, meaning both algebraic K-theory and analytic K-theory are obtained from the same machinery. I'm hoping that the seminar will be fairly accessible to non-specialists in K-theory.
Sep 26	Mon	Susan Vu/Victor Ambrus (Sheffield)
16:00		Inflationary cosmology and string theory/Rotating fermions
		Hicks Seminar Room F30
Sep 29	Thu	Sawaporn Siripanthana (Sheffield)	Statistics Seminar
14:20		Multivariate surveillance for outbreak detection
		LT-6
	Abstract: Early detection with a low false alarm rate is the main aim of outbreak detection as used in public health surveillance or in regard to bioterrorism. Several statistical methods have been implemented and used for monitoring the occurrence of outbreaks. For simplicity, univariate surveillance or parallel surveillance, separate monitoring of each continuous series, is usually implemented in practice. However, this has severe limitations arising because of multiplicity from multiple hypothesis testing and ignoring correlation between series which might reduce detection performance of systems if data are truly correlated. Additionally correlation within series is another issue which is often ignored but which should be considered, as health data are normally dependent over time. This talk will summarise existing univariate methods used for outbreak detection with their strength and weaknesses and look at extensions to the multivariate case. For dimensionality reduction in multivariate surveillance, a method based on the sufficiency property will be introduced.
Oct 3	Mon	David Barnes (Sheffield)	Topology Seminar
15:00		E-local Framings
		Hicks Seminar Room J11
	Abstract: Framings provide a way to construct homotopically interesting functors from simplicial sets to any given model category. A more structured set-up studies stable frames, giving Quillen functors from spectra to stable model categories. We will investigate how this is compatible with Bousfield localisation to gain insight into the deeper structure of the stable homotopy category. We further show how these techniques relate to rigidity questions and how they can be used to study algebraic model categories.
Oct 3	Mon	Brief research updates
16:00
		Hicks Lecture Theatre 9
Oct 4	Tue	Thomas Cottrell (Sheffield)	Category Theory
15:00		Computads.
		Hicks Seminar Room J11
Oct 5	Wed	Simon Willerton (Sheffield)	Pure Maths Colloquium
16:00		Tight spans of metric spaces and Isbell completion of categories
		Hicks Seminar Room J11
	Abstract: I will describe how two seemingly different constructions are examples of a more general construction. The first construction, the tight span of a metric space, is a way of possibly embedding a finite metric space in a tree, and has applications in biological evolutionary trees and in network theory. The second construction, the Dedekind-MacNeille completion of a poset, is familiar as one way of completing the rational numbers to the real numbers, via Dedekind cuts. I will then explain how these are two examples of a construction from cateogory theory and say how this allows useful generalization.
Oct 7	Fri	Richard Morton (Sheffield)
13:05		Solar jets and magneto-seismology
		Lecture Theatre 9
	Abstract: Solar jets are a common feature in the chromosphere, transition region and corona and are suspected to play a major role in determining the energy and mass balance in the upper atmosphere. Due to limitations on board the imaging satellites such as Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA) and Hinode, determining the features of these jets geometry and plasma properties proves challenging. As demonstrated for coronal loops, magneto-seismology can play a role in helping to estimate otherwise unmeasurable plasma parameters. I present the observations of a UV/EUV 'blow-out' solar jet using SDO/AIA. In particular we focus on a thin dark thread seen to rise with jet. The thread supports a propagating kink wave, which we analyse and exploit with magneto-seismology. We are able to estimate the plasma temperature, density gradient, magnetic field gradient and sub-resolution expansion of the dark thread. The dark thread is found to be cool (3x10^4 K) with both strong density and magnetic field gradients. The expansion of the flux tube along its length is ~300-400km.
Oct 10	Mon	Pokman Cheung (Sheffield)	Topology Seminar
15:00		A geometric description of the Witten genus
		Hicks Seminar Room J11
	Abstract: The study of elliptic genera and elliptic cohomology, which started in the 80s, has provided interactions between such areas as homotopy theory, elliptic curves \& modular forms, topology \& geometry of free loop spaces, and mathematical structure of quantum field theory. Roughly speaking, this topic is like a higher version of topological K-theory and index theory. However, unlike its classical counterpart, this higher version still lacks a geometric interpretation, which has been a central problem of the topic. I will discuss some recent work towards this goal.
Oct 10	Mon	Brief research updates
16:00
		Hicks Seminar Room F41
Oct 11	Tue	Thomas Cottrell (Sheffield)	Category Theory
15:00		Computads 2.
		Hicks Seminar Room J11
Oct 12	Wed	Pieter Kok (Sheffield)	Applied Mathematics Colloquium
14:00		The ultimate limits to quantum measurements
		LT10
	Abstract: Precision measurements are the cornerstone of the scientific enterprise, and whenever new measurement techniques have become available, new natural phenomena were discovered. One important question is therefore what the ultimate limits to precision measurements are. In particular, what is the best precision we can achieve with a particular quantum mechanical setup given a certain amount of resources? Traditionally, this question is answered in quantum mechanics by the so-called Heisenberg limit. However, there have been recent claims that this limit is broken. We demonstrate that the Heisenberg limit is in fact optimal for all parameter estimation procedures in quantum metrology, but it requires careful consideration as to which resource is appropriate for expressing the scaling behaviour of the precision.
Oct 12	Wed	Mark Davis (Imperial College)	Statistics Seminar
14:15		Pathwise stochastic calculus and applications to options on realized variance.
		K14
	Abstract: If $S_t, t\in[0,T]$ is the price of a financial asset, the realized variance is $\mathrm{RV}^d_T=\sum_{i=1}^n(\log(S_{t_i}/S_{t_{i-1}}))^2$ where $t_i$ a pre-specified increasing sequence of times in $[0,T]$. Most of the literature on this subject studies the continuous-time limit, which is $\mathrm{RV}^c_T=[\log S]_T$, the quadratic variation of the `log-returns' process $X_t=\log S_t$. Questions to be answered are how to price options on realized variance consistently with other options in the market and how to hedge these options. Recent research has focussed on model-free approaches to these questions: we want to say as much as possible without committing ourselves to any particular stochastic process realization of $S_t$. However, this poses an immediate problem of interpretation in the passage from $\mathrm{RV}^d$ to $\mathrm{RV}^c$: we cannot use the standard probabilistic notions of convergence, since we do not have a probability space! An answer to this problem is provided in Hans Föllmer's 1981 paper Calcul d'Itô sans probabilités, where he derives an Itô formula just using real analysis for paths having the `quadratic variation property'. In some cases, we need an Itô formula valid for functions whose second derivatives are not continuous, say $f\in {\cal H}^2$. The standard approach to this in stochastic analysis goes via the Tanaka formula and local time, so the question arises whether we can have a pathwise theory of local time. Föllmer, with a Diploma student, did consider this question, but it seems there may be decisive advantages in considering `Lebesgue' partitions rather than `Riemann' partitions as Föllmer did, thereby getting a direct connection with Lévy's downcrossing representation of local time. This is a preliminary account of work in progress with Jan Ob\lój (Oxford).
Oct 12	Wed	Claudia Klϋppelberg (TU Munich)	Statistics Seminar
15:45		An introduction to COGARCH modelling with financial applications.
		K14
	Abstract: Modelling of stochastic volatility has triggered important research in the theory of stochastic processes. New models have been proposed to capture the ``stylized facts'' of volatility such as jumps, heavy-tailed marginals, long range dependence, and clusters in extremes. In recent years particular emphasis has been given to continuous-time modelling, since financial time series in liquid markets are high-frequency and irregularly spaced because of random trading times. Natural candidates of continuous-time models with jumps are Lévy or Lévy-driven models, and we shall discuss some of the prominent examples for volatility modelling. Special emphasis is given to COGARCH models, which are continuous time versions of the very popular GARCH models.
Oct 12	Wed	Chris Hughes (York)	Pure Maths Colloquium
16:00		The distribution of values of $L$-functions
		Hicks Seminar Room J11
	Abstract: Random matrix theory has played a huge role in the last decade in aiding the understanding of the distribution of $L$-functions. This talk will survey some of that material, and look forward to newer results on their extreme values.
Oct 17	Mon	Arjun Malhotra (Muenster)	Topology Seminar
15:00		Spin(c) bordism of elementary abelian groups
		Hicks Seminar Room J11
	Abstract: The Gromov-Lawson-Rosenberg conjecture for a group G says that a spin manifold with fundamental group G admits a metric of positive scalar curvature if and only if a topological obstruction lying in the real connective k-theory of G vanishes. I will indicate how we construct explicit spin projective bundles to prove the conjecture for elementary abelian groups, and discuss how the problem can be reduced to describing the complex connective k-theory via spin-c projective bundles.
Oct 17	Mon	Carsten van de Bruck (Sheffield)
16:00		Chapter 2 of Zwiebach's string theory book
		Hicks Lecture Theatre 9
Oct 18	Tue	Nick Gurski (Sheffield)	Category Theory
15:00		Gray-categories.
		Hicks Seminar Room J11
Oct 19	Wed	Jennifer Barrett, Mark Iles (Leeds)	RSS Seminar
10:00		Pre-meeting introductory workshop on statistical genetics (10:00-13:00)
		Hicks Room K14
	Abstract: Aimed at career-young statisticians and will provide an introduction and background to issues and terminology in statistical genetics (in preparation for the afternoon RSS Seminar)
Oct 19	Wed	John Billingham (Nottingham)	Applied Mathematics Colloquium
14:00		How do droplets climb up a vibrating hill?
		LT10
	Abstract: Recent experiments by Phillipe Brunet have shown that when a millimetric droplet of fluid is placed on a slope that strongly vibrates vertically it can climb up the slope. In this talk I will present some shallow water models for this phenomenon. I will begin with a model that includes just surface tension and the applied acceleration, but which can be solved numerically in its three-dimensional form. This model cannot capture the phenomenon. I will then include the effect of inertia in a two-dimensional model. The interaction of swaying and spreading modes of oscillation can cause the droplet to rise. However, we find that the behaviour of the moving contact lines is not realistic. Finally, we include the effect of viscosity, and model the moving contact lines more carefully.
Oct 19	Wed	Cathryn Lewis, David Balding, David Evans (King's College, University College, Bristol)	RSS Seminar
14:00		Risk Prediction Modelling in Genetic Epidemiology: Estimating risks of disease from genetic and environmental risk factors; Prediction of phenotype from genome-wide SNP data allowing for kinship; Improving risk prediction in complex diseases (14:00-17:00)
		LT7
	Abstract: Genetic epidemiology is a rapidly developing field within medical science. High-throughput genetic technologies applied to epidemiological collections have enabled large panels of genetic variations, densely covering the whole of the human genome, to be tested for association with disease risk. Such genome wide association studies have proved to be successful identifying many well replicated associations. However, as these identified genetic variants are frequently associated with modest changes in disease risk, attention is now turning to the development and implementation of multivariate risk prediction models. The meeting will focus on advances and challenges in the statistical methods required to develop and apply multivariate risk prediction models in the diagnostic and prognostic management of complex diseases.
Oct 19	Wed	Robrigo Bañuelos (Purdue)	Pure Maths Colloquium
16:00		Weyl asymptotics for eigenvalues
		Hicks Seminar Room J11
	Abstract: During a series of lectures titled ``Old and new problems in physics'' delivered to the faculty of the University of Göttingen in 1910 (with David Hilbert and his student Hermann Weyl in the audience), the Dutch physicist, Hendrik Antoon Lorentz, conjectured that the number of eigenvalues for the Laplacian (under suitable boundary conditions) for a region of area $A$ that do not exceed the positive number $n$, is proportional to $A$ times $n$, when $n$ is large. While (apparently) Hilbert predicted that the conjecture would not be proved in his lifetime, the result was proved by Weyl in 1912. From this point on, Weyl's celebrated theorem (commonly referred to as Weyl's Law) has been studied, extended, generalized, etc., by mathematicians and physicists in many different settings. After recalling some of the classical results we will look at similar problems when the Brownian motion, which "goes'' with the classical Laplacian, is replaced by other Lévy processes, in particular the rotationally invariant stable processes which "go" with fractional powers of the Laplacian.
Oct 20	Thu	Simon Wood (University of Bath)	Statistics Seminar
14:00
		LT-6
Oct 21	Fri	Viktor Fedun (Sheffield)
13:05
		Lecture Theatre 9
Oct 24	Mon	Nora Seeliger (Oberwolfach)	Topology Seminar
15:00		Group models for fusion systems and cohomology
		Hicks Seminar Room J11
	Abstract: Fusion systems are categories modelled on the conjugacy relations of a Sylow p-subgroup in a finite group. Every finite group gives rise to a fusion system for every prime dividing its order however there are fusion systems which cannot be realized as a fusion system of any finite group. This led to the concept of an exotic fusion system. In 2007 Robinson and independently Leary-Stancu constructed infinite groups realizing arbitrary fusion systems, a third one is due Libman-Seeliger in 2009. In this talk we will present a new model realizing arbitrary fusion systems and discuss some of its properties and moreover compare the cohomology of all these group models to the cohomology of the fusion system.
Oct 24	Mon	Carsten van de Bruck (Sheffield)
16:00		Sections 3.1 - 3.6 of Zwiebach's string theory book
		Hicks Seminar Room F41
Oct 25	Tue	Eugenia Cheng (Sheffield)	Pure Maths Postgraduate Seminar
14:00		An introduction to model categories.
		Hicks Seminar Room J11
	Abstract: The idea of category theory is to give a framework for abstraction. In this talk I will discuss one example of this: model categories give a framework for abstract homotopy theory. The idea is that the powerful techniques used in topology to handle homotopies and homotopy equivalence can then be used to study other objects such as chain complexes, simplicial sets, operads, categories or $n$-categories. One key idea when studying topological spaces is that homeomorphism is too strict as a notion of ``sameness``---homotopy equivalent spaces should also be treated as being ``the same'' as each other. Thus we pass from the category Top of topological spaces and continuous maps, to the category Ho(Top) of topological spaces and homotopy classes of continuous maps; in the former only homemorphisms are isomorphisms, but in the latter homotopy equivalences are too. This is a process of ``localisation'', in which a class of maps is made invertible. In general for an arbitrary category and an arbitrary class of maps that we wish to invert, the process is very difficult to understand. In this talk I will describe how a model structure on a category is some extra structure that enables us to perform the localisation with a much more tractable outcome. This talk will be introductory. In particular I will assume little knowledge of category theory beyond the definitions of category and functor.
Oct 25	Tue	Nick Gurski (Sheffield)	Category Theory
15:00		Gray-categories 2.
		Hicks Seminar Room J11
Oct 26	Wed	Rekha Jain (Sheffield)	Applied Mathematics Colloquium
14:00		Absorption and scattering of acoustic waves by thin magnetic flux tubes in a gravitationally stratified atmosphere
		LT10
	Abstract: The sun's acoustic oscillations, p-modes, are observed to have more than half of their power absorbed by sunspots and almost 20-30% by plages. Sunspots are also observed to have strong phase shifts but plages lack measurable phase shifts. The magnetic field within these structures is complex and highly structured which makes helioseismic observations troublesome to interpret and model. We study the propagation of acoustic waves through regions of plage, modeling the magnetic field therein as a collection of thin flux tubes. In this talk, I will present the background to this problem followed by the computation of the absorption and scattering coefficients arising from a single, axisymmetric magnetic tube. Implications for the measured absorption and phase shifts will also be discussed.
Oct 26	Wed	Mike Prest (Manchester)	Pure Maths Colloquium
16:00		Modules, additive categories and toposes
		Hicks Seminar Room J11
	Abstract: Modules are usually thought of as sets with structure but they may also be seen as functors, indeed by increasing the exactness requirements on these functors we are led to quite different views of modules and, from there, to close links between various kinds of additive categories. These links can be expressed as (anti-)equivalences between certain 2-categories. I will describe this and also mention how this picture in the additive context parallels one, which involves toposes, in the Set-based context.
Oct 31	Mon	Nick Gurski (Sheffield)	Topology Seminar
15:00		Icons
		Hicks Seminar Room J11
	Abstract: The first thing many people learn about higher categories is that monoidal categories are just 2-categories with a single object. This statement is supposed to prepare you for learning about 2-categories, since monoidal categories are extremely common. As with many not-quite-theorems in category theory, the truth of this statement depends on what the word "are" means. This talk is intended to introduce some basic concepts in the study of 2-categories (or maybe even n-categories in general), with one goal being to discuss the icons of the title and why they are interesting.
Nov 1	Tue	Thomas Athorne (Sheffield)	Pure Maths Postgraduate Seminar
14:00		An introduction to Galois connections
		Hicks Seminar Room J11
	Abstract: The central insight of Galois Theory is an interesting relationship between subgroups of the galois group on one hand, and intermediate field extensions on the other hand. In the last two centuries, more and more structures have been discovered---in many different fields of mathematics---that behave in a similar way. In the talk I will be discussing this kind of structure from a general point of view. I will describe a number of examples: ranging from the original Galois Theory, through to examples in Algebraic Geometry, Topology, Model Theory and even possibly "Real Life"! I will finish by explaining how the notion of a galois connection fits nicely into the more general language of Category Theory.
Nov 2	Wed	William George (Chalmers)	Applied Mathematics Colloquium
14:00		Reconsidering Kolmogov for Non-stationary Turbulent Flows
		LT10
	Abstract: One of the most important contributions to turbulence over the past century was the theory of Kolmogorov 1941. Since its introduction to the western world by Batchelor in 1946 it has dominated turbulence, both the interpretation of experiments and the development of turbulence models and scaling laws. It has been commonly assumed since the tidal channel measurements of Grant et al. 1961 that experiments have been uniformly supportive and that the coefficients are universal. Unfortunately the most important parameter, the turbulent dissipation, can almost never be measured directly and quite frequently is determined by `fitting' the measured data to the `established' results. Thus the `perfect' agreement is largely illusory, and in fact there is a considerable disagreement about what the `universal' constants are (or even if they are universal). Also it is seldom pointed out that almost all of the experiments cited are in statistical equilibrium, so that Kolmogorov's crucial first hypothesis of `local' equilibrium is statisfied identically. Thus none of these experiments can be regarded as a test of its generality. Worse, recent experiments and DNS in non-stationary turbulence show significant departures from Kolmolgorov behavior. These non-stationary homogeneous experiments are, however, consistent with the equilibrium similarity theory of George 1992 for these flows. So together the non-stationary theory and experiments together provide some confidence in these iconoclastic results. Therefore they present by counter-example a challenge to the Kolmogorov-based ideas for non-stationary flows, suggesting that we need to modify at least one of our fundamental beliefs.
Nov 2	Wed	Thomas Kahle (Newton Institute, Cambridge)	Pure Maths Colloquium
16:00		How primary decomposition of congruences and binomial ideals is wrong
		Hicks Seminar Room J11
	Abstract: In a polynomial ring, a binomial says that two monomials are scalar multiples of each other. Forgetting about the scalars, a binomial ideal describes an equivalence relation on the monoid of exponents. Ideally one would want to carry out algebraic computations, such as primary decomposition of binomial ideals, entirely in this combinatorial language. We will present a calculus that enables one to carry out algebraic computations by "looking at pictures".
Nov 3	Thu	Nicola Loperfido (Universita degli Studi di Urbino)	Statistics Seminar
14:00		Kurtosis and the Black Swan: some Fine Financial Findings
		LT-6
	Abstract: The Black Swan: The Impact of the Highly Improbable is a book which became a bestseller by pointing out the relevance of extreme (i.e. tail) events in finance. It also depicted statisticians as being totally inept at dealing with such events, but very apt in deceiving themselves and others using the normal distribution and more complicated models. This is unfair, given the vast statistical literature devoted to non normal models for extreme financial events. However, it is also true that most of it is better suited for professional statisticians than for financial analysts with limited statistical backgrounds and little time to learn advanced statistical techniques. These analysts might find kurtosis a simple and useful tool for dealing with tail events. This seminar examines some properties of kurtosis and apply them to financial decisions. Theoretical results will be illustrated by using data collected from several financial markets.
Nov 4	Fri	Andrew Newton (University of Sheffield)
13:05
		Lecture Theatre 9
Nov 9	Wed	Johan Anderson (Chalmers)	Applied Mathematics Colloquium
14:00
		LT10
Nov 14	Mon	Sarah Whitehouse (Sheffield)	Topology Seminar
15:00		Derived A-infinity algebras from the point of view of operads
		Hicks Seminar Room J11
	Abstract: A-infinity algebras arise whenever one has a multiplication which is ``associative up to homotopy". There is an important theory of minimal models which involves studying differential graded algebras (dgas) via A-infinity structures on their homology algebras. However, this only works well over a ground field. Recently Sagave introduced the notion of a derived A-infinity algebra in order to extend the theory of minimal models to a general ground ring. I will put derived A-infinity algebras into the context of operads and show that the operad for derived A-infinity algebras can be viewed as a free resolution of the operad for bidgas, in the same sense that the A-infinity operad is a free resolution of the operad for dgas. This is joint work with Muriel Livernet and Constanze Roitzheim. \\ Cake will be provided by Jonathon
Nov 15	Tue	Magdalena Kedziorek (Sheffield)	Pure Maths Postgraduate Seminar
14:00		An introduction to sheaves.
		Hicks Seminar Room J11
	Abstract: Presheaves on a topological space X capture the idea of associating data to open sets in a way which respects inclusions. This data can be of various forms for example groups, abelian groups, rings, R-modules. A sheaf is a presheaf that satisfies a "gluing condition" enabling us to move from local properties to global properties. The notion of sheaf was first introduced in 1946 by Leray for computing cohomology groups of spaces. Today sheaves provide a wonderful tool in algebraic topology and algebraic geometry. In this talk I will define presheaves and sheaves, with many examples. At the end I will show that there is a way to construct a sheaf from a presheaf in a universal way.
Nov 16	Wed	Chuong Van Tran (St Andrews)	Applied Mathematics Colloquium
14:00		A dynamical systems approach to fluid turbulence
		LT10
	Abstract: This seminar presents an analytic approach to fluid turbulence as an alternative to Kolmogorov's phenomenology. The new approach uses basic elements and concepts in dynamical systems theory and applies to a variety of fluid models, allowing us to recover key predictions made by the classical method. These include the number of degrees of freedom, the dissipation wavenumber and the exponent of the power-law energy spectrum of the inertial range. The two-dimensional surface quasi-geostrophic and magnetohydrodynamic systems are used as illustrative examples, with the theoretical predictions corroborated by numerical results.
Nov 16	Wed	David Barnes (Sheffield)	Pure Maths Colloquium
16:00		Rational $G$-equivariant Cohomology Theories
		Hicks Seminar Room J11
	Abstract: Cohomology theories are of great importance for studying topological spaces. They take as input topological spaces and as output give a collection of abelian groups. They satisfy a useful collection of axioms which (in theory) make these groups computable. If $X$ is a space with an action of a compact Lie group $G$ and $E$ is a cohomology theory, then $E^*(X)$ also has a $G$-action. But this doesn't usually tell us a great deal about the action, for example if $G$ is the circle group, then the action on cohomology is always trivial. So there is a need for cohomology theories that use the $G$-actionin a more fundamental way. These are called equivariant cohomologytheories, we discuss the definition, consider some examples and show that rationally, they are very well-behaved.
Nov 17	Thu	Sofia Dias (University of Bristol)	Statistics Seminar
14:00		Checking consistency in Mixed Treatment Comparison Meta-analysis
		LT-6
	Abstract: Indirect and mixed treatment comparisons (MTC), also known as network meta-analysis, represent an important development in evidence synthesis, particularly in decision making contexts. Rather than pooling information on trials comparing treatments A and B, A and C, B and C etc separately, MTC combines data from randomised comparisons, A vs B, A vs C, A vs D, B vs D, and so on, to deliver an internally consistent set of estimates while respecting the randomisation in the evidence. MTC allows coherent judgements on which of several treatments is the most effective and produces estimates of the relative effects of each treatment compared to every other treatment in a network -- even though some pairs of treatments may not have been directly compared. However, doubts have been expressed about the validity of MTC, particularly the assumption of consistency between ``direct'' and ``indirect'' evidence. Inconsistency can be thought of as a conflict between ``direct'' evidence on a comparison between treatments B and C, and ``indirect'' evidence gained from A vs C and A vs B trials. Like between-trial heterogeneity, inconsistency is caused by effect-modifiers, and specifically by an imbalance in the distribution of effect modifiers in the direct and indirect evidence. I will begin by defining inconsistency as a property of ``loops'' of evidence, and then provide details of the node-split and other, simpler, methods to assess whether there is inconsistency in a network and where it might be located. The merits and drawbacks of each method will be discussed using illustrative examples.
Nov 18	Fri	Amy Scott (Sheffield)
13:05
		Lecture Theatre 9
Nov 21	Mon	Danny Stevenson (Glasgow)	Topology Seminar
15:00		A classical construction for simplicial sets revisited
		Hicks Seminar Room J11
	Abstract: Simplicial sets became popular in the 1950s as a combinatorial way to study the homotopy theory of topological spaces. They are more robust then the older notion of simplicial complexes, which were introduced for the same purpose. We will review some functors arising in the theory of simplicial sets, some well-known, some not-so-well-known, and show how the latter give a very useful perspective on the Kan loop group functor. We will also describe a generalized Cartier-Dold-Puppe theorem for simplicial sets, and show how this leads to a very simple proof of a classical theorem of Kan. \\ Cake will be provided by Vikki
Nov 22	Tue	Thomas Cottrell (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Fundamental $n$-groupoids.
		Hicks Seminar Room J11
	Abstract: One of the basic notions of algebraic topology is that of the fundamental group of a topological space. This is a useful tool, but it has several drawbacks, including its reliance on a choice of basepoint, and its inability to detect multiple path components. In this talk I will explore some categorical alternatives to the fundamental group, namely, the fundamental $n$-groupoid. A groupoid is a category in which all morphisms are invertible. The fundamental groupoid of a topological space has as its objects points of the space, and as its morphisms homotopy classes of paths between them. If we take our morphisms to be paths rather than homotopy classes of paths, we can use $n$-dimensional groupoids in order to handle homotopies between paths, homotopies between those homotopies, and so on. In this talk, I will introduce the fundamental $n$-groupoid in low dimensions, and discuss the possibilities that arise at higher dimensions.
Nov 22	Tue	Jonathan Elliott (Sheffield)	Category Theory
15:00		Weighted limits and colimits
		Hicks Seminar Room J11
Nov 23	Wed	Zhivko Stoyanov (Reading)	Applied Mathematics Colloquium
14:15		Communicability in the brain
		LT10
	Abstract: Given a network of relationships between people, we naturally want to find the "big players" in the network. Furthermore, with the constant progress in technology, we are now able to capture the interactions between people in real time. We no longer have a static, but an evolving network of relationships. So we can now trace the flow of information on the network (passing of rumours, etc.). Therefore the term "big players" could have different meanings: it might mean people who are great broadcasters, but it could also mean people who are great receivers. Marketing companies, for example, might want to find the most influential people in the network, while the MoD could be interested in approaching the people with most information about the network. I will be interested in both: broadcasters and receivers, but instead of a social network, I shall be looking at the brain. In this talk I will suggest a simple way of using fMRI data to represent the brain as an evolving network. Then, using Network Theory and, in particular, a recently introduced notion of communicability, I will show a way to calculate the communicability score of each voxel (the 3D version of a pixel) in the brain. This score, which might be seen as a possible generalisation of PageRank, determines the extent to which a particular voxel is a broadcaster or a receiver. However, in our case there are around one million voxels in the brain. So there is little use in knowing the score for each voxel. Therefore, I shall discuss our attempt at summarising this information using the Discrete Fourier Transform. Furthermore, once we have "compressed" the communicability of the brain, I will try to discriminate between brains with a clinically diagnosed condition and healthy brains, using simple tools from Bayesian Statistics.
Nov 23	Wed	Neil Dummigan (Sheffield)	Pure Maths Colloquium
16:00		Congruences of modular forms and values of L-functions
		Hicks Seminar Room J11
	Abstract: I will describe Ramanujan's mod 691 congruence and its proof, then describe an instance of a conjecture about related congruences, and the search for numerical evidence.
Nov 25	Fri	James McLaughlin (Northumbria University)
13:05
		Lecture Theatre 9
Nov 28	Mon	Jacob Rasmussen (Cambridge)	Topology Seminar
15:00		Torus knots, Hilbert schemes, and Khovanov homology
		Hicks Seminar Room J11
	Abstract: Khovanov homology is an invariant of knots in S^3 which generalizes the Jones polynomial. I'll discuss some conjectures which relate the Khovanov homology of torus knots to some objects in algebraic geometry (Hilbert schemes of singular curves) and algebra (rational Cherednik algebras). Joint work with E. Gorsky, A. Oblomkov, and V. Shende. \\ Cake will be provided by Matt
Nov 29	Tue	Mohammad Mahdi Abbasirad (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Injective objects
		Hicks Seminar Room J11
	Abstract: In the category of modules and chain complexes, injective modules play a prominent role, especially, in homological algebra and the classical approach toward derived categories. Injective modules can be defined by the following property: M is injective if and only if Hom(-,M) preserves exact sequences. However, this definition is not very practical. In this talk I will explain Baer's test which gives a more practical characterisation of injective modules, and show how to generalise this to other categories. I will finish with some calculations to demonstrate the usefulness of exact sequences and role of injective modules in building an exact sequence.
Nov 30	Wed	Tom Bridgeland (Oxford)	Pure Maths Colloquium
16:00		Hall algebras and quantum groups (POSTPONED)
		Hicks Seminar Room J11
	Abstract: Quantized enveloping algebras are Hopf algebras that are q-deformations of universal enveloping algebras. Despite being defined by a bunch of peculiar looking relations, they have found applications in many parts of maths and physics. Twenty years ago Ringel showed how to give a conceptual description of the positive half of a quantized enveloping algebra using Hall algebras of quiver representations. I'll attempt to explain why introducing Z_2 graded complexes into the picture leads to a similar description of the whole thing.
Dec 1	Thu	Dario Spano (University of Warwick)	Statistics Seminar
14:00		Canonical correlation for dependent gamma random measures.
		LT-6
	Abstract: We will focus on the construction of dependent completely random measures (CRMs), with fixed margins, motivated by applications to Bayesian inference and Population Genetics. In particular, we will deal with vectors of gamma CRMs and characterize their distribution in terms of their canonical correlations, that is: we characterize the class of all dependent gamma measures whose finite dimensional distributions are given by a transition kernel with orthogonal polynomial eigenfunctions. We thus provide a results that shows that the canonical correlations (i.e. the kernel eigenvalues) are mixed moments of linear functionals of Dirichlet means evaluated at a random function. Markov-Krein and other identities on Dirichlet random means thus allow for several explicit representation for joint and conditional moment measures of our bivariate CRMs. We provide a few illustrations that show how some well--known dependent vectors are included in our more general framework. Finally, if time allows, we will discuss an extension to measure--valued Markov processes.
Dec 2	Fri	Michael K Griffiths (University of Sheffield)
13:05		Computational Magnetohydrodynamics Using Graphical Processing Units
		Lecture Theatre 9
	Abstract: Parallel MHD algorithms are important for numerical modelling of astrophysical plasmas. Parallelisation techniques have been exploited most successfully by the gaming/graphics industry with the adoption of graphical processing units (GPU's) possessing hundreds of processing units. The success has been recognised by the computational science and engineering commuinties who have harnessed the computational power of GPU's. In this seminar we describe the implementation of Magnetohydrodynamic codes for gravitationally stratified media on GPU's. We present the numerical methods used and the techniques for porting the code to this novel and highly parallel compute architecture. The methods employed are justified by the presentation of validation results and performance benchmarks.
Dec 6	Tue	Konstantinos Tsaltas (Sheffield)	Pure Maths Postgraduate Seminar
14:00		An introduction to zeta-integrals
		Hicks Seminar Room J11
	Abstract: Zeta functions are essential in studying number theory. For instance, we know the connection of the Riemann zeta-function and the distribution of primes. Moreover, one can consider zeta-functions of modular forms, which are conjecturally equal to zeta-functions of geometric objects like elliptic curves. After describing the adèle ring over the rational numbers, which is basically the right domain for evaluating zeta-integrals, I will define the notion of a zeta-integral, which provides a unified treatment of zeta-functions. As an application, I will consider the simplest case, and I am going to recover the Riemann zeta-function via a particular zeta-integral.
Dec 7	Wed	Kevin Houston (Leeds)	Pure Maths Colloquium
16:00		The Geometry of Shape
		Hicks Seminar Room J11
	Abstract: The mathematical theory of the shape of objects is still in its infancy - as yet there is no "language" of shape. In this talk I will consider different approaches via differential geometry to the problem of shape description and show how one in particular, involving the Laplace-Beltrami operator, captures the geometry of a shape. Since in practice shapes are defined by discrete data such as a triangulation or point cloud, I shall show how one can, via a discrete version of exterior calculus, construct a discrete version of the Laplace-Beltrami operator, the eigenvalues and eigenfunctions of which encode an immense amount of useful information about the shape. Applications can be made to a variety of situations, eg leaf shape, medical imaging.
Dec 9	Fri	Adam Scaife (Met Office Hadley Centre)
13:05		Solar Variability Forcing of Regional Winter Climate in the Northern Hemisphere
		Lecture Theatre 9
	Abstract: An influence of solar irradiance variations on Earth's surface climate has been repeatedly suggested, based on correlations between solar variability and meteorological variables. Specifically, weaker westerly winds have been observed in winters with a less active sun, for example at the minimum phase of the 11-year solar cycle. It has proved difficult for climate models to consistently reproduce this signal. However, recent Spectral Irradiance Monitor (SIM) satellite measurements indicate that variations in solar ultraviolet irradiance may be larger than previously thought. In this talk we will review some of the historical evidence for these links and then show what happens when we drive an ocean--atmosphere climate model with ultraviolet irradiance variations based on the SIM observations. We find that the model responds to the solar minimum with patterns in surface pressure and temperature that resemble the negative phase of the North Atlantic or Arctic Oscillation (a signature associated with cold conditions in northern Europe) and are of similar magnitude to observations. The signal descends through the depth of the extratropical winter atmosphere. If the updated measurements of solar ultraviolet irradiance are correct, low solar activity, as observed during recent years, drives cold winters in northern Europe and the United States, and mild winters over southern Europe and Canada. Note that there is little direct change in globally averaged temperature and therefore no impact on the anthropogenic interpretation of global warming. However, given the quasi-regularity of the 11-year solar cycle, our findings suggest a potentially important application in improving decadal climate predictions for highly populated extratropical regions in winter.
Dec 12	Mon	Roald Koudenburg (Sheffield)	Topology Seminar
15:00		Homotopy theory for generalised algebraic operads and their algebras
		Hicks Seminar Room J11
	Abstract: The homotopy theory for classical operads and algebras over them is well understood. In more detail: we know what homotopy algebras are, how they can be transferred along weak equivalences and when they can be rectified to strict algebra structures. To start with we will recall these notions and results, working throughout in the category of chain complexes over a field of charateristic zero. We will then define classical operads as symmetric monoidal functors, as introduced by E. Getzler. Using this approach we can easily generalise to structures in which operations have multiple outputs (properads) or where the distinction between inputs and outputs is removed (cyclic operads). Following this we will think about how to obtain model structures on categories of such generalised operads, as well as on the categories of their (lax) algebras. Cake will be provided by Eugenia
Dec 14	Wed	Stephen Coombes (Nottingham)	Applied Mathematics Colloquium
14:00		Patterns and waves in cortical models
		LT10
	Abstract: The tools of dynamical systems theory are having an increasing impact on our understanding of patterns of neural activity. In this talk I will describe how to build tractable tissue level models that maintain a strong link with biophysical reality. These models typically take the form of nonlinear integro-differential equations. Their non-local nature has led to the development of a set of analytical and numerical tools for the study of waves, bumps and patterns, based around natural extensions of those used for local differential equation models. Here I will present an overview of these techniques, and discuss the relevance of neural field models for describing the brain at the large scales necessary for interpreting EEG data. I will also discuss recent results on an interface approach for describing the evolution of intricate labyrinthine structures seen in planar neural field models.
Dec 14	Wed	Marta Mazzocco (Loughborough)	Pure Maths Colloquium
16:00		Upper-triangular bilinear forms and braid group action
		Hicks Seminar Room J11
	Abstract: In this talk we study a quadratic Poisson algebra structure on the space of bilinear forms on $\mathbb C^{N}$ with the property that for any $n,m\in\mathbb N$ such that $n m =N$, the restriction of the Poisson algebra to the space of bilinear forms with block upper triangular matrix of $n^2$ blocks of size $m\times m$ is Poisson. We characterise all central elements of this Poisson algebra and construct the braid-group action that preserves the Poisson algebra on each Poisson restriction. If time allows, we will discuss quantisation.
Dec 15	Thu	Peter Craig (University of Durham)	Statistics Seminar
14:00		Ecotoxicological Risk Assessment: Beyond the Standard Species Sensitivity Distribution Model --- Advantages and Benefits of Being Bayesian and Matters Arising.
		LT-6
	Abstract: Ecotoxicological risk assessment deals with the potential for unwanted ecological effects of chemicals. A key statistical tool for risk assessors and managers is the use of the species sensitivity distribution (SSD) model as a proxy for the effects of a chemical in real ecosystems; in particular, the "safe concentration" calculation is based on an estimate of the 5th percentile of the SSD, obtained from relatively small amount of data. The standard procedure (Aldenberg and Jaworska, 2000) is based on a log-normal model assuming exchangeability. Much of this talk will discuss a number of recent developments in the modelling and use of SSDs: drawing strength from other data; use of loss functions; assessing and modelling non-exchangeability and the consequences for decision-making; handling the issue of "measurement error" (inter-test variation); understanding and exploiting inter-species correlation; hierarchical random effects models. In parallel, I will consider the ongoing shift from frequentist to Bayesian methodology/philosophy in ecotoxicology, the advantages for the statistician of the Bayesian approach and the benefits this provides for ecotoxicology. I will finish by discussing some of the problems of being Bayesian, the questions they raise and some of the issues which Bayesians need to address.
Dec 15	Thu	Georg Struth (Sheffield, Computer Science)
15:00		Formalising Mathematics with the Interactive Theorem Prover Isabelle (A Tutorial)
		G22 Regent Court
	Abstract: Interactive Theorem Provers (ITPs) support the specification of mathematical theories and the formalisation of proofs on a computer. Isabelle, one of the most popular ITPs, has recently been extended with specific support for proof automation, which makes it particularly easy to use and potentially appealing to mathematicians. The development of repositories for mathematical theories and proofs, and the use of ITPs in undergraduate teaching of mathematics seems nowadays possible. In this tutorial I will present the main features of Isabelle, its proof system and proof scripting language, its mechanisms for structuring and modularising mathematical reasoning, and its proof automation facilities. I will demonstrate the tool on simple automated algebraic reasoning examples. I will also try to elaborate the possibilities and limitations for Isabelle for formalising more advanced mathematics. Complementing this presentation, Simon Foster will give a presentation on the dependently typed programming language and ITP Agda in early January.
Jan 19	Thu	Simon Foster (Sheffield Computer Science)
15:00		Dependently Typed Programming and Proof in Agda
		G22 Regent Court
	Abstract: Agda is a dependently typed programming language in the style of the functional programming language Haskell. What sets it apart from Haskell is its inclusion of dependent types which allow much finer grained constraints on data and functionality to be specified. Furthermore Agda doubles as a powerful ITP, in which properties about implemented programs can be proved. In this tutorial I will introduce the Agda interface and demonstrate the key features of the language. I will create some datatypes, functions and show how to build some proofs about them, some of which will be (semi-)automated.
Feb 2	Thu	Mohammad Al-Boshmki (Sheffield)	Pure Maths Postgraduate Seminar
13:00		Classifying spaces
		Hicks Seminar Room J11
	Abstract: Classifying spaces have played a central role in homotopy theory over the last fifty years. The classifying space of a group G is a path-connected space with fundamental group G and no other non-trivial homotopy groups. In this talk we will give a construction of classifying spaces for any topological group G, showing that classifying spaces always exist and are unique up to homotopy. We will illustrate this with examples such as Z, Z_2 and S^1.
Feb 2	Thu	James Cranch (Sheffield )
15:00		Dependently Typed Programming and Proof in Agda
		G22 Regent Court
	Abstract: James will show some more realistic examples of datatypes (including ordered list maps) and some portions of his work with categories.
Feb 8	Wed	Paul Linden (Cambridge)	Applied Mathematics Colloquium
14:20		Gravity-driven flows in stratified fluids
		LT6
	Abstract: This talk will describe experiments on flows driven by horizontal density gradients in fluids which are stably stratified. Examples are intrusions on density interfaces or in stratified ambient fluids, and cases where the intruding fluid is also stably stratified. Traditional approaches that have been applied to unstratified fluids have been to use ideas of energy conversion from available potential energy to kinetic energy to predict the speeds of the gravity-driven flows, which in this simple case are gravity currents. I will explore how well these approaches work in systems which can support internal waves and discuss the resulting dynamics.
Feb 8	Wed	Tom Bridgeland (Oxford)	Pure Maths Colloquium
16:00		Hall algebras and quantum groups
		Hicks Seminar Room J11
	Abstract: Quantized enveloping algebras are Hopf algebras that are $q$-deformations of universal enveloping algebras. Despite being defined by a bunch of peculiar looking relations, they have found applications in many parts of maths and physics. Twenty years ago Ringel showed how to give a conceptual description of the positive half of a quantized enveloping algebra using Hall algebras of quiver representations. I'll attempt to explain why introducing $Z_2$ graded complexes into the picture leads to a similar description of the whole thing.
Feb 9	Thu	Vanessa Didelez (University of Bristol)	Statistics Seminar
14:00		Mendelian Randomisation as an Instrumental Variable Approach to Causal Inference
		LT-6
	Abstract: In epidemiology we often want to estimate the causal effect of an exposure on a health outcome based on observational data, where the possibility of unobserved confounding cannot be excluded. To deal with this problem, it has recently become popular to use a technique called Mendelian randomisation, where it is exploited that the exposure is associated with a genetic variant, which can be assumed to be unaffected by the same confounding factors and which makes it suitable as a so-called instrumental variable. In my talk, this technique is illustrated with various examples, in particular with the effect of alcohol consumption on blood pressure / hypertension. Different methods of using an instrumental variable to estimate the causal effect on a binary outcome are compared based on their theoretical properties as well as by simulation. Finally, it will be discussed if a Bayesian approach is useful in the context of Mendelian randomisation. References:Didelez and Sheehan (2007). Mendelian randomisation as an instrumental variable approach to causal inference, Statistical Methods in Medical Research, 16, 309-330. Didelez, Meng and Sheehan (2010). Assumptions of IV methods for observational epidemiology, Statistical Science, 25, 22-40. Palmer, Sterne, Harbord, Lawlor, Sheehan, Meng, Granell, Davey Smith, Didelez (2011). Instrumental variable estimation of causal risk ratios and causal odds ratios in Mendelian randomization analyses, The American Journal of Epidemiology, 173 (12). Jones, Thompson, Didelez and Sheehan (2012). On the choice of parameterisation and priors for the Bayesian analyses of Mendelian randomisation studies. To appear in Statistics in Medicine.
Feb 9	Thu	David Barnes (Sheffield)	Topology Seminar
15:00		Stable Model Categories
		Hicks Seminar Room J11
	Abstract: A model category is a way of giving a category a notion of homotopy. Hence in a model category we can talk of maps being homotopic or objects being homotopy equivalent. The two basic examples of model categories are topological spaces and chain complexes. Hence model categories are of interest to both topologists and algebraists. One condition that a model category may satisfy is that of stability. This is where there is a shift functor or suspension functor which is an equivalence on the homotopy category. Chain complexes are such an example, however the category of topological is not a stable model category. In this talk I will define the notion of stability more carefully, and try to describe how one may alter a category to make it stable. In particular, we will see that spectra are the stabilisation of spaces.
Feb 10	Fri	Giuseppe Colantuono (Sheffield)
13:05		A simple model to evaluate photovoltaics with energy storage: initial results and ideas
		Lecture Theatre 9
	Abstract: Energy storage can be a means of smoothing out the unpredictability of "green" energy sources and increase the availability of power at times of peak demand. Efforts for integrating photovoltaics (PV) with batteries are already going on, even if they still suffer from high costs. A possible metric to evaluate the impact of storage coupled to a PV array is "Loss Of Load Hours" (LOLH). LOLH represents the total amount of time, for a given period (e.g one month), during which the demand (e.g. the power usage of the home where the PV array is installed) cannot be satisfied and electricity must be drawn from the grid. An analogous measure is the total time during which the battery is fully charged, energy cannot be stored any longer and is therefore uploaded to the grid. A simple model for the computation of LOLH will be presented . The inputs of the model are given by the timeseries of the solar irradiance incident on the PV array and the timeseries of the power load. Some preliminary results and possible developments for both real-world and idealized loads will be discussed.
Feb 14	Tue	Jonathan Elliott (Sheffield)	Pure Maths Postgraduate Seminar
13:00		Introduction to profunctors
		Hicks Seminar Room J11
	Abstract: Functors provide the appropriate notion of structure-preserving map between categories, but many applications require a more general notion of relation between categories. I will begin by discussing relations between sets, and bimodules over rings or monoids. I will then explain how profunctors simultaneously generalise relations, bimodules and functors. Finally I will discuss how to compose profunctors by analogy with tensor products of bimodules, so that profunctors are the 1-cells of a bicategory.
Feb 15	Wed	Fionntan Roukema (Sheffield)	Pure Maths Colloquium
16:00		Dehn Fillings of Manifolds with Small Volume
		Hicks Seminar Room J11
	Abstract: Dehn surgery is a classical area of low dimensional topology with many beautiful results connecting the subject matter to the description of 3-manifolds, the original Poincare conjecture, and the geometry of knot exteriors. In this talk we will introduce and motivate Dehn surgery with a view to speaking about ``exceptional surgeries"; this will naturally bring us to a well known tabulation of 3-manifolds of ``small volume". It will be our goal to discuss an unusually simple description of the ``exceptional fillings" associated with this tabulation. The presentation will attempt to be intuitive and contain many pictures.
Feb 16	Thu	Emma Jones (University of Sheffield)	Statistics Seminar
14:00		Using A Bayesian Hierarchical Model for Tree-Ring Dating
		LT-6
	Abstract: The width of tree-rings are determined by several factors including a local climatic signal apparent in that year, and the tree's growth trend. The climatic signal influences growth such that if the summer is warm and wet, the ring tends to be wider than if the summer is cold and dry. The growth trend describes the fast growth of the tree when it is young producing wide rings, followed by narrower rings as it ages. Other factors such as the soil conditions, presence of pests and diseases and competition for light and nutrients can also effect the ring width. The impact of these latter factors are collectively known as noise. It is assumed that trees within the same geographical region are exposed to the same climatic signal in each year, but that this differs from year to year. Tree-ring dating involves matching sequences of tree-ring widths from timbers of unknown age to dated sequences known as 'master' chronologies. Before matching takes place, all data are preprocessed to remove the growth trends. The timbers of unknown age (typically from a single building or woodland) are, firstly, sequentially matched against one another to identify the relative offsets with the 'best' match. The sequence produced is known as a 'site'chronology. The site chronology is then further matched to a local master chronology, to attempt to produce a date estimate for the site chronology. Traditionally the quality of the matches (both within the site chronology and between the site chronology and the master chronology) are assessed via the classical statistical t-test. A match at a particular offset is only considered to be 'best' if it produces the largest t-value of all of the possible offsets and is greater than (an arbitrary value of) 3.5. The success rate of dating varies within sites and across regions; the national average being approximately 60-70% but in some geographical areas the success rate can be much lower. One of the reasons for this is that the t-test does not utilise the wide range of information that could be used if a Bayesian model was used for tree-ring dating. A Bayesian model for tree-ring dating allows important prior information on parameters to be drawn into the inference process; this prior information can be taken from trees and can also be elicited from expert dendrochronologists. The model assumes that each ring width is composed of an overall climatic signal and some noise, and can be further extended to include climatic signals at varying geographic scales. Probabilities for a match at each offset can be produced conditional on the data and the prior specifications. The method removes the need to identify a single 'best' match, but it does rely on careful prior specification of parameters. Consequently, we have collated ring width data from trees of known age from several woods in the UK and are using these to provide informative prior knowledge.
Feb 16	Thu	Seungjin Han (University of Sheffield)	Statistics Seminar
14:30		Adaptive filtering for algorithmic pairs trading
		LT-6
	Abstract: Pairs trading as a statistical arbitrage methodology has received considerable attention and popularity since its initial application in the 1980's. It is based on the assumption that a spread of two assets is mean-reverted, and any violating fluctuations are taken advantage in order to realize profits. For real time detection of mean reversion, we employ a time-varying autoregressive model in a state-space form, online estimation of which is achieved by recursions of Kalman filtering and adaptive forgetting. Two novel algorithms for a variable forgetting factor are proposed and compared with a standard recursive least squares algorithm with adaptive memory.
Feb 16	Thu	Fionntan Roukema (Sheffield)	Topology Seminar
15:00		Dehn Fillings of Manifolds with Small Volume 2
		Hicks Seminar Room J11
	Abstract: In this talk we will recall some basic notions from Dehn surgery and remind ourselves about why we care about ``exceptional surgeries'' and ``exceptional pairs''. We then return to a tabulation of 3-manifolds of ``small volume'' and speak how it is possible to enumerate the set of exceptional slopes, pairs and fillings of ``most'' manifolds in this tabulation. If time permits we will speak about questions for future consideration. \\ Cake will be provided by Eugenia
Feb 21	Tue	Victoria Quigley (Sheffield)	Pure Maths Postgraduate Seminar
13:00		Classification of AF-algebras
		Hicks Seminar Room J11
	Abstract: C*-algebras are a type of algebra commonly studied in functional analysis. In this talk we will discuss a special class of C*-algebras called "approximately finite-dimensional" (AF). An AF-algebra is the inductive limit of a sequence of finite-dimensional C*-algebras. Such algebras retain relatively simple structure which makes them easier to analyse than other C*-algebras, but their study has led to many results which apply to more general classes of C*-algebras. In the 1970's, George Elliott gave a classification theorem for AF-algebras using their K-theory. We will end the talk by presenting this theorem, after first covering some basic theory of AF-algebras, as well as some of the properties of analytic K-theory.
Feb 22	Wed	No seminar (Exam boards)	Pure Maths Colloquium
16:00
		Hicks Seminar Room J11
Feb 23	Thu	Jim Griffin (University of Kent)	Statistics Seminar
14:00		Shrinking to some purpose
		LT-6
	Abstract: In Bayesian statistics there has recently been interested in using priors whose density has a spike at zero in regression problems. These priors can lead to adaptive shrinkage of regression effects and so can be used for sparse regression problems where many of the regression coefficients are assumed to be zero (or very close to zero). This talk will consider the Normal-Gamma prior and extensions of it to encourage more general forms of shrinkage. For example, we might want to shrink differences of regression effects, or we might want to allow the ``importance'' of regression effects to change over time.
Feb 23	Thu	Eugenia Cheng (Sheffield)	Topology Seminar
15:00		Multivariable adjunctions and mates
		Hicks Seminar Room J11
	Abstract: (Joint work with Nick Gurski and Emily Riehl.) The so-called ``mates correspondence'' (named by Australians) arises in the presence of adjunctions. It enables us neatly to pass between natural transformations involving left adjoints and those involving right adjoints, and is used efficaciously in Emily Riehl's work on algebraic model categories. When Emily visited us last year, she was extending her work to algebraic monoidal model categories. For this, she was looking for a multivariable generalisation of the mates correspondence, and a framework in which to describe it. The ordinary mates correspondence is elegantly described using double categories, and Nick and I sat down with Emily and produced the theory of ``cyclic double multicategories'', which not only answers her question but is also a satisfying piece of category theory: the best of both worlds. Moreover, it is an output directly resulting from MSRC funding.
Feb 23	Thu	Keith Still (Bucks New University)	RSS Seminar
16:30		Crowd Modelling to Assess Risks in Crowded Spaces
		Hicks LT2
	Abstract: In this lecture Prof. Still will outline the background to modelling crowd flow, fill and failure using a wide range of examples of crowded spaces and how 'simple' maths could have been used to prevent mass fatalities. Drawing on over 20 years of experience in consulting around the world, his talk is illustrated with examples of modelling tools and techniques, from some of the world's largest, most dangerous and challenging, crowd modelling projects. He also illustrates how shockwaves form and how they can be predicted, and prevented, in crowded spaces.
Feb 24	Fri	Richard Morton (Sheffield)
13:05
		Lecture Theatre 9
Feb 28	Tue	Timothy Eardley (Sheffield)	Pure Maths Postgraduate Seminar
13:00		Representations of Galois groups
		Hicks Seminar Room J11
	Abstract: Galois groups play an important role in algebraic number theory and an effective way of studying them is via representations. We shall motivate this study and then focus on representations over finite fields. These in turn are studied via deformations to certain more general rings. We will give hypotheses under which there is a 'universal deformation ring', which classifies these deformations. In fact, this is an application of the categorical notion of representable functors. We will end with some examples of deformation rings.
Feb 29	Wed	Ati Sharma (Sheffield)	Applied Mathematics Colloquium
14:00		Predicting structure in turbulence
		LT6
	Abstract: How to find a simple model that predicts the important structural and statistical features of turbulence is a central unsolved problem in classical physics. Most commonly found flows are turbulent, for instance flow of air over an aeroplane wing or water past a ship's hull, flow of oil through an trans-continental pipeline, or the movement of the atmosphere. All these flows experience chaotic three-dimensional motion, but nonetheless show persistent, repeating structure. This talk will cover significant new advances, involving the application of systems-theoretic ideas to the equations governing turbulence, which predict these structures. The computationally cheap approach explains and predicts structures and velocity statistics that have previously been identified only in experiments or by direct numerical simulation. Short Biography After graduating as a physicist from UCL, Dr Sharma completed his doctoral thesis in control engineering at Imperial College, London on the modelling and control of tokamak nuclear fusion reactors. Following two years in industry, he returned to academia as a postdoc to work on fluid flow control, and was then awarded an Imperial College Junior Research Fellowship in that area. Dr Sharma joined ACSE as a lecturer in July.
Feb 29	Wed	Kazuma Shimomoto	Pure Maths Colloquium
16:00		Modular forms and Galois representations; its algebraic aspect
		Hicks Seminar Room J11
	Abstract: In this talk, I will begin to give a brief review on the algebraic or p-adic aspect of modular forms. Then I will move on to the modern view of modular forms with its relation to Iwasawa theory. If time permits, I would like to mention some recent topics. This talk is elementary.
Mar 1	Thu	Chris Sherlock (University of Lancaster)	Statistics Seminar
14:00		A hidden Markov model for disease interactions
		LT-6
	Abstract: Interactions between parasite species in a host are of great interest to ecologists but are often too complex to predict a priori. A longitudinal study of a population of field voles was undertaken with presence or absence of six different parasite species measured repeatedly. Although trapping sessions were regular, a different set of voles was caught at each session leading to incomplete profiles for all subjects. A simple analysis, which discards much of the data, has already been carried out; we offer a more powerful alternative. We use a discrete-time hidden Markov model for each disease with transition probabilities dependent on covariates via a set of logistic regressions. For each disease the hidden states for each of the other diseases at a given time point form part of the covariate set for the Markov transition probabilities from that time point to the next. This allows us to gauge the influence of each parasite species on the transition probabilities for each of the other parasite species. Inference is performed via a Gibbs sampler, one iteration of which cycles through each of the diseases, first using an adaptive Metropolis-Hastings step to sample from the conditional posterior of the covariate parameters for that particular disease given the hidden states for all other diseases and then sampling from the hidden states for that disease given the parameters using the Forward-Backward algorithm.
Mar 1	Thu	Ieke Moerdijk (Sheffield)	Topology Seminar
15:00		On categories with two objects
		Hicks Seminar Room J11
	Abstract: In this talk we'll analyse cofibrant objects in the model category of categories on two objects enriched in a monoidal model category. As an application, we will obtain a Bergner type model structure on the category of all such enriched categories with arbitrary set of objects. Cake will be provided by Jonathon
Mar 6	Tue	David O'Sullivan (Sheffield)	Pure Maths Postgraduate Seminar
13:00		The Atiyah-Singer Index Theorem
		Hicks Seminar Room J11
	Abstract: The Atiyah-Singer Index Theorem -- the work of Michael Atiyah and Isadore Singer in the 1960s - has been described as ``one of the deepest and most beautiful results in modern geometry'', incorporating results such as the Riemann-Roch Theorem (algebraic geometry), the Hirzebruch Signature Theorem and the Gauss-Bonnet Theorem as special cases. The theorem equates two very different quantities: The first is an analytic property of a particular type of operator that is used to model systems of differential equations. In particular, it gives information about the dimension of the solution space -- and hence the number of solutions to such a system. This is easy to define, but usually impossible to calculate directly. The second quantity is a value related to the topology of the space on which the operator is defined. By contrast this is more difficult to define, but readily computable. In this talk I will introduce the concepts necessary to define the both of the above quantities and state the theorem.
Mar 7	Wed	John Hinch (Cambridge)	Applied Mathematics Colloquium
14:00		Large drops of a power-law fluid in a thin film on a vertical fibre
	Abstract: We study a thin liquid film on a vertical fibre. Without gravity, there is a Rayleigh-Plateau instability in which surface tension reduces the surface area of the initially cylindrical film. Spherical drops cannot form because of the fibre, and instead, the film forms bulges of roughly twice the initial thickness. Large bulges then grow very slowly through a ripening mechanism. A small non-dimensional gravity moves the bulges. They leave behind a thinner film than that in front of them, and so grow. As they grow into large drops, they move faster and grow faster. When gravity is stronger, the bulges grow only to finite amplitude solitary waves, with equal film thickness behind and in front. We study these solitary waves, and the effect of shear-thinning and shear-thickening of the fluid. In particular, we will be interested in solitary waves of large amplitudes, which occur near the boundary between large and small gravity. Frustratingly, the speed is only determined at the third term in an asymptotic expansion. The case of Newtonian fluids requires four term.
Mar 7	Wed	Christopher Douglas (Oxford)	Pure Maths Colloquium
16:00		Fusion categories and field theories.
		Hicks Seminar Room J11
	Abstract: I will describe a relationship between certain monoidal categories called fusion categories and 3-dimensional topological field theories, focusing on the correspondence between algebraic properties of the categories and topological properties of the associated field theories. Fusion categories are monoidal categories that have the nice properties of the category of representations of a finite group: each object has a dual, there are finitely many simple objects, and any object decomposes into a finite sum of simples. We show that any fusion category gives rise to a 3-dimensional topological field theory. A key question about the algebraic structure of a fusion category is whether the double dual operation is trivial, as it is in the representation category of a finite group. I will explain why this question corresponds to the question of whether the 3-manifold invariants of the associated field theory depend on a spin structure. This is joint work with Chris Schommer-Pries and Noah Snyder.
Mar 8	Thu	Ieke Moerdijk (Sheffield)	Topology Seminar
15:00		Two models for infinity-operads
		Hicks Seminar Room J11
	Abstract: I will explain the Lurie model category for infinity operads based on the theory of marked simplicial sets over the nerve of Gamma, the model category for infinity operads based on dendroidal sets which I introduced with Cisinski, and a comparison between the two. \\ Cake will be provided by Matt
Mar 8	Thu	Ari Laptev (Imperial)
17:30		Spectral Inequalities for Partial Differential Equations and their Applications
		LT7
	Abstract: We shall discuss properties of the discrete and continuous spectrum of different classes of self-adjoint differential operators including Schrödinger operators.
Mar 13	Tue	Matthew Gadsden (Sheffield)	Pure Maths Postgraduate Seminar
13:00		An introduction to coarse geometry
		Hicks Seminar Room J11
	Abstract: Coarse geometry is the study of large scale properties of spaces. In coarse geometry, we want to consider two spaces as being the same if they "behave the same at infinity", neglecting the fine detail. For example we consider the real numbers and the integers as being the same, as they look the same when you view them from far away. In this talk, we shall begin by introducing coarse maps and coarse equivalences, and by explaining how these definitions capture the geometry of large scale. I shall give many examples of coarsely equivalent spaces, with geometrical interpretations. One of the first key questions in coarse geometry was how do we tell metric spaces apart? To do this, we need to study coarse invariants. We will define and discuss two of them: the ends of a space and the ends of a group. Finally, we shall present a classification theorem regarding the ends of finitely-generated groups, including examples.
Mar 14	Wed	Joab Winkler (Sheffield)	Applied Mathematics Colloquium
14:00		The computation of multiple roots of polynomials whose coefficients are inexact
		LT6
	Abstract: This lecture will show by example some of the problems that occur when the roots of a polynomial are computed using a standard polynomial root solver. In particular, polynomials of high degree with a large number of multiple roots will be considered, and it will be shown that even roundoff error due to floating point arithmetic, in the absence of data errors, is sufficient to cause totally incorrect results to be obtained. Since data errors are usually larger than roundoff errors (and fundamentally different in character), the errors encountered with real world data are significant and emphasise the need for a computationally robust polynomial root solver. The inability of commonly used polynomial root solvers to compute high degree multiple roots correctly requires investigation. A method developed by Gauss for computing the roots of a polynomial will be discussed, and it will be shown that it has an elegant geometric interpretation in terms of pejorative manifolds, which were introduced by William Kahan (Berkeley). Polynomials defined by points on these manifolds satisfy properties that are fundamentally different from the properties of polynomials defined by points that are not on these manifolds. The numerical interpretation of this difference provides the motivation for the method of Gauss, and the geometric properties of pejorative manifolds will therefore be emphasised and considered in detail. Furthermore, these properties explain why multiple roots are preserved in a floating point environment when the coefficients of the polynomial are corrupted by noise. This numerical interpretation leads naturally to a discussion of a structured condition number of a root of a polynomial, where structure refers to the form of the perturbations that are applied to the coefficients. It will be shown that this structured condition number, where the perturbations are such that the multi- plicities of the roots are preserved, differs significantly from the standard componentwise and normwise condition numbers, which refer to random (unstructured) perturbations of the coefficients. Several ex- amples will be given and it will be shown that the condition number of a multiple root of a polynomial due to a random perturbation in the coefficients is large, but the structured condition number of the same root is small. This large difference is typically several orders of magnitude. The computational implementation of the method of Gauss raises some non-trivial issues -- the determi- nation of the rank of a matrix in a floating point environment and the quotient of two inexact polynomials -- and they will be discussed because they are ill-posed operations. They must be implemented with care because simple methods will necessarily lead to incorrect results. Furthermore, problems occur when the coefficients of the polynomial span several orders of magnitude, in which case the polynomial must be processed before its roots are computed in order to guarantee computationally reliable arithmetic operations. I will finish the talk by demonstrating Matlab code that implements the method on several high degree polynomials whose coefficients have been corrupted by noise and whose theoretically exact forms have multiple roots of high degree.
Mar 14	Wed	Michael Bate (York)	Pure Maths Colloquium
16:00		Fixed points in spherical buildings (and why I care about them)
		Hicks Seminar Room J11
	Abstract: In the 1950s Jacques Tits formulated a conjecture about spherical buildings, which he had recently invented. In the intervening years, several important special cases of this conjecture have been proved, but the full conjecture is still open. In this talk I will explain what spherical buildings are, from a variety of different viewpoints, and what Tits's conjecture says about their structure. I'll illustrate the various known cases with some straightforward examples which shouldn't need more than a smattering of linear algebra and some geometric intuition. If time permits I'll also detail my small contribution to the effort to prove the full conjecture.
Mar 15	Thu	Simona Paoli (Leicester)	Topology Seminar
15:00
		Hicks Seminar Room J11
	Abstract: Cake will be provided by Vikki
Mar 15	Thu	James Fotheringham, Richard Jacques; Andy Sutherland, Alyson Whitmarsh, Simone Chung (Sheffield; Dept of Health Information Centre, Leeds)	RSS Seminar
15:00		The Summary Hospital Mortality Index (SHMI)
		LT10
	Abstract: Background and Derivation of the New SHMI (James Fotheringham, Richard Jacques - Sheffield) Development and Issues in the Production of the SHMI (Andy Sutherland, Alyson Whitmarsh, Simone Chung - DoH Information Centre) The SHMI is now in use by the NHS to monitor hospital performance in England, to complement or replace other ratings such as Dr Foster's Hospital Standardised Mortality Ratio. Uniquely, it links mortality data from ONS to hospital episode statistics to examine deaths either in hospital or 30 days after discharge from hospital. In a series of linked talks, speakers from Sheffield will describe how they developed the model for computing the expected deaths, and speakers from the DoH will discuss issues in the production and use of the SHMI. The meeting will last until 17:30 and there will be a break at 16:00.
Mar 16	Fri	Ondrej Rypacek (Sheffield Computer Science)
13:00		A syntactical approach to weak $\omega$-groupoids
		G22 Regent Court
	Abstract: When moving to a Type Theory without proof irrelevance the notion of a setoid has to be generalized to the notion of a weak $\omega$-groupoid. As a first step in this direction we study the formalisation of weak $\omega$-groupoids in Type Theory. This is motivated by Voevodsky's proposal of univalent type theory which is incompatible with proof-irrelevance and the results by Lumsdaine and Garner/van de Berg showing that the standard eliminator for equality gives rise to a weak $\omega$-groupoid.
Mar 16	Fri	Khalil Al-Ghafri (Sheffield)
13:05		The effect of variable background on oscillating hot coronal loop due to thermal conduction
		Lecture Theatre 9
	Abstract: We investigate the effect of a variable, i.e. time-dependent, background on the standing acoustic (i.e. longitudinal) modes generated in a hot coronal loop. A theoretical model of 1D geometry describing the coronal loop is applied. The background temperature is allowed to change as a function of time and undergoes an exponential decay with characteristic cooling times typical for coronal loops. The magnetic field is assumed to be uniform. Thermal conduction is the dominant mechanism of cooling the hot background plasma in the presence of an unspecified thermodynamic source that maintains the initial equilibrium. The influence of the rapidly cooling background plasma on the behaviour of standing acoustic (longitudinal) waves is investigated analytically. The temporally evolving dispersion relation and wave amplitude are derived by using the WKB theory. An analytic solution for the time-dependent amplitude that describes the influence of thermal conduction on the standing longitudinal (acoustic) wave is obtained by exploiting the properties of Sturm-Liouville problems. Next, numerical evaluations further illustrate the behaviour of the standing acoustic waves in a system with variable, time dependent background. The results are applied to a number of detected loop oscillations. We find a remarkable agreement between the theoretical predictions and the observations. The cooling of the background plasma due to thermal conduction is found to cause a strong damping for the slow standing magneto-acoustic waves in hot coronal loops in general. Further to this, the increase in the value of thermal conductivity leads to a strong decay in the amplitude of the longitudinal standing slow MHD waves.
Mar 21	Wed	Alex Best (Sheffield)	Applied Mathematics Colloquium
14:00		Modelling the coevolution of parasites and their hosts
		LT6
	Abstract: Understanding the dynamics of infectious diseases in human, animal and plant hosts is one of the biggest challenges for modern science, with considerable health, social and financial implications. Mathematical models of these host-parasite interactions can allow us to understand and predict the behaviour of many disease systems. Here I shall focus on the evolutionary dynamics of parasites and hosts, applying the evolutionary framework of adaptive dynamics to a classic model of host-parasite interactions. I shall show how parasite infectivity and host defence may be expected to evolve, both in isolation and when they coevolve with one another. Throughout I shall highlight the important role of the evolutionary trade-offs on the eventual outcome, particularly focussing on the potential for variation to arise through evolutionary branching.
Mar 21	Wed	Marco Streng (Warwick)	Pure Maths Colloquium
16:00		Smaller class invariants for quartic CM-fields
		Hicks Seminar Room J11
	Abstract: The theory of complex multiplication allows one to construct elliptic curves with a given number of points. The idea is to construct a curve over a finite field by starting with a special curve $E$ in characteristic $0$, and taking the reduction of $E$ modulo a prime number. Instead of writing down equations for the curve $E$, one only needs the minimal polynomial of its $j$-invariant, called a Hilbert class polynomial. The coefficients of these polynomials tend to be very large, so in practice, one replaces the j-invariant by alternative 'class invariants'. Such smaller class invariants can be found and studied using an explicit version of Shimura's reciprocity law. The theory of complex multiplication has been generalized to curves of higher genus, but up to now, no class invariants were known in this higher-dimensional setting. I will show how to find smaller class invariants using a higher-dimensional version of Shimura's reciprocity law.
Mar 22	Thu	Philipp Wruck (Sheffield)	Topology Seminar
15:00		Equivariant Transversality: Overview and Recent Developments
		Hicks Seminar Room J11
	Abstract: The notion of transversality allows us to successfully describe generic behaviour of smooth maps and has important impacts in various branches of topology. A simple adaption in the equivariant context is not possible, but using techniques from real algebraic geometry and the theory of stratified spaces, a natural concept of equivariant transversality has been developed. We sketch the basic ideas and give some applications of equivariant transversality. Then we show how these ideas can be adapted to define a notion of equivariant non-degeneracy, which is important for the investigation of fixed orbits of equivariant maps and their relation to equivariant homotopy invariants. \\ Cake will be provided by Thomas
Mar 23	Fri	Nabil Freji (University of Sheffield)
13:05		MHD Sausage Oscillations in Magnetic Wave guides in the lower Solar Atmosphere
		Lecture Theatre 9
	Abstract: The lower solar atmosphere is host to a wide range of magnetic wave guides. From sunspots to inter-granular bright points, they are constantly buffeted by the surrounding photosphere from granulation, p-modes or by coherent sub-photospheric drivers. Here, we present the results of an observational study of MHD sausage waves in magnetic wave guides (pores and sunspots). By studying the temporal variations in area and intensity of these magnetic wave guides, it allows the observation and identification of MHD sausage waves. Using series of high-resolution intensity images with a small cadence and employing wavelet analysis in conjunction with empirical mode decomposition allows us to have a robust method for searching for and identifying characteristic periods hidden in the area and intensity data series. We found that the magnetic pore in Active Region 10968 displays three strong periods, 2-3, 8 and 13-14 minutes. The most plausible conclusion is that both the 2-3 and 8 minute periods detected are a harmonic of the fundamental 13-14 minute period. Due to the sharp gradients in the background equilibrium plasma parameters that exist at the boundaries of the photosphere and the transition region sets up a cavity that can support standing waves. This is the first observation of concurrent higher harmonics in a solar magnetic wave-guide in the lower solar atmosphere while the third reported observation of sausage modes in solar pores.
Mar 27	Tue	Robin Allan (Sheffield)	Pure Maths Postgraduate Seminar
13:00		An introduction to Morse Theory
		Hicks Seminar Room J11
	Abstract: Topological manifolds are spaces that are locally homeomorphic to Euclidean space. It is known that every 1-, 2- and 3-dimensional manifold has a unique smooth structure; however in higher dimensions there exist non-smoothable manifolds. This suggests that the existence of a smooth structure should impose restrictions on the topological invariants of the manifold, or in other words, we should should be able to study its topology using calculus. In this talk I will present some ideas and results from Morse Theory. The basic idea is to use the properties of smooth functions to deduce topological facts about smooth manifolds. This is mostly achieved by looking at the behaviour of functions near critical points, which will allow us to deduce facts about the homotopy type of a manifold and even calculate its Euler characteristic and homology groups. Since the general theory is quite technical, the talk will be focussed on demonstrating some of the main results through interesting examples.
Mar 28	Wed	Ian Leary (Southampton)	Pure Maths Colloquium
16:00		Platonic polygonal complexes and curvature
		Hicks Seminar Room J11
	Abstract: Examples of platonic polygonal complexes include the five regular solids, and the tesselations of the Euclidean and hyperbolic planes by regular polygons. There appear to be too many of them to hope to classify them all, but there are good results for some subfamilies. I shall state some of these results, and explain why the case when the polygons have at least six sides is the simplest case. [This is a self-contained talk, but if you enjoy this then you might be interested in the topology seminar on Thursday which will follow on from it.]
Mar 29	Thu	Eleanor Stillman (University of Sheffield)	Statistics Seminar
14:00		Optimal design for multiresponse experiments
		LT-6
	Abstract: Many statistical investigations require data to be collected so that the influence of explanatory variables on responses of interest can be deduced. Once there is more than a single response variable, there are potential conflicts of interest in selecting experiments which are efficient at estimating all responses. In this talk I will begin by introducing the general ideas of optimal experimental design and then focus on extensions to multiple responses. In particular, I will introduce a new composite optimality criterion which seeks to estimate a primary continuous response efficiently particularly when a second, binary, response has a positive outcome. I will also examine the practically important case of simultaneous estimation of both mean and variance of a single response.
Mar 29	Thu	Ian Leary (Southampton)	Topology Seminar
15:00		Platonic polygonal complexes II
		Hicks Seminar Room J11
	Abstract: A flag in a polygonal complex is a triple consisting of a mutually incident vertex, edge and polygon. A polygonal complex is said to be platonic if it admits a flag transitive group of symmetries. In this talk I shall go into more detail concerning the classification of some families of platonic polygonal complexes, focusing especially on the (rather degenerate) cases when the polygons have 3, 4 or 5 sides. (The original parts of this talk are joint work with T Januszkiewicz, R Valle and R Vogeler.) Cake will be provided by Sarah
Apr 2	Mon	Dr Dipankar Banerjee (Indian Institute of Astrophysics, Koramangala, Bangalore 560034, India)
10:00		Propagating Disturbances in open and closed magnetic structures of the Sun
		Lecture Theatre 9
	Abstract: Propagating disturbances are observed along open and closed magnetic structures of the sun. For characterizing the nature of the propagating disturbances a combination of spectroscopy and imaging is essential. In this talk I will show examples of such observations using SUMER/SoHO, EIS/Hinode with imaging sequences from AIA/SDO. We find two different groups of periodicities, short (<3 min) and long (>9 min) at different locations and circumstances. In the short range we find oscillations with periodicities as low as 50 s. Shorter periodicities show oscillations inall the three line parameters and the longer ones only show in intensity and Doppler shift butnot in line width. Often Line profiles at these locations do not show any visible blue-shiftedcomponent and can be fitted well with a single Gaussian. This allows us to conclude that the propagating disturbances represent waves and not flows. In the last part of my Talk I will also provide an update on the current status of the two large Indian solar observatory projects, namely the space coronagraph project called /Aditya/ and ground based facility from Himalayas called /NLST/.
Apr 24	Tue	Nadia Gheith (Sheffield)	Pure Maths Postgraduate Seminar
13:00		The rough cofibration category
		Hicks Seminar Room J11
	Abstract: Baues introduced a notion of cofibration category as a generalisation of a Quillen model category. He defined it to be a category together with two classes of morphisms called cofibrations and weak equivalences such that specific axioms are satisfied. In this talk I will introduce a notion of rough maps---these are maps between spaces preserving the large scale structure---and prove that the category of spaces and rough maps with two classes of morphisms called rough cofibrations and coarse homotopy equivalences satisfy the cofibration category axioms. This category will be called the rough cofibration category.
Apr 25	Wed	Nick Monk (Sheffield)	Applied Mathematics Colloquium
14:00		Modelling decision making in multicellular tissues.
		LT6
	Abstract: During the development of multicellular organisms, cells need to make decisions about their fate by integrating information from their neighbours, their surroundings, and their history. I will describe mathematical models of cellular decision making that reveal how cells can adopt different strategies depending on their setting, allowing them to make either rapid coordinated decisions or more measured decisions that provide more scope for the generation of cellular diversity.
Apr 25	Wed	Sam Marsh (Sheffield)	Pure Maths Colloquium
16:00		Non-standard analysis
		Hicks Seminar Room J11
	Abstract: Do infinitesimals exist? Bearing in mind that Pete and Bernie's Philosophical Steakhouse is now closed\footnote{http://www.youtube.com/watch?v=6Za2WFVrvpQ#t=275s}, I'll discuss two approaches to a non-standard system of analysis which starts from the premise that maybe they should. The original approach due to Abraham Robinson (1960s) has model theory as its basis and I'll cover this set-up from scratch. A reworking due to Edward Nelson (1970s) is based on an extension of ZF set theory and I'll discuss similar ground from this alternative viewpoint, where a possible conclusion is that infinitesimals were always knocking around, we just didn't notice them.
Apr 26	Thu	Ronnie Loeffen (University of Manchester)	Statistics Seminar
14:00		Spectral representations for affine processes
		LT-6
	Abstract: Affine processes are widely used in various areas of mathematical finance, like credit risk modelling, interest rate modelling and stochastic volatility models. One of the advantages of working with affine processes is that one can compute European option prices via Laplace/Fourier inversion after solving a system of non-linear, first order ODEs. However, an explicit solution to this system exists only in a limited number of cases and numerically solving it seems cumbersome. Based on the work of Ogura (1974/75) on continuous-state branching processes, we discuss an alternative method in which the system of ODEs is replaced by a number of decoupled, linear, first order PDEs. Pros and cons of the method will be indicated and also some examples will be provided.
Apr 26	Thu	Martin Crossley (Swansea)	Topology Seminar
15:00		Conjugation Invariants in the Adem-free Steenrod algebra
		Hicks Seminar Room J11
	Abstract: In work with Sarah Whitehouse we attempted to calculate the invariants of the mod 2 dual Steenrod algebra under the Hopf algebra conjugation. In work with Deniz Turgay we now tackle this problem by removing the Adem relations and working with a free associative algebra instead. We give a description of the linear structure of the conjugation invariants there, and comment on the remaining problem of deriving information on the Steenrod algebra.
Apr 26	Thu	Mike Payne, intro by Carol Calvert (Department of Work and Pensions)	RSS Seminar
16:30		Developing the DWP's Official Statistics Release - Tabulation Tool, Visualisation, and a Glimpse into the Future
		Hicks LT10
	Abstract: The Department of Work and Pensions have recently used published statistics on out-of-work benefit claimants to feed into Google's Public Data Explorer, which offers rich and powerful visualisations of the vast amount of statistics we release (see how over 50,000 figures can be displayed in one, interactive chart), and have complemented this with the publication of an interactive Google map showing the proportion of out-of-work benefit claimants across the country. The talk will briefly review the current DWP Tabulation Tool, describe how DWP's data is really suited to data visualisation, and demonstrate features to come - users will be able to create multi-dimensional tabulations, with the ability to download data directly in a number of formats (including the internationally recognised Statistical Data and Metadata Exchange - SDMX - format).
Apr 27	Fri	Peter Whyper (University of Sheffield)
13:05
		Lecture Theatre 9
May 3	Thu	Simon Wood (University of Bath)	Statistics Seminar
14:00		Simple statistical models for complex ecological data
		LT-6
	Abstract: Much ecological theory is based on models that are relatively simple to write down and simulate from, while at the same time being capable of displaying very complicated dynamics. This talk suggests that such near chaotic dynamics provide a case where it is sensible to abandon conventional likelihood or Bayesian approaches in favour of inference based on carefully chosen statistics of the data. The statistics should be designed to avoid the irregularity produced by highly non-linear dynamics, while still being informative about the dynamic structure of the system being modelled. A simple approach to inference is proposed, which requires only the ability to simulate from the model. The approach has links to ABC, generalized method of moments, indirect inference and similar approaches, but requires rather little tuning.
May 3	Thu	Andrew Lobb (Durham)	Topology Seminar
15:00		Two-strand twisting and knot homologies
		Hicks Seminar Room J11
	Abstract: We give an introduction to some quantum knot homologies and show how twisting up a pair of adjacent strands in a knot, combined with some straightforward homological algebra, allows us to deduce some interesting consequences.
May 4	Fri	Michael Bareford (University of St Andrews)
13:05		The Energy Released from Relaxing Coronal Loops
		Lecture Theatre 9
	Abstract: Relaxation theory offers a straightforward method for determining the energy released from a magnetic field when it undergoes an instability. Thus, an upper limit to the heating caused by ensembles of coronal loops can be estimated and compared with the coronal heating requirement. This talk will discuss the results obtained from the nonlinear magnetohydrodynamic (MHD) simulations of a sample of idealised coronal loops that are known to be linearly kink unstable. The principle aim is to determine whether or not these results agree with helicity-conserving Taylor relaxation (Taylor 1986, 1974). A three-dimensional (3D) MHD Lagrangian-remap code is used to simulate the evolution of specific line-tied field configurations based on a cylindrical coronal loop model. Initially, all configurations carry zero net current and are in ideally unstable equilibrium. Helicity is conserved to an acceptable level for all numerically-stable simulations. In addition, the energy release and final field profiles produced by the numerical simulations are in agreement with the predictions of relaxation theory: the relaxed field approximates a linear force-free state. Magnetic energy dissipation predominantly occurs within thin currents sheets. These results support the use of relaxation theory for calculating the heating-event distributions produced by ensembles of marginally unstable loops (Bareford et al. 2011). Bareford, M. R., Browning, P. K., and Van der Linden, R. A. M. 2011, Sol.Phys., 273, 93 Taylor, J. B. 1986, Rev. Mod. Phys., 58, 741 Taylor, J. B. 1974, Phys. Rev. Lett., 33, 1139
May 9	Wed	Anantanarayanan Thyagaraja (Bristol)	Applied Mathematics Colloquium
14:00		A KdV-like advection-diffusion equation with remarkable properties
		LT6
	Abstract: Nonlinear partial differential equations which arise naturally in the theory of wave propagation in many branches of physics have both a rich history and wealth of novel properties, not shared by their linearized equivalents. The Korteweg-de Vries Equation (KdVE), which is now more than 100 years old, occupies a special place in this class, along with the complex Nonlinear Schrödinger Equation (NLSE), and forms the core of the modern theory of the Inverse-Scattering-Transform technique of solving equations of this type. Some colleagues and I have recently encountered a close ''cousin'' of this equation [cf. Abhijit Sen et al, (2012), in press, Communications in Nonlinear Science and Numerical Simulations, also available as an ArXiv preprint] which has novel and interesting properties. It arose in a curious way during a ''genetic programming'' search looking for equations which share solutions in common with the KdVE. In this talk, I will outline some of the more in- teresting features of this equation which also serves as a counter-example to some commonly held views about recurrent solutions in certain con- servative nonlinear dispersive wave equations. The new equation also has some properties which are not shared by the KdVE and appears to define a new class of interesting nonlinear partial differential equations describing wave motions.
May 9	Wed	Sotiris Bersimis (University of Piraeus)	Statistics Seminar
14:00		Multivariate SPC with emphasis in multi-attribute processes
		LT-10
	Abstract: Initially, the area of multivariate SPC will briefly overviewed and the basic procedures for implementing multivariate statistical process control via control charting will be reviewed. Specifically, multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart type control charts, MCUSUM control charts, and MEWMA control charts will be summarized and the problem of interpreting an out-of-control signal will be briefly discussed. Additionally, since in the literature, little work has been done to deal with multivariate attributes processes, which are very important in practical production processes, the presentation will close by presenting the special case, which arises when the quality of process of interest is not characterized by continuous characteristics. Furthermore, after the key points of multi-attribute process will presented, some procedures for controlling such processes will be discussed.
May 11	Fri	Andrew Gascoyne (Sheffield)
13:05		PARTICLE TRAJECTORIES AND ACCELERATION DUE TO 3D MAGNETIC RECONNECTION
		Lecture Theatre 9
	Abstract: Magnetic reconnection is thought to be a primary mechanism in the acceleration of particles during flares in the solar corona. Particle acceleration by reconnection has been widely studied in 2D geometry, and thanks to recent work, particle acceleration in 3D is being investigated. We investigate the trajectories and acceleration of a particle injected into various 3D magnetic and electric field configurations by adopting a test particle approach. The electromagnetic fields studied here are solutions to the steady state, kinematic, resistive MHD equations (Wyper and Jain 2010). We numerically solve the equations that govern the motion of a charged particle in these electromagnetic fields and for various initial conditions, we analyse the kinetic energy of the particle and determine the regimes where efficient particle acceleration takes place.
May 17	Thu	Lee Fawcett (University of Newcastle)	Statistics Seminar
14:00		Estimating return levels from serially dependent extremes
		LT-6
	Abstract: In this talk, we investigate the relationship between return levels of a process and the strength of serial correlation present in the extremes of that process. Estimates of long period return levels are often used as design requirements, and peaks over thresholds (POT) analyses have, in the past, been used to obtain such estimates. However, analyses based on such declustering schemes are extremely wasteful of data, often resulting in great estimation uncertainty represented by very wide confidence intervals. Using simulated data, we show that - provided the extremal index is estimated appropriately - using all threshold excesses can give more accurate and precise estimates of return levels, allowing us to avoid altogether the sometimes arbitrary process of cluster identification. We then apply our method to two data examples concerning sea-surge and wind speed extremes.
May 17	Thu	Ivan Panin (St.Petersburg Department of V.A.Steklov Institute of Mathematics of the Russian Academy of Sciences)	Topology Seminar
15:00		Construction of the triangulated category DK_(k) of K-motives
		Hicks Seminar Room J11
	Abstract: We construct a triangulated category $DK_{(k)}$ of $K$-motives in the style of Voevodsky's construction of the category $DM(k)$. Each smooth $k$-variety has its $K$-motive $M_K(X)$ in the category $DK_{(k)}$ of $K$-motives and $\text{Hom}(M_K(X),M_K(pt)[n])=K_n(X)$, where $pt=Spec(k)$ and $K_n(X)$ is Quillen's $K$-groups of $X$. The $K$-motive $M_K(pt)$ of the point has a natural Grayson's "filtration". Due to Suslin's results successive cones of the "filtration" are the motivic complexes $Z(n)$. This observation gives rise to a new construction of a spectral sequence which starts at motivic cohomology of a smooth variety $X$ and converges to its Quillen $K$-groups. The results have been obtained joint with G. Garkusha.
May 18	Fri	Alistair Williamson (University of Sheffield)
13:05		Resonant damping of kink waves in a loop with a time dependent density
		Lecture Theatre 9
	Abstract: Resonant absorption is a popular and viable mechanism to model the twin problems of MHD wave damping in solar coronal structures (e.g. coronal loops or prominences) and the heating of the plasma in the magnetised corona. Earlier modelling applied the concept of resonant absorption of slow and Alfven waves in stationary plasma where the background equilibrium is time-independent. However, high-resolution observations of the current cohort of solar instruments clearly indicate that often there is a time-dependent plasma behaviour associated with loop oscillations. In this presentation we show the first steps made to address the challenges in the development of resonant MHD wave theory in a time-dependent plasma. Expressions for the decrease in wave amplitude and wave dissipation across both the Alfven and slow resonant points have been found for plasma structures within time-dependent models. This work also aims to show how the wave amplitude across the resonant point changes in time and contributes to the rapid damping of resonantly coupled driven MHD kink waves.
May 23	Wed	Jingsong He (Ningbo University, China)	Applied Mathematics Colloquium
14:00		Some new patterns of the higher order rogue waves of the NLS equation
		Lecture Theatre 10
	Abstract: The rogue wave of the Nonlinear Schrodinger equation is one kind of hot topic in the studies of water wave, plasma, nonlinear optics and mathematical physics. One core problem is the generating mechanism of this very novel phenomenon. In this talk I shall discuss how to make different patterns (including circular, triangle and their combinations) of the higher order rogue waves of the NLS from breather solutions, which provides a new insight of the mechanism of the rogue wave. I also hope to show similar results of Hirota equation if the time is sufficient.
May 30	Wed	Tobias Galla (Manchester)	Applied Mathematics Colloquium
14:00		Agent-based modelling of the nest-site choice by honeybee swarms
		LT10
	Abstract: In a recent paper List, Elsholtz and Seeley [Phil. Trans. Roy. Soc. B. 364, 755 (2009)] have devised an agent-based model of the the nest-choice dynamics in swarms of honeybees, and have concluded that both interdependence and independence are needed for the bees to reach a consensus on the best nest site. I here present a simplified version of the model which can be treated analytically with the tools of statistical physics and which largely has the same features as the original dynamics. Based on analytical approaches it is possible to characterize the co-ordination outcome exactly on the deterministic level, and to a good approximation if stochastic effects are taken into account, reducing the need for computer simulations on the agent-based level. In the second part of the talk I will discuss a spatial extension, and show that transient non-trivial patterns emerge, before consensus is reached. Reference: T. Galla, Independence and interdependence in the nest-site choice by honeybee swarms: Agent-based models, analytical approaches and pattern formation, J. Theor. Biol. 262 (2010) 186
Jun 6	Wed	Dave Benson (Aberdeen)	Pure Maths Colloquium
16:00		Cohomology of groups: a crossroads in mathematics.
		Hicks Seminar Room J11
	Abstract: I shall give an introduction to the cohomology of (mostly finite) groups for a general mathematical audience, from the points of view of homological algebra, topology, commutative algebra, representation theory, and (time permitting) number theory.
Jun 8	Fri	Stuart Mumford (University of Sheffield)
13:05
		Lecture Theatre 9
Jun 14	Thu	Etienne Ghys (Lyon)	Hardy Lecture Tour
16:00		The History of the Uniformization Theorem
		LT A
	Abstract: Marking the 100th anniversary of the death of Poincaré, this is a colloquium talk for a general mathematical audience.
Aug 13	Mon	Kris Klosin (New York)
11:00		Ihara's Lemma for imaginary quadratic fields
		Hicks Seminar Room J11
Sep 20	Thu	Jose M Redondo (UPC)	Applied Mathematics Colloquium
11:00		Dispersion in Coastal/complex flows
		LT9
	Abstract: Experimental and numerical KS results of turbulent flows in the sea surface near the coastline have been performed using both Lagrangian and Eulerian methods, field tests are presented using video recordings and velocity sensors. The spatial and temporal resolution is limited by the measuring instruments, which results in "filtering" out the very small scales. The experimental field-results obtained during the large-scale surf zone experiments carried out in the Ebro Delta, Vilanova and Recife (Spain), under spilling/plunging breaking waves are compared with experiments performed at the enclosed Barcelona and Olinda harbours. The field-measurements include several tests across the surf zone with high vertical resolution measuring dispersion coefficients both in time and space. The measured turbulent properties are compared with turbulence characteristics and length parameterisations. Diffusion from KS models, applied to oil slicks and buoy tracers is evaluated and compared with measurements in a complex non-homogeneous parameter space. The Diffusivity dependence with time D = c t^n is related to the local velocity spectra so that a generalized Richardson law may be used and evaluated as a function of local parameters such as distance from the coast.
Sep 24	Mon	Paul Mitchener (Sheffield)	Topology Seminar
15:00		Semigroup Algebras and Homology
		Hicks Seminar Room J11
	Abstract: In this talk, we look at the question of how we might compute the K-theory of a semigroup $C^*$-algebra. On the way, we look at a few features of equivariant homology for semigroups. I intend to take an elementary approach here, introducing all relevant concepts.
Sep 26	Wed	John Parker (Durham)	Pure Maths Colloquium
16:00		Constructing non-arithmetic lattices
		Hicks Seminar Room J11
	Abstract: A lattice is a discrete subgroup of a Lie group with finite covolume (with respect to Haar measure). Often the discreteness follows (in a rather general and abstract sense) from the discreteness of the integers in the reals, in which case the lattice is said to be arithmetic. In this talk I will survey lattices and arithmetic groups; constructions of non-arithmetic lattices and an ongoing project to produce new examples.
Oct 1	Mon	David Barnes (Sheffield)	Topology Seminar
15:00		Localisations of Stable Model Categories
		Hicks Seminar Room J11
	Abstract: Most of the homotopy theories that we are interested in are extremely complicated and it is hard to discern patterns in this data. To remedy this, we often discard some of the information of the homotopy theory in return for more structure. The canonical way of doing so is Bousfield localisation. In this talk I will introduce the notion of Bousfield localisations of model categories and show how in the stable case these localisations are very simple to construct.
Oct 3	Wed	Kevin McGerty (Oxford)	Pure Maths Colloquium
16:00		Noncommutative deformations and localisation
		Hicks Seminar Room J11
	Abstract: The classical localization theorem of Beilinson and Bernstein shows that the representation theory of semisimple Lie algebras can be studied geometrically via modules for the sheaf of differential operators on the flag variety. Recently there has been much interest understanding other contexts in which a similar localization results hold. We will review the classical theory and explain some of the recent developments.
Oct 4	Thu	Sigurd Assing (University of Warwick)	Statistics Seminar
14:00		On the spatial dynamics of the stochastic heat equation
	Abstract: When modeling complex phenomena by random fields $u(x,t)$ depending on a $d$-dimensional space parameter $x$ and time $t$ it is often useful to describe the dynamical behaviour of these fields by stochastic partial differential equations (SPDE). If a random field $u(x,t)$ is a solution of an SPDE then it is usually understood as a Markov process $u(\cdot,t)$, $t \geq 0$, taking values in a function space. Unfortunately this wipes out any structure of the solutions in the space parameter $x$. In this talk we recover this structure in the case where the SPDE is the so-called stochastic heat equation which is a simple toy example. The method used is mainly based on the technique of enlargement of filtrations and on Malliavin calculus. There is hope that it can be also applied w.r.t. other SPDEs.
Oct 8	Mon	Constanze Roitzheim (Kent)	Topology Seminar
15:00		Modular Rigidity of E-local Spectra
		Hicks Seminar Room J11
	Abstract: One key objective in stable homotopy theory is finding Quillen functors between model categories. Stable frames provide a way to construct and classify Quillen functors from spectra to any given stable model category. Furthermore, they equip the homotopy category of a stable model category with a module structure over the stable homotopy category Ho(Sp). We will investigate how this is compatible with Bousfield localisations and how it can be used to study the deeper structure of the stable homotopy category. We will then see that the Ho(Sp)-module structure completely determines the homotopy type of the E-local stable homotopy category for any homology theory E. Cake will be provided by Vikki
Oct 9	Tue	Eugenia Cheng (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Categorification
		Hicks Seminar Room J11
	Abstract: Categorification may be thought of as the general process of taking a theory of something and making a higher-dimensional version. The aim is to express greater subtleties and more closely model the higher-dimensional structures that appear in various branches of modern mathematics including homotopy theory, cohomology, K-theory, sheaves, topological quantum field theory, as well as in theoretical physics and theoretical computer science. Category theory provides a framework for the process of categorification, but the process is not straightforward or canonical. In this talk we will compare and contrast two methods: enrichment, in which the morphisms of a category are equipped with extra structure, and internalisation, in which the entire category is computed inside another one. While some familiarity with category theory will of course be useful, we will not actually assume any for this talk.
Oct 10	Wed	Neil Strickland (Sheffield)	Pure Maths Colloquium
16:00		An interesting surface of genus two
		Hicks Seminar Room J11
	Abstract: Any smooth surface of genus $g>1$ embedded in $S^3$ has a canonical structure as a Riemann surface. It can thus be expressed as a branched cover of the Riemann sphere, or as the quotient of the open unit disc by the action of a Fuchsian group. This is a remarkably rich structure, but the literature does not seem to contain any examples where it can all be made explicit. In this talk we will describe a certain highly symmetric surface with many interesting features, where we are close to finding parametrizations of the types described. Some computations for this project were carried out by Gemma Halliwell as a summer research project, supported by a Burkill studentship.
Oct 11	Thu	Andrew Beckerman (Sheffield (Animal and Plant Sciences))	Statistics Seminar
14:00		Graphs and Covariance in Ecology and Evolution
		K14
	Abstract: Here I introduce two major research themes in ecology and evolution: food web networks and quantitative genetics. Food web network theory borrows heavily, if inelegantly, from graph theory with vertices/nodes typically representing species and edges representing anything from binary connection to process. In this section I introduce two classes of food web models, and issues currently facing their use centred on observation and process error. Quantitative genetics centres on estimating genetic variation and covariation among traits that are important to survival and reproduction of organisms. We focus on these, represented as a variance-covariance matrix, because variation is required for evolution to happen, and positive and negative covariation represents constraint on what can happen among traits. In this section I introduce the hierarchical modelling we typically use, important eigensystem properties of the var-cov matrix, and recent transitions from parametric to Bayesian MCMC tools. The Bayesian MCMC methods appear to allow several types of comparisons among groups of individuals with strong inference.
Oct 12	Fri	Richard Boynton (Sheffield)	SP2RC seminar
13:00		How data analysis techniques can help advance knowledge of the magnetosphere
		Lecture Theatre B
	Abstract: The standard scientific approach is to develop knowledge from first physical principles, which are then combined to form a model of complex physical systems. However, there are many complex dynamical systems where a mathematical model cannot be deduced from first principles with our present level of knowledge. A few examples are biological systems such as the human brain or stem cells. The systems science approach is able to advance understanding of these highly complex systems. The approach involves advanced data analysis methodologies to identify relationships that describe the overall system behaviour. However, the systems approach in combination with partial knowledge from experimental data and first principles, can provide greater opportunities to uncover processes that determine the evolution of the physical systems. Here, system science is applied to the evolution of the magnetosphere. It is explained how the Error Reduction Ratio (ERR) concept of the NARMAX system identification technique, can be used to find nonlinear dependencies of the solar wind parameters on various aspects of the magnetospheric dynamics and how this technique aided in the validation of an analytical model for the reconnection geometry at the Earth's magnetopause. The analysis of the electron fluxes at geosynchronous orbit, employing the same technique, is shown to to give insight into the processes of particle acceleration and loss within the radiation belt. Finally, NARMAX models are shown to produce reliable forecasts using the identified dependencies as inputs.
Oct 15	Mon	Pokman Cheung (Sheffield)	Topology Seminar
15:00		Spinors on formal loops
		Hicks Seminar Room J11
	Abstract: tba
Oct 16	Tue	Robin Allan (Sheffield)	Pure Maths Postgraduate Seminar
14:00		An introduction to simplicial sets
		Hicks Seminar Room J11
	Abstract: A simplicial set can be thought of in three different ways; categorically, combinatorially or geometrically. Using the latter interpretation we could roughly say that a simplicial set is an object pieced together using simplices (n-dimensional triangles) that is rigid enough to be described using discrete information, but flexible enough to be able to perform basic constructions such as collapsing subspaces. This talk is my attempt to give the kind of introduction to simplicial sets that I would have wanted before attempting to understand the theory. Using the above geometric idea, we will start with simplicial complexes and then see how by considering some basic examples we are naturally lead to the definition of a simplicial set. We will then consider some interesting constructions and examples before finishing with a preview of some of the bigger picture; how the theory of simplicial sets can be used to transfer homotopy theoretic problems in the continuous world of topological spaces to the discrete world of combinatorics.
Oct 17	Wed	Prof. T. Talipova (Institute for Applied Physics, Nizhny Novgorod, Russia)	SP2RC seminar
13:50		Wave propagation in nonreflected media.
		Lecture Theatre 9
	Abstract: TBA
Oct 17	Wed	Fred Diamond (London)	Pure Maths Colloquium
16:00		Modular forms and mod p Langlands correspondences
		Hicks Seminar Room J11
	Abstract: A major part of the Langlands programme is a conjectural relationship between number-theoretic objects, such as Galois representations, and analytic ones, for example automorphic forms. These conjectures are now mostly proved in the context of classical modular forms on the one hand, and two-dimensional representations of Galois groups over Q on the other. One of the key results is Serre's Conjecture, proved by Khare and Wintenberger, which can be viewed as a mod p Langlands correspondence. An important feature of Langlands correspondences is a local-global compatibility principle, but it is not even known how to formulate a conjectural mod p version of this principle beyond the context of classical modular forms. I'll discuss what's known and what some of the difficulties are.
Oct 18	Thu	Markus Riedle (Kings College London)	Statistics Seminar
14:00		The stochastic heat equation driven by cylindrical Levy processes
		K14
	Abstract: The heat equation driven by Gaussian noise is the most fundamental and simplest example of a stochastic partial differential equation. Most of its properties and characteristics are well understood. However, given the restriction of Gaussian noise it is important to understand this fundamental equation if driven by a more general noise. In this talk we consider the heat equation driven by cylindrical Levy processes. These kinds of processes were introduced together with D. Applebaum a few years ago and they are a natural generalisation of the Gaussian noise. We give several examples of cylindrical Levy processes and introduce a stochastic integral with respect to these processes. In the main part, we explain how the heat equation can be solved and we show some of the phenomena which arise if the heat equation is no longer perturbed by a Gaussian noise but by a cylindrical Levy process.
Oct 23	Tue	Daniel Fretwell (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Splitting of primes in number fields.
		Hicks Seminar Room J11
	Abstract: We are all familiar with the prime numbers as being the multiplicative building blocks for all numbers bigger than 2. However if we move beyond the realm of the rational numbers certain primes may factorise further. Unfortunately uniqueness of factorisation is not always guaranteed so we must move into the setting of ideals (where factorisation is unique). In this talk we will answer the question of which primes split in general number fields, providing a few examples. We will also study the factorisation type of a prime by introducing Frobenius elements, special elements of the Galois group which encode arithmetic data about the splitting type. Finally we will see how the Artin reciprocity law lets us connect splitting types of primes in abelian extensions with classes mod N (for some integer N).
Oct 24	Wed	David Smith (Birmingham)	Applied Mathematics Colloquium
13:50		The fluid mechanics of sperm motility
		LT9
Oct 24	Wed	Martin Hyland (Cambridge)	Pure Maths Colloquium
16:00		Identity and Existence in Homotopy Type Theory
		LT4
	Abstract: The Dependent Type Theory of Per Martin-Lof is one of the most remarkable developments in Logic of the last 50 years; but its significance is difficult to pin down. It was taken up very early as the basis both for programming and specification languages and it stimulated work in theoretical computer science. However little serious attention was paid to one striking feature, the identity types. These are a clear pointer to a connection with basic ideas of homotopy theory, but it was not evident how to exploit this idea. Recently Voevodsky has made proposals for so-called Homotopy Type Theory and the outlines of a mathematical theory are beginning to emerge. I shall try to make the underlying ideas accessible to all.
Oct 25	Thu	Charles Taylor (University of Leeds)	Statistics Seminar
14:00		Regression for circular data
	Abstract: We consider data of the form $(x_i,y_i)$ in which either $x$ and/or $y$ is measured as an angle and we seek to model a relationship in which $y$ can be predicted from $x$. Starting with a review of existing parametric models, we put these into a common framework and discuss problems with estimation. Various nonparametric models, which make use of circular kernels, are described, as well as their asymptotic behaviour and approaches to bandwidth selection.
Oct 26	Fri	Nabil Freij (Sheffield)	SP2RC seminar
13:00		Whodunit? Pores
		LT 10
	Abstract: Magnetic pores are small-scale magnetic structures that are seen on the solar surface. Only high-resolution ground-based telescopes could really resolve the structure of pores until the launch of Hinode enabled great quality images to be taken from space. The formation and decay of a pore will be discussed. Then the focus will then turn to the oscillations and flows that exist in and around pores. Finally, a brief look into the formation of a penumbra.
Oct 29	Mon	Ines Henriques (Sheffield)	Topology Seminar
15:00		Quasi-complete intersections
		Hicks Seminar Room J11
	Abstract: Over a local ring $R$, we define an ideal $I$ to be quasi-complete intersection if the homology of the Koszul complex $E$ on a generating set of $I$ is free as a module over $S = R/I$, and the canonical map of graded S-algebras $\bigwedge_{*}^{S} ( H_{1} (E))$ → $H_{*} (E)$ is bijective. This class of ideals strictly contains the class of complete intersection (c.i.) ideals. The simplest type of quasi-c.i. ideals that are not complete intersections are generated by one exact zero-divisor. We will discuss the behavior of some basic homological and structural invariants with respect to the change of rings $R \to S$. Several basic invariants of $R$ determine those of the residue ring $R/I$ and recover the formulas that hold in the particular case when $I$ is generated by a regular sequence. Under additional hypothesis, we conclude that $R$ and $S$ are equally far from being Cohen-Macaulay, Gorenstein, or complete intersection.
Oct 31	Wed	Sarah Whitehouse (Sheffield)	Pure Maths Colloquium
16:00		A-infinity structures and minimal models
		Hicks Seminar Room J11
	Abstract: A-infinity structures arise in topology to describe a multiplication which is "associative up to homotopy". They have become important in various different areas of mathematics, including algebra, geometry and mathematical physics. After a brief survey, my main emphasis will be on the theory of minimal models. This involves studying differential graded algebras (dgas) via A-infinity structures on their homology algebras. I will also discuss a recent generalisation of these ideas.
Nov 1	Thu	Post-graduate talks - Mike Spence and Steph Llewelyn (Sheffield)	Statistics Seminar
14:00		Parameter Estimation of Individual-based models (Mike) and Statistical Modelling of Fingerprints (Steph)
		K14
	Abstract: Mike's Talk: Parameter Estimation of Individual-based models \par Individual-based models are increasingly used in ecological modelling as a way of trying to understand how individuals' behaviour leads to the emergent behaviour of the system. Generally the behaviour of the individuals is determined through a series of rules or algorithms, rather than described in a formal mathematical way, and this can represent a good way of capturing an ecologist's expertise and intuition. \par Quantifying uncertainty, estimating parameters and so on for a model of this sort are complicated by the fact that its probabilistic behaviour is implicit in its rules, rather than made explicit as in a more conventional statistical or stochastic model. This means that there is generally no explicit likelihood function available. I will discuss a number of methods of dealing with this and illustrate these methods with Railsback and Grimm's (2012) simplified model of woodhoopoe population dynamics. Stephanie's Title: Statistical Modelling of Fingerprints \par It is believed that fingerprints are determined in embryonic development. Unlike other personal characteristics the fingerprint appears to be a result of a random process. For example fingerprints of identical twins (whose DNA is identical) are distinct, and extensive studies have found little evidence of a genetic relationship in terms of types of fingerprint, certainly at the small scale. At a larger scale the pattern of ridges on fingerprints can be categorised as belonging to one of five basic forms: loops (left and right), whorls, arches and tented arches. The population frequencies of these types show little variation with ethnicity and a list of the types occurring on the ten digits can be used as an initial basis for identification of individuals. However, such a system would not uniquely identify an individual although the frequency of certain combinations could be extremely small. At a smaller scale various minutiae or singularities can be observed in a fingerprint. These include ridge endings and bifurcations, amongst others. Typical fingerprints have several hundred of these as well as two key points (with the exception of a simple arch) referred to as the core and delta, which are focal points of the overall pattern of ridges. Modern identification systems are based upon ridge endings and bifurcations, not least because they are the easiest to determine automatically from image analysis. The configuration of these minutiae is unique to the individual. \par The presentation will give an introduction to fingerprints from a forensic context and also outline a method use for matching a finger mark to a fingerprint.
Nov 5	Mon	Marcy Robertson (Western Ontario)	Topology Seminar
15:00		On Topological Triangulated Orbit Categories
		Hicks Seminar Room J11
	Abstract: In 2005, Keller showed that the orbit category associated to the bounded derived category of a hereditary category under an auto equivalence is triangulated. As an application he proved that the cluster category is triangulated. We show that this theorem generalizes to triangulated categories with topological origin (i.e. the homotopy category of a stable model category). As an application we construct a topological triangulated category which models the cluster category. This is joint work with Andrew Salch.
Nov 6	Tue	Thomas Athorne (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Monads in computer science
		Hicks Seminar Room J11
	Abstract: In the last few decades an interesting subject in Computer Science has been the development of 'functional' programming languages. These languages use a different paradigm to classical 'imperative' languages, and they come with some notable benefits. However, they also make some things much harder at first---especially processes with side effects, such as Input/Output, which is obviously of great importance to programmers. This problem has been overcome using a concept from category theory: that of a monad. In this talk, I will describe monads in category theoretic terms, give some simple examples, and note their great importance to mathematics by looking at the categories of algebras they produce. Then I will discuss another construction, that of the Kleisli category of a monad. Finally I will explain how the latter construction provides the necessary formalism to cleanly overcome the limitations of the functional paradigm.
Nov 6	Tue	John Greenlees (Sheffield)
17:00		Symmetries and Spaces
		Hicks Lecture Theatre 6
Nov 9	Fri	Alexander Hague (Sheffield)	SP2RC seminar
00:13		MHD Waves in a Magnetic Flux Tube with Applications
		LT 10
	Abstract: The aim of this talk is to look at MHD waves in a homogeneous flux tube and then at consequences of having an inhomogeneous background. The theory will be applied to oscillations in spicules. We conclude by briefly looking at resonant coupling of p-modes to waves in the solar atmosphere.
Nov 13	Tue	Magdalena Kedziorek (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Which finite groups act freely on spheres?
		Hicks Seminar Room J11
	Abstract: At the end of nineteenth century mathematicians asked which manifolds can be covered by spheres. This led to a slightly easier question: which finite groups can act freely on spheres? It turns out that this question is easy to answer in the even-dimensional case; for odd dimensions the proof is rather complicated although the answer is easy to state. The complete answer to the odd-dimensional sphere question was given by Madsen, Thomas and Wall more than half a century after the question was posed, In this talk we will give a proof of the result for even-dimensional spheres. Before we do that we will introduce all the tools from algebraic topology used in the proof. We will assume only the knowledge of basic topology - like topological space and homeomorphism.
Nov 14	Wed	Shigeo Kida (Kyoto)	Applied Mathematics Colloquium
14:00		What does the flake pattern represent in flows?
		LT9
	Abstract: Tiny and thin reflective flakes, such as aluminum powders, mica flakes or Kalliroscope, are widely used to visualize the flow structure in a closed container. From their brightness distribution we may obtain useful information on the flow, such as the occurrence of instability, the location of turbulent/non-turbulent boundaries, etc. However, it is not straightforward to identify which properties of the flow are reflected in the visualized patterns. We should note that it is not the orientation itself of the flake surface but its time-derivative that responds instantaneously to the velocity gradient. The orientation of flake surface has history effect and may not represent the local flow structure. In this talk we consider the mechanism of formation of brightness distribution of reflective flakes in flows in a precessing spherical cavity.
Nov 14	Wed	Pokman Cheung (Sheffield)	Pure Maths Colloquium
16:00		Vertex algebras and loop spaces
		Hicks Seminar Room J11
	Abstract: After a brief introduction of vertex algebras in general, I will describe an explicit example (the Weyl vertex algebra) related to the loop space of $R^n$. When $R^n$ is replaced by a more general manifold $M$, the construction encounters an obstruction, and provides a partial formulation of an important quantum field theory associated to $M$. This construction was first given by patching local data over coordinate charts, but there is also a `cleaner' method using principal bundles and semi-infinite cohomology. In fact, the latter is a special case of a more general construction that should have an interpretation in terms of the loop space of $M$.
Nov 15	Thu	Simon Spencer (University of Warwick)	Statistics Seminar
14:00		Causal inference for biochemical networks
	Abstract: In observation experiments it is impossible to distinguish between association and causation. To uncover causal relationships, interventions must be included in the experimental design. In complex systems, such as biochemical networks, there is frequently a high degree of association between interacting parts of the system. The aim of causal network inference is to untangle the causal structure behind these associations. In this study we developed a statistical model that captures the effect of inhibitors (an intervention) in a protein signalling network. We then used this model to perform causal network inference on protein microarray data from breast cancer cell lines. We were able to demonstrate that a causal inference approach increases the accuracy of the inferred networks.
Nov 15	Thu	David Jordan (Sheffield)
15:00		Poisson prime ideals in polynomial algebras
		Hicks Seminar Room J11
	Abstract: This is the first of a short series of seminars on Poisson algebras. A Poisson algebra $A$ is a commutative algebra with some extra structure that encodes a shadow of noncommutativity. Often a Poisson algebra is one of a parametrised family of algebras in which all the others are noncommutative and the lost noncommutativity is encoded in a Poisson bracket, this being a Lie bracket for which all the maps $\{a,-\}:A\rightarrow A$ are derivations. I will begin with an introduction, assuming not a lot, and proceed to some recent results, from joint work with S-Q Oh, classifying the Poisson prime ideals for a class of Poisson brackets on the polynomial ring $\mathbb{C}[x_1,\ldots,x_n]$ in $n\geq 3$ variables. The methods and results will be illustrated by examples in the case $n=4$.
Nov 15	Thu	Simon Shibli; Tom Fanshawe (Sheffield Hallam; Lancaster)	RSS Seminar
16:00		Olympic Statistics
		Hicks Room K14
	Abstract: A Review of Team GB's Performance in London 2012: 100 days before the start of London 2012, Simon Shibli predicted Team GB to win 27 gold medals, based on a combination of simple linear regression and quantification of the host nation effect. This talk will demonstrate the forecasting model, review the results of his other London 2012 forecasts and the performance of Team GB, and will conclude with the prospects for the host nation Brazil in Rio 2016. Multiple Event Competitions at the Olympic Games: In many sports, such as Olympic heptathlon or modern pentathlon, participants compete over different disciplines. How are performances on diverse events best summarised to declare an overall winner and are the current scoring systems fair? Tom Fanshawe will introduce issues in assessing multiple event data, using principal components analysis with data from the women's heptathlon at the 2008 and 2012 Olympics.
Nov 19	Mon	Jon Woolf (Liverpool)	Topology Seminar
15:00		Whitney Categories and the Tangle Hypothesis
		Hicks Seminar Room J11
	Abstract: Baez and Dolan's Tangle Hypothesis is that 'higher categories of tangles' have an algebraic characterisation as 'free multiply-monoidal categories with duals'. I will try to explain what this means and to make it precise within the context of `Whitney categories'. These are a geometric notion of 'higher category with duals', based on Whitney stratified spaces. I will then sketch how the Tangle Hypothesis for Whitney categories reduces to the Pontrjagin-Thom construction. This is joint work with Conor Smyth.
Nov 20	Tue	Konstantinos Tsaltas (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Monstrous Moonshine
		Hicks Seminar Room J11
	Abstract: In this talk I will present an introduction to the famous "Moonshine conjectures" of Conway and Norton (now a theorem due to Borcherds). These conjectures describe the connection between two (at first sight) different objects of mathematics; the largest sporadic finite simple group, the so-called Monster, and a very important complex function in number theory, the so-called J-function. An important feature of the Moonshine conjectures is that new and useful mathematical structures appeared in order to understand the connection, showing what a powerful object the Monster group is. Firstly, I will describe the Monster group and the J-function, and then I will discuss in which sense these are connected, by giving numerical evidence and by stating the conjecture.
Nov 20	Tue	Vic Snaith (Sheffield)	Number Theory seminar
15:00		Monomial resolutions in Number Theory: Galois descent, adelification
		F38 Hicks
Nov 20	Tue	Irakli Patchkoria (Bonn)	Topology Seminar
17:00		Rigidity in equivariant stable homotopy theory
		Hicks Seminar Room J11
	Abstract: Let G be a finite abelian group or finite (non-abelian) 2-group. We show that the 2-local G-equivariant stable homotopy category, indexed on a complete G-universe, has a unique G- equivariant model in the sense of Quillen model categories. This means that the suspension functor, homotopy cofiber sequences and the stable Burnside category determine all "higher order structure" of the 2-local G-equivariant stable homotopy category such as for example equivariant homotopy types of function G-spaces. The theorem can be seen as an equivariant generalization of Schwede's rigidity theorem at prime 2.
Nov 21	Wed	Sarah Rees (Newcastle)	Pure Maths Colloquium
16:00		When Artin groups are sufficiently large...
		Hicks Seminar Room J11
	Abstract: An Artin group is a group with a presentation of the form $$ \langle x_1,x_2,\cdots,x_n \mid x_ix_jx_i\cdots(m_{ij} \text{ terms })= x_jx_ix_j \cdots (m_{ij} \text{ terms }), i,j \in \{1,2,\cdots,n\}, i\neq j\rangle$$ for $m_{i,j} \in \mathbb{N} \cup \infty, m_{ij} \geq 2$, which can be described naturally by a Coxeter matrix or graph. This family of groups contains a wide range of groups, including braid groups, free groups, free abelian groups and much else, and its members exhibit a wide range of behaviour. Many problems remain open for the family as a whole, including the word problem, but are solved for particular subfamilies. The groups of finite type (mapping onto finite Coxeter groups), right-angled type (with each $m_{ij} \in \{2,\infty\}$), large and extra-large type (with each $m_{ij}\geq 3$ or $4$), FC type (every complete subgraph of the Coxeter graph corresponds to a finite type subgroup) have been particularly studied. After introducing Artin groups and surveying what is known, I will describe recent work with Derek Holt and (sometimes) Laura Ciobanu, dealing with a big collection of Artin groups, containing all the large groups, which we call `sufficiently large'. For those Artin groups we have elementary descriptions of the sets of geodesic and shortlex geodesic words, and can reduce any input word to either form. So we can solve the word problem, and prove the groups shortlex automatic. For many of those groups we can deduce the rapid decay property and verify the Baum-Connes conjecture. I'll explain some background for these problems, and outline their solution.
Nov 22	Thu	Barbel Finkenstadt (University of Warwick)	Statistics Seminar
14:00		Modeling and inference for gene expression time series data (an overview)
	Abstract: A central challenge in computational modeling of dynamic biological systems is parameter inference from experimental time course measurements of gene expression. We present an overview of the modeling approaches based on stochastic population dynamic models and their approximations. On the mesoscopic scale (small populations), we present a two dimensional continuous-time Bayesian hierarchical model which has the potential to address the different sources of variability that are relevant to the stochastic modelling of transcriptional and translational processes at the molecular level, namely, intrinsic noise due to the stochastic nature of the birth and deaths processes involved in chemical reactions, extrinsic noise arising from the cell-to-cell variation of kinetic parameters associated with these processes and noise associated with the measurement process. Inference is complicated by the fact that only the protein and rarely other molecular species are observed which is typically entailing problems of parameter identification in dynamical systems. On the macroscopic (or large populations) scale, we introduce a mechanistic 'switch' model for encoding a continuous transcriptional profile of genes over time with the aim of identifying the timing properties of mRNA synthesis which is assumed to switch between periods of transcriptional activity and inactivity, each time leading to the transition of a new steady state, while mRNA degradation is an ongoing linear process. The model is rich enough to capture a wide variety of expression behaviours including periodic genes. Finally, I will also give a brief introduction to some recent work on inferring the periodicity of the expression of circadian and other oscillating genes. Joint work with: Maria Costa, Dan Woodcock, Dafyd Jenkins, David Rand, Michal Komorowski (Warwick Systems Biology)
Nov 23	Fri	Stuart Mumford (Sheffield)	SP2RC seminar
00:13		Magnetic Bright Points and Solar Convection
		LT 10
	Abstract: This talk will look at recent observations of vortex events in the solar atmosphere. Observations of small scale convective downdrafts support modern solar convective theory. As well as providing an interesting possible source for the generation of torsional waves aligned with regions of enhanced magnetic field strength. We shall look at 4 observational papers from the first recorded observations of these vortices to a very recent paper observing torsional motions extending through many layers of the solar atmosphere. The implications for the generation of waves from these structures will be commented on and the implications of this as a coronal heating mechanism.
Nov 26	Mon	Andrew Stacey (Trondheim)	Topology Seminar
15:00		That which we call a manifold ...
		Hicks Seminar Room J11
	Abstract: It's well known that the mapping space of two finite dimensional manifolds can be given the structure of an infinite dimensional manifold modelled on Frechet spaces (provided the source is compact). However, it is not that the charts on the original manifolds give the charts on the mapping space: it is a little bit more complicated than that. These complications become important when one extends this construction, either to spaces more general than manifolds or to properties other than being locally linear. In this talk, I shall show how to describe the type of property needed to transport local properties of a space to local properties of its mapping space. As an application, we shall show that applying the mapping construction to a regular map is again regular. Note: the theme of this talk is the same as a talk I gave in Sheffield a little over a year ago so this can be thought of as a report on how my ideas have developed over the intervening time. I shan't assume that anyone remembers the original talk, whilst for anyone who does then there is definite progress to report. Cake will be provided by Philipp
Nov 27	Tue	Serena Murru (Sheffield)	Pure Maths Postgraduate Seminar
14:00		Gröbner bases
		Hicks Seminar Room J11
	Abstract: Gröbner bases were introduced in 1960 by Hironaka who first called them "normal bases". Independently, in 1965 Buchberger in his PhD thesis called them Gröbner bases (GB) in honour of his supervisor. Such bases for an ideal can be used to solve problems in different areas of maths such as algebraic geometry, commutative algebra, polynomial ideal theory, invariant theory, coding theory, partial differential equations, statistics and many others. Given a set F of polynomials in $K[x_1,..,x_n]$, we can transform F into another set G of polynomials with certain "nice properties" (called a "Gröbner basis") such that F and G generate the same ideal. From the theory of GB we know that many problems that are difficult for general F are easier for Gröbner bases G. Moreover there is an algorithm for transforming an arbitrary F into an equivalent Gröbner basis G, and the solution of the problem for G can often be easily translated back into a solution of the problem for F. In this talk we define Gröbner bases and we use them to solve some problems from commutative algebra. Moreover, we learn how to check if a basis for an ideal is Gröbner basis or not and we give a method to construct a Gröbner basis.
Nov 27	Tue	Daniel Loughran (Bristol)	Number Theory seminar
15:00		Rational points of bounded height and the Weil restriction
		F38 Hicks
	Abstract: If one is interested in studying diophantine equations over number fields, there is a clever trick due to Weil where one may move the problem from the number field setting to the usual field of rational numbers by performing a "restriction of scalars". In this talk, we consider the problem of how the height of a solution (a measure of the complexity of a solution) changes under this process, and in particular how the number of solutions of bounded height changes.
Nov 28	Wed	Sam Dolan (SoMaS, Sheffield)	Applied Mathematics Colloquium
14:00		Black hole instabilities: a cure for baldness?
		LT9
	Abstract: 'A black hole has no hair', suggested John Wheeler in 1973, summarizing the standard view that black holes have just three 'bald' characteristics: mass, electric charge and angular momentum. All other information is rapidly lost beyond the black-hole event horizon. In this talk, I will argue that in fact 'black holes are hirsute', if there exists in nature an ultra-light bosonic field with a Compton wavelength similar to the event horizon radius. If so, the black hole's 'hair' (i.e. certain modes in the bosonic field) will re-grow exponentially-fast in the linear regime. Hair-growth is generated by a phenomenon known as superradiance, which leads to stimulated extraction of rotational energy from the black hole. Through a variety of simulations I will explore the superradiant instability in detail to show how it may generate a 'black hole bomb': a radical cure for black-hole baldness!
Nov 28	Wed	László Németh (Sopron)	Pure Maths Colloquium
16:00		The crystal-growing ratios of hyperbolic honeycombs
		Hicks Seminar Room J11
	Abstract: In 3- and 4-dimensional hyperbolic spaces there exist regular tilings/mosaics (honeycombs). A belt can be created around an arbitrary base vertex of a mosaic. The construction can be iterated and a crystal-growing ratio can be determined by using the number of the cells of the considered belts. In my talk I would like to introduce some hyperbolic regular mosaics and determine their crystal-growing ratios.
Nov 29	Thu	Christopher Brignell (Nottingham)	Statistics Seminar
14:00		Statistical shape analysis, with an application to chemoinformatics
		K14
	Abstract: Statistical methods for evaluating and comparing shapes are necessary is a wide range of disciplines. For example, in biology we may wish to classify an organism based on its shape, or in computer science we may wish to develop methods for automated face or fingerprint recognition. One emerging application is to molecular structures such as proteins and DNA to investigate properties of chemical bonding. In this talk I will provide an introduction to shape analysis and then apply the results to chemoinformatics.
Dec 3	Mon	Dmitry Kaledin (Steklov Institute of Mathematics)	Topology Seminar
15:00		Derived Mackey functors
		Hicks Seminar Room J11
	Abstract: Mackey functors associated to a finite group $G$ appear both in equivariant stable homotopy theory and in finite group theory, and are quite useful in both areas. Since Mackey functors form an abelian category, one can consider its derived category. However, I going to argue that there is a better alternative: a triangulated category containing the abelian category of Mackey functors but different from its derived category, with a better behavior, more natural definition, and more closely approximating equivariant stable homotopy category. Moreover, our derived Mackey exist in bigger generality, and what is the natural counterpart of this in stable homotopy seems to be an interesting question. Cake will be provided by Pokman
Dec 4	Tue	Jonathan Elliott (Sheffield)	Pure Maths Postgraduate Seminar
14:00		The Yoneda Lemma
		Hicks Seminar Room J11
	Abstract: The Yoneda lemma is a fundamental result in category theory with applications to many areas of mathematics, including algebra and topology. In particular, it allows us to interpret presheaves in a meaningful way as describing such concepts as limit points in a metric space or, more abstractly, as so-called "virtual objects" of a category. I will start by recalling Cayley's theorem, which states that every group is isomorphic to a subgroup of a group of permutations, and of which the Yoneda lemma is a vast generalisation. After introducing the main result, I aim to put across some sense of its significance and what it really means, as this can be somewhat hard to appreciate at first. To conclude, I will give a sketch proof.
Dec 5	Wed	Gavin Brown (Loughborough)	Pure Maths Colloquium
16:00		Geography of projective varieties
		Hicks Seminar Room J11
	Abstract: I will review well-known parts of the classification of complex algebraic varieties in low dimension, starting with curves, which are classified into irreducible families by their genus, and surfaces, where additional invariants come into play. My aim is to survey the extent to which we know all Fano 3-folds, which are the (complex) 3-dimensional analogues of curves of genus zero. I will draw a map (that is, a region in a space of integer invariants like the genus) where they all must live, and explain recent attempts to populate this. In particular, I will sketch a method that constructs different families of varieties that have the same basic algebro-geometric invariants (their associated commutative Gorenstein coordinate rings have the same Hilbert series) but are distinguished by their topology (they have different Euler characteristic).
Dec 6	Thu	Ian Vernon (Durham)	Statistics Seminar
14:00		Galaxy Formation: A Bayesian Uncertainty Analysis
		K14
	Abstract: The question of whether there exists large quantities of Dark Matter in our Universe is one of the most important problems in modern cosmology. This project deals with a complex model of the Universe known as Galform, developed by the ICC group, at Durham University. This model simulates the creation and evolution of approximately 1 million galaxies from the beginning of the Universe until the current day, a process which is very sensitive to the presence of Dark Matter. A major problem that the cosmologists face is that Galform requires the specification of a large number of input parameters in order to run. The outputs of Galform can be compared to available observational data, and the general goal of the project is to identify which input parameter specifications will give rise to acceptable matches between model output and observed data, given the many types of uncertainty present in such a situation. As the model is slow to run, and the input space large, this is a very difficult task. We have solved this problem using general techniques related to the Bayesian treatment of uncertainty for computer models. These techniques are centred around the use of emulators: fast stochastic approximations to the full Galform model. These emulators are used to perform an iterative strategy known as history matching, which identifies regions of the input space of interest. Visualising the results of such an analysis is a non-trivial task. The acceptable region of input space is a complex shape in high dimension. Although the emulators are fast to evaluate, they still cannot give detailed coverage of the full volume. We have therefore developed fast emulation techniques specifically targeted at producing lower dimensional visualisations of higher dimensional objects, leading to novel, dynamic 2- and 3-dimensional projections of the acceptable input region. These visualisation techniques allow full exploitation of the emulators, and provide the cosmologists with vital physical insight into the behaviour of the Galform model.
Dec 7	Fri	Samuel Bennett (Sheffield)	SP2RC seminar
00:13		Macrospicules and other Chromospheric objects
		LT 10
	Abstract: 'We will be looking at how our understanding of Macro spicules has changed over the last 15 years as new instruments have been utilised to study the objects. We will look at the chromosphere through different wavelengths and ask whether what we are looking at is what we think it is.'
Dec 10	Mon	Tom Leinster (Edinburgh)	Topology Seminar
15:00		Entropy is inevitable
		Hicks Seminar Room J11
	Abstract: The title refers not to the death of the universe, but to the fact that the concept of entropy is present in the pure-mathematical heartlands of algebra and topology, whether we like it or not. I will describe a categorical machine which, when fed as input the concepts of topological simplex and real number, produces as output the concept of Shannon entropy. The most important component of this machine is the notion of "internal algebra" in an algebra for an operad (generalizing the notion of monoid in a monoidal category). The resulting characterization of Shannon entropy can be stripped completely of its categorical garb, to obtain a simple, new, and entirely elementary characterization. This last theorem is joint work with John Baez and Tobias Fritz. Cake will be provided by Callan
Dec 11	Tue	Victoria Quigley (Sheffield)	Pure Maths Postgraduate Seminar
14:00		An introduction to (positive) scalar curvature
		Hicks Seminar Room J11
	Abstract: In Riemannian geometry, there are different notions of the curvature of a manifold. Scalar curvature is perhaps the simplest curvature invariant of a manifold, and associates with each point of a manifold a single real number. There are a number of problems in general relativity which relate to the scalar curvature of a manifold. These, along with the purely topological and geometrical applications, mean that scalar curvature is a thriving area of mathematical research. In this seminar I will assume no knowledge of Riemmanian geometry, and will introduce the definition of scalar curvature. I will then briefly discuss manifolds with positive scalar curvature specifically, and talk about the idea of a topological obstruction to positive scalar curvature.
Dec 11	Tue	Neil Dummigan (Sheffield)	Number Theory seminar
15:00		Ramanujan-style congruences of local origin
		F38 Hicks
	Abstract: I will give a proof of an analogue (apparently discovered recently by Harder) of Ramanujan's mod 691 congruence. The modulus is a prime dividing an Euler factor for $\zeta(k)$, hence dividing a value of an incomplete zeta function, but not of the complete zeta function (whereas 691 comes from the complete $\zeta(12)$). Though I will briefly review something of modular forms, this seminar is probably a waste of time if you've never seen them before.
Dec 12	Wed	David O'Sullivan	Pure Maths Postgraduate Seminar
14:00		Quasicrystals, Penrose Tilings and C*-Algebras
		Hicks Seminar Room J11
	Abstract: The 2011 Nobel prize for Chemistry was awarded for the discovery of a type of non-repeating crystal structure exhibiting 5-fold rotational symmetry that was previously thought impossible. This discovery of a so called "quasicrystal" spawned a branch of chemistry called mathematical crystallography, in which quasicrystals (and crystals in general) are studied using the mathematics of non-commutative topology and geometry. This mathematical description comes from looking at their diffraction patterns. These form tilings of the Euclidean plane, and it turns out that the diffraction pattern of the first ever quasicrystal forms an example of one of the most famous tilings of the plane - a Penrose Tiling. Such tilings have a natural description in terms of a particular nice class of C*-algebras which can be completely characterised by the K_0 group of analytic K-theory. In this talk we will look at how the mathematics of the first quasicrystal is the same as that of a Penrose tiling, and then construct the C*-algebraic description of the space of all Penrose tilings.
Dec 12	Wed	Tim Browning (Bristol)	Pure Maths Colloquium
16:00		How frequently does the Hasse principle fail?
		Hicks Seminar Room J11
	Abstract: Counter-examples to the Hasse principle are known for many families of geometrically rational varieties. We discuss how often such failures arise for Chatelet surfaces and, if time permits, for certain higher-dimensional hypersurfaces. This is joint work with Regis de la Breteche.
Dec 13	Thu	Jenny Barrett (Leeds)	Statistics Seminar
14:00		Identifying causal genetic variants and other related problems in statistical genetics
		K14
	Abstract: Genome-wide association (GWA) studies have been successful in recent years at finding associations between common genetic variants and disease by careful application of simple statistical methods. For most common diseases, this has led to the identification of a number of genetic regions that clearly harbour a genetic variant or variants that influence risk of disease. However, due to strong and complex patterns of correlation between genetic variants located close together, it is usually still unknown which variant(s), and often even which gene, in the region actually has a causal effect on the trait. We are applying statistical approaches to shed light on what is going on in the genetic regions associated with melanoma. Our primary approach is to select the most parsimonious model(s) that explain the association signal in the region (e.g. using penalized logistic regression of all variants in the regions simultaneously), and then as a second step to look at biological plausibility of the models. There are various outstanding problems in this area. Is there a more effective way of combining statistical and biological information? Regions may be genotyped at several different levels of density, right down to the highest resolution of knowing the entire genetic sequence in the region. If data are available at different densities on different subsets of individuals, how can they best be combined? Can including related individuals in the analysis help in the identification of causal variants, especially if these are rare? These problems will be discussed in further detail, with time for questions -- and any suggestions of answers!
Dec 21	Fri	Eamon Scullion (University of Oslo)	Applied Mathematics Colloquium
13:00		Type-II spicule heating and magnetic fields
		LT 09
	Abstract: Over the past decade there has been a resurgence in the study of small-scale chromospheric jets known, classically, as spicules. Recent observations have lead us to conclude that there are two distinct varieties of spicule, namely, slower type-I (i.e. mottles, dynamic fibrils, H-alpha spicules etc.) and faster type-II (RBEs: Rapid Blue-shift Excursions on-disk). Such events dominate the dynamics of the chromosphere. Joint SDO (Solar Dynamics Observatory) and Hinode observations have revealed that fast spicules are the source of hot plasma channelling into the corona. Here we report on the properties of this widespread heating with observations from the high resolution CRISP (CRisp Imaging SpectroPolarimeter) instrument at the SST (1-m Swedish Solar Telescope, La Palma) and co-aligned NASA/SDO data. We reveal new insight into the formation mechanism of type-II spicules through considering the distribution of RBEs with respect to their magnetic fields rooted in the photosphere.
Jan 11	Fri	David Kuridze (Queen's University (Belfast))	SP2RC seminar
13:00		Observations of a failed filament eruption in a solar active region
		LT 10
	Abstract: TBA
Jan 18	Fri	Chris Nelson (Sheffield)	SP2RC seminar
13:00		Ellerman Bombs: Why should we be interested in small-scale, photospheric events?
		LT 9
	Abstract: Ellerman bombs, often written as EBs, are small-scale events in the photosphere. They are easily observed around emerging active regions in the wings of the H-alpha line profile and manifest as increases in intensity in the line wings. In this talk, we will discover why there has been such an interest in these events in the past decade, including basic properties, links to the magnetic field and, interactions with other photospheric events. We will also discuss future questions to answer with regard to EBs.
Jan 29	Tue	Daniel Lopez-Fogliani (UBA-IFIBA CONICET, Argentina)
14:00		Probing the $\mu$-from-$\nu$ supersymmetric standard model with displaced multileptons from the decay of a Higgs boson at the LHC
		Hicks Lecture Theatre 5
	Abstract: The $\mu$-from-$\nu$ supersymmetric standard model ($\mu$-$\nu$-SSM) is an R-parity breaking model that solves the $\mu$-problem and explains the origin of neutrino masses by simply using right-handed neutrinos, and thus has been proposed as an alternative to the minimal supersymmetric standard model (MSSM). Since the search for supersymmetry is one of the main objectives of the LHC, it is of paramount importance a rigorous study of an unmistakable signature of the model. In this talk we place special emphasis on a signal featuring non-prompt multileptons, arising from the decay of the 125 GeV boson detected at the LHC into a pair of long-lived neutralinos.
Jan 30	Wed	Yohann Duguet (LIMSI-CNRS, Orsay)	Applied Mathematics Colloquium
14:00		Oblique laminar-turbulent interfaces in wall-bounded shear flows
		LT9
	Abstract: The onset of transition to turbulence in subcritical wall-bounded flows is characterised by large-scale localised structures such as turbulent spots or turbulent stripes. Interestingly, the laminar-turbulent interfaces associated with these structures always display obliqueness with respect to the mean direction of the flow. We will attempt to explain this phenomenon using an assumption of scale separation between large and small scales, and we can show analytically that the corresponding laminar-turbulent interfaces are always oblique with respect to the mean direction of the flow. In the case of plane Couette flow, the mismatch between the streamwise flow rates near the boundaries of a single turbulence patch generates a large-scale flow with a non-zero spanwise component. Advection of the small-scale turbulent fluctuations by the corresponding large-scale flow distorts the shape of the turbulence patch and is responsible for its oblique growth. This mechanism can be easily extended to other flows such as Plane Poiseuille flow or Taylor-Couette flow.
Jan 30	Wed	James Norris and Jean Bertoin (Sheffield Probability Day) (Cambridge and ETH Zurich)	Statistics Seminar
14:15		James Norris (Cambridge) 2.15 pm A consistency estimate for Kac's model of elastic collisions in a dilute gas. Jean Bertoin (ETH Zurich) 3.45 pm The 2012 Applied Probability Trust Lecture: Almost giant clusters for percolation on large trees with logarithmic heights.
		LT 7
	Abstract: Abstract for James Norris's talk: Kac's process is a natural stochastic particle model, of mean field type, for the evolution of particle velocities under elastic collisions. Formally this should converge to the spatially homogeneous Boltzmann equation in the large particle number limit. In one of the physically interesting cases, namely hard sphere collisions, this was proved by Sznitman. We will discuss a new proof this result, which leads to some quantitative refinements, based on the simple approach of treating the martingale decomposition for linear functions of Kac's process as a random perturbation of Boltzmann's equation. Abstract for Jean Bertoin'ss talk: We consider Bernoulli bond percolation on a tree with size $n\gg 1$, with a parameter $p(n)$ that depends on the size of that tree. Our purpose is to investigate the asymptotic behavior of the sizes of the largest clusters for appropriate regimes. We shall first provide a simple characterization of tree families and percolation regimes which yield giant clusters, answering a question raised by David Croydon. In the second part, we will review briefly recent results concerning two natural families of random trees with logarithmic heights, namely recursive trees and scale-free trees. We shall see that the next largest clusters are almost giant, in the sense that their sizes are of order $n/\ln n$, and obtain precise limit theorems in terms of certain Poisson random measures. A common feature in the analysis of percolation for these models is that, even though one addresses a static problem, it is useful to consider dynamical versions in which edges are removed, respectively vertices are inserted, one after the other in certain order as time passes.
Feb 4	Mon	John McCleary (Vassar College)	Topology Seminar
15:00		Topology for Combinatorics
		Hicks Seminar Room J11
	Abstract: Topology studies spaces that include spaces of all possible configurations of combinatorial problems. Often the configurations come with symmetry and the problem at hand can be rewritten as a linear condition on a test map. Within this framework, topological methods can be made to give concrete combinatorial results. In joint work with Pavle and Alexandra Blagojevic, we use algebraic topology to carry out this method.
Feb 5	Tue	Matthew Gadsden (Sheffield)	Pure Maths Postgraduate Seminar
13:00		Asymptotic dimension of large scale spaces
		Hicks Seminar Room J11
	Abstract: Coarse geometry is the study of large scale properties of spaces. In coarse geometry, we want to consider two spaces as being the same if they "behave the same at infinity", neglecting the fine detail. For example we consider the real numbers and the integers as being the same, as they look the same when you view them from far away. In topology there are notions of assigning a topological invariant to a space which captures the idea of dimension. I will give an overview of a coarse analog of this, known as asymptotic dimension. Asymptotic dimension plays a key role in coarse geometry, and is needed in proofs of many important theorems. In this talk we shall begin by introducing coarse maps and coarse equivalences, and then we shall move on to defining covering dimension and asymptotic dimension with examples. In the final section, I will give a general overview of some main results in coarse geometry. No prior knowledge will be assumed other than the concept of a metric space.
Feb 6	Wed	Dror Bar-Natan (Toronto)	Pure Maths Colloquium
16:00		Meta-Groups, Meta-Bicrossed-Products, and the Alexander Polynomial
		Hicks Seminar Room J11
	Abstract: I will define "meta-groups" and explain how one specific meta-group, which in itself is a "meta-bicrossed-product", gives rise to an "ultimate Alexander invariant" of tangles, that contains the Alexander polynomial (multivariable, if you wish), has extremely good composition properties, is evaluated in a topologically meaningful way, and is least-wasteful in a computational sense. If you believe in categorification, that's a wonderful playground. All the terms used in the above paragraph will be defined during my talk. Please see http://www.math.toronto.edu/~drorbn/Talks/Sheffield-130206/ for further information and a handout.
Feb 7	Thu	Amy Baddeley and Stefan Blackwood	Statistics Seminar
14:00		Any Baddeley: Using Bayes Factors to analyse fine-mapped genotype data Stefan Blackwood: Partially observed systems
		K14
	Abstract: Abstract for Amy Baddeley's talk: Recent developments in genetic analysis mean that we have been able to identify many associations between genetic variants and common diseases. However, it is likely that most of the variants identified so far are not actually the causal variants, but are in fact confounders. Now the priority is shifting to identifying the causal variant in a disease association region (fine-mapping). Methods utilised in published studies to identify causal variants include the likelihood ratio (LR) and other frequentist methods. However, high levels of correlation, rare causal variants and those with small effect sizes mean such analyses may not work in all situations. The restrictive effects of these may be partially countered by incorporating functional biological information into an analysis. I will begin by giving a brief introduction to the genetic setting of the problem and the problem itself. I will then outline a general framework of analysis, "filtering", and the main method that will be presented uses the Bayes Factor (BF) in this framework. BF is the ratio of the probability of the data under alternative and null hypotheses, with a larger value indicating more evidence in favour of the alternative hypothesis. I will show the results of analyses using realistic simulated datasets and explore using fairly uninformative priors compared to using priors based on functional data. Our results indicate that BFs are a promising tool for incorporating functional information into fine-mapping studies. Abstract for Stefan Blackwood's talk: Suppose you have a random system which is not directly observable, instead you have a sequence of partial observations. Using the information gathered from these observations, what can we infer about the underlying system? Using stochastic models to make these deductions is known as stochastic filtering. During this talk I will provide a brief account of linear and non-linear stochastic filtering in the presence of Lévy noise and their respective cornerstones the Kalman Bucy filter, and the Zakai equation.
Feb 8	Fri	Rebecca White (Warwick University)	SP2RC seminar
13:00		Transverse loop oscillations in the solar corona: First observation at flare temperatures.
		LT 10
	Abstract: In this study we report and analyse the first observation of a transverse oscillation in a hot coronal loop with the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO), following a linked coronal-flare mass-ejection event on the 3 November 2010. The oscillating coronal loop is observed off the east solar limb and exclusively in the 131 angstrom and 94 angstrom bandpasses, indicating a loop plasma of temperature in the range of 9 - 11 MK. Furthermore, the loop is not observed to cool into the other AIA channels, but just disappears from all bandpasses at the end of the oscillation. This is the first observation of a transverse loop oscillation observed exclusively in the hot coronal lines. The loop oscillation is vertically polarised and is dominated by a higher order harmonic mode. We conclude that the excitation mechanism of this 5 min period oscillation is directly connected with the reconnection processes that form the post flare loop, which differs from the blast wave excitation mechanism often proposed as the cause of cooler transverse loop oscillations.
Feb 12	Tue	Andrew Jones (Sheffield)	Pure Maths Postgraduate Seminar
13:00		Riemann Hypothesis
		Hicks Seminar Room J11
	Abstract: The Riemann hypothesis is one of the most famous unresolved problems in mathematics today. Proposed by Bernhard Riemann in the mid-19th Century, it concerns the location of the zeros of the Riemann zeta function, and has implications for the distribution of prime numbers. In this talk I will introduce the Riemann zeta function, outline the problem itself, and consider the consequences that a proof would have on the distribution of primes. I will then briefly discuss an interesting connection between the zeros of the Riemann zeta function and the eigenvalues of random matrices.
Feb 13	Wed	Eugenia Cheng (Sheffield)	Pure Maths Colloquium
16:00		The periodic table of n-categories
		Hicks Seminar Room J11
	Abstract: Degenerate $n$-categories are those whose lowest $k$ dimensions are trivial, for some $k>0$. These can be thought of as the categorical analogue of loop spaces. The resulting multiplicative structures are interesting in their own right, and fit into a table known as the ``Periodic table of $n$-categories''. The table has various interesting patterns observable in low-dimensions and conjectured in general by Baez and Dolan. The structures that arise in this way include monoids and commutative monoids, as well as monoidal, braided, and symmetric monoidal categories. We will outline the main ideas behind the Periodic Table, its patterns and predictions, including the crucial stabilisation property which lead Baez and Dolan to conjecture a beautiful universal property to characterise higher-dimensional tangles. The talk will be introductory, and knowledge of definitions of $n$-category will not be assumed.
Feb 14	Thu	Elizabeth Boggis and Samuel Touchard	Statistics Seminar
13:30		Elizabeth Boggis: Exploiting Bayesian Shrinkage within a Linear Model Framework to identify Exome Sequence Variants associated with Gene Expression Samuel Touchard: MicroRNA predictions using Bayesian graphical models
		K14
	Abstract: Elizabeth's Abstract: Next-Generation exome sequencing identifies thousands of DNA sequence variants in each individual. Methods are needed that can effectively identify which of these variants are associated with changes in gene expression. The Normal-Gamma prior has been shown to induce effective and flexible shrinkage in the Bayesian linear model framework (Griffin and Brown 2010). Using simulated data we assess the efficacy and limitations of this Bayesian shrinkage framework in parsimoniously identifying such sequence variants. We further develop a Bayesian linear model to include the uncertainty in gene expression; SNP functional information obtained from on-line databases; and the uncertainty in the allele calls as quantified by the quality score. Samuel's Abstract: In this presentation we describe miRNA networks for patients suffering from Acute Coronary Syndrome (ACS). miRNA are non-coding RNAs that regulate gene expression. We are interested in building an association network, which will identify (within quantifiable uncertainty) miRNAs that regulate particular genes (or groups of genes) and thus providing important information of genetic functionality or dis-functionality. Data were collected, consisting of gene expression levels of miRNAs and mRNAs of patients who suffer from ACS. RNA was extracted from blood samples at two time points, and expression levels were quantified with affymetrix genechip arrays and normalised using puma package for microarray data analysis. The method is broken down to 3 stages. In the first stage a dimensionality reduction is performed; using TargetScan association scores the miRNA expressions are narrowed down, as are the gene expressions by using distance similarity procedures such as clustering and latent process decomposition. In the second stage a Bayesian graphical model is proposed, according to which associations of gene expressions and miRNA expressions are inferred and an association matrix is extracted. The methodology uses simulation-based methods, in particular Markov chain Monte Carlo, and benefits by managing uncertainty at a complex network. Finally, in the third stage and using the association matrix the network is constructed. Some extensions of this model will be discussed.
Feb 14	Thu	Muriel Livernet (Université Paris 13)	Topology Seminar
15:00		On the homology of the Swiss-Cheese operad
		Hicks Seminar Room J11
	Abstract: In this talk I will define the Swiss-cheese operad (a combination of the little discs and the interval operad), and show our main resuls: the homology of the Swiss-cheese operad is Koszul the spectral sequence associated to the geometric Swiss-cheese operad degenerates at $E_2$. In order to do this I will briefly explain how it has been done for the little discs operad, and point out the difficulties inherent to the Swiss-cheese operad.
Feb 15	Fri	Davina Innes (Max-Planck-Institute for Solar System Research (Germany))	SP2RC seminar
13:00		Observations of quiet-Sun transition region and coronal transients
		LT 9
	Abstract: The Solar Dyanamics Observatory is revolutionizing our view of solar plasma processes. Coronal and transition-region brightenings are now seen as jets and flows, and eruptions produce multiple waves and oscillations. Here we focus on the response of the transition-region and coronal plasma to small bursts of energy release in the supergranular network. Numerous names have been given to these events (e.g. explosive event, network flare, blinker, mini-CME) and it is often asked how they are related and if there is a common triggering mechanism. The majority appear along network lanes and junctions where supergranular flows sweep up small concentrations of mixed-polarity magnetic flux. We use images and spectra to investigate small-scale transient phenomena in the context of their underlying magnetic field and supergranular flows, paying special attention to explosive events with jet-like signatures in their spectral line profiles.
Feb 19	Tue	Mohammad Abbasirad (Sheffield)	Pure Maths Postgraduate Seminar
13:00		Introduction to the category of differential graded modules.
		Hicks Seminar Room J11
	Abstract: The concept of grading and differential appear in homological algebra and topology. Differential graded algebras and differential graded modules are a kind of machinery which formulates these concepts. In this talk, DG algebras and DG modules will be introduced and some important examples will be explained as well. Additionally, the category of DG modules will be compared with the category of topological spaces briefly and a nice class of modules, called semi-free modules will be presented. At the end, a theorem, stating every DG module has a semi-free approximation, will be explained.
Feb 19	Tue	Tom Oliver (Nottingham)	Number Theory seminar
16:00		Arithmetic Surfaces and Associated Zeta and L-Functions
		LT11 Hicks
	Abstract: Much of modern number theory is concerned with non-commutative extensions of Tate's thesis in the direction of the Langlands program. Slightly less common are commutative extensions to higher dimensions. One of the natural goals of such an extension is an integral representation of the zeta function of an arithmetic surface, and the study of meromorphic continuation and functional equation. In the case of models of curves over global fields, connections to the L-function allow us to study the same analytic properties in a way that does not depend on automorphicity. I will sketch the basic landscape of this theory and look for relationships with classical theory in two contexts: modular and CM elliptic curves.
Feb 20	Wed	Patrick Fowler (Sheffield)	Pure Maths Colloquium
16:00		Fries numbers of benzenoids: Even faulty algorithms can be interesting.
		Hicks Seminar Room J11
	Abstract: One simple chemical model for stability of benzenoids uses the Fries number (the maximum number of benzenoid hexagons over all perfect matchings (a.k.a Kekule structures) of the molecular graph. A recently published algorithm purports to find perfect matchings realising the Fries number of a general benzenoid molecule. We show that this algorithm does not always work correctly, and discuss the chemical significance of what the algorithm is 'really' doing and why it might be useful in spite of its faults. This talk is based on joint work with Wendy Myrvold, Dept. of Computer Science, University of Victoria
Feb 21	Thu	Steven Perkins (Bristol)	Statistics Seminar
14:00		Stochastic Fictitious Play with Continuous Action Sets
		K14
	Abstract: Stochastic approximation is a widely used tool which allows the limiting behaviour of a stochastic, discrete time, learning procedures on $\mathbb{R}^K$ to be studied using an associated continuous time, deterministic, dynamical system. We extend the asymptotic pseudo-trajectory approach to stochastic approximation so that the processes can take place on any Banach space. This allows us to consider an iterative process of probability measures (or probability densities) on a compact subset of $\mathbb{R}$ as opposed to the regular stochastic approximation framework which is limited to probability mass functions on $\mathbb{R}^K$. A common application of stochastic approximation in game theory is to study the limiting behaviour of a discrete time learning algorithm, such as stochastic fictitious play, in normal form games. However, whilst learning dynamics in normal form games are now well studied, it is not until recently that their continuous action space counterparts have been examined. Our Banach space stochastic approximation framework shows that in a continuous action space game the limiting behaviour of stochastic fictitious play can be studied using the associated smooth best response dynamics on the space of finite signed measures. We show that stochastic fictitious play will converge to an equilibrium point in single population negative definite games, two-player zero-sum games and $N$-player potential games, when they have Lipschitz continuous rewards over a compact subset of $\mathbb{R}$.
Feb 21	Thu	Christine Vespa (University of Strasbourg)	Topology Seminar
15:00		Stable homology of groups with polynomial coefficients
		Hicks Seminar Room J11
	Abstract: We say that the homology of a sequence of groups $(G_n)$ stabilizes if the homology groups, of each degree, of the groups $G_n$ is independent of n, for n big enough. Stability with constant coefficients or more generally polynomial coefficients has been proved for many families of groups. In this talk I will consider the question of the computation of this stable value. In particular, I will present the following recent result obtained in collaboration with Aurélien Djament: the stable homology of automorphism groups of free groups with coefficients given by a polynomial covariant functor like the abelianization or any tensor power of it, is trivial.
Feb 26	Tue	Daniel Fretwell (Sheffield)	Pure Maths Postgraduate Seminar
13:00		The Leech lattice and two remarkable applications
		Hicks Seminar Room J11
	Abstract: The problems encountered in the theory of sphere packing have been around for a very long time and yet we still know very little about their solutions. One particular problem asks the following: "Given a sphere in n-dimensional space, what is the maximum number of non-overlapping equal spheres that can touch its boundary?". Such a problem might be important in coding theory since we may be interested in error detection/correction properties. This problem has only been answered completely in low dimensions (namely for dimensions 1 to 8) but it is quite mysterious that we do happen to know the optimal answer in 24 dimensions. The Leech lattice is a special lattice in 24-dimensional space that provides this answer. In this talk we will see the above result by using theta series, specific modular forms attached to lattices. Also by studying the coefficients in this series more closely we will see a famous congruence of Ramanujan appear as a simple consequence.
Feb 26	Tue	Mahesh Kakde (London (King's College))	Number Theory seminar
15:00		Kato's local epsilon conjecture
		Hicks LTD
	Abstract: Let K be a field of characteristic zero and local characteristic l. A conjecture of Fukaya and Kato conjectures existence of local epsilon constants for representations of the absolute Galois group of K on Iwasawa algebras of p-adic Lie groups. These are related to Deligne-Langlands local epsilon constants through specialisations. I will sketch a proof of the conjecture of Fukaya-Kato in the case l is not equal to p.
Feb 26	Tue	Nick Bingham
17:00		Mathematical finance after the 2007/8 financial crisis
		LT7
Feb 28	Thu	Marian Farah (MRC Cambridge)	Statistics Seminar
14:00		Bayesian Emulation and Calibration of a Dynamic Epidemic Model for H1N1 Influenza
		K14
	Abstract: Increasingly, mechanistic epidemic models are playing an important role in strategies for epidemic management. In the attempt to control an epidemic, the goal of model development is to provide efficient estimation of model parameters to allow timely assessment and prediction of the epidemic evolution as new data become available. In this work, we address the problem of efficient parameter estimation in the context of a model for H1N1 influenza, implemented as a dynamic computer simulator. We propose an efficient approximation to the dynamic simulator using an emulator, a statistical model, that combines a Gaussian process prior for the output function of the simulator with a dynamic linear model for its evolution through time. This modelling framework is both flexible and tractable, resulting in efficient posterior inference through Markov Chain Monte Carlo. We illustrate the proposed methodology using simulated H1N1 influenza epidemic data.
Feb 28	Thu	Nadia Gheith (Sheffield)	Topology Seminar
15:00		Coarse Cofibration Category
		Hicks Seminar Room J11
	Abstract: Baues introduced a notion of cofibration category as a generalisation of a Quillen model category. He defined it to be a category together with two classes of morphisms called cofibrations and weak equivalences such that specific axioms are satisfied. In this talk I will introduce a notion of closeness equivalence classes of coarse maps-these are maps between spaces preserving the large scale structure. And prove that the category of spaces and closeness equivalence classes with two classes of morphisms called coarse cofibration classes and coarse homotopy equivalence classes satisfy the cofibration category axioms. This category will be called the Coarse cofibration category.
Mar 5	Tue	Mohammad Al-Boshmki (Sheffield)	Pure Maths Postgraduate Seminar
13:00		Koszul complexes
		Hicks Seminar Room J11
	Abstract: Koszul complexes play an important role in the homological aspects of commutative algebra and algebraic geometry. They are used to define cohomology for Lie algebras. In this talk, I will explain the Koszul complex over R-modules where R is a commutative ring and the higher homology modules of it are all zero. Also, I am going to show how to calculate the Koszul homology of graded algebras. Because the Koszul complex is free, it will give us a free resolution which is used to define homological degree.
Mar 6	Wed	Peter Lewis (Imperial)	Applied Mathematics Colloquium
14:00		Are quantum states real?
		LT9
	Abstract: Perhaps quantum states represent only the information available to an agent, or incomplete information about a real state of affairs. This---the psi-epistemic view of quantum states---is an attractive idea because if quantum states represent only information then measurement induced collapse, for example, is analogous to (and only as confusing as) the Bayesian updating of a probability distribution given new data. Recently, however, a few theorems (most notably by Pusey, Barrett and Rudolph) have been proven demonstrating that indeed the quantum state must play a role in the description of the real state of affairs---the psi-ontic view. Making use of the ‘ontological models’ formalism, we demonstrate that models can be constructed such that more than one quantum state is consistent with a single underlying real state. Thus all PBR-like theorems, and the restrictions they place on recovering quantum theory from a deeper theory, necessarily require assumptions beyond those required for a well-defined ontological model.
Mar 6	Wed	Iain Gordon (Edinburgh)	Pure Maths Colloquium
16:00		Galois problems in Schubert Calculus, and related problems
		Hicks Seminar Room J11
	Abstract: I will discuss some recent developments in Schubert calculus and a potential relation to classical combinatorics for symmetric groups and possible extensions to complex reflection groups.
Mar 7	Thu	Dennis Prangle (Lancaster)	Statistics Seminar
14:00		Summary statistics for likelihood-free model choice
		LT C
	Abstract: A central statistical goal is to choose between alternative explanatory models. This work is motivated by population genetic models, which are typically complicated stochastic processes whose likelihoods are numerically intractable. Hence it is not possible to use statistical methods based on evaluating likelihood functions. Approximate Bayesian computation (ABC) is a commonly used likelihood-free method for such situations. ABC simulates data for many parameter values under each model and compares these to the observed data. The comparison is based on vectors of summary statistics of the data. More weight is given to models which produce simulated vectors close to that for the observations. The choice of summaries turns out to be crucial to the efficiency and accuracy of the inference algorithm. This talk presents a method to select good summary statistics for ABC model choice. An application is also presented, choosing between demographic models of Campylobacter jejuni, a bacterial pathogen responsible for a large proportion of gastroenteritis cases.
Mar 7	Thu	Ralph Kaufmann (Purdue University)	Topology Seminar
15:00		Feynman categories
		Hicks Seminar Room J11
	Abstract: There is a plethora of operad type structures and constructions which arise naturally in classical and quantum contexts such as operations on cochains, string topology or Gromov-Witten invariants. We give a novel categorical framework which allows us to handle all these different beasts in one simple fashion. In this context, many of the relevant constructions are simply Kan extensions. We are also able to show how in this framework bar constructions, Feynman transforms, master and BV equations appear naturally.
Mar 7	Thu	Danny Dorling (Sheffield)	RSS Seminar
16:00		The Census: What surprises are emerging and how they show that cancellation of the 2021 Census may be foolhardy
		LT 7
	Abstract: Danny Dorling's research focuses on the changing social, political and medical geographies in Britain and elsewhere, and social and spatial inequalities to life chances and how these may be narrowed.
Mar 12	Tue	Callan McGill (Sheffield)	Pure Maths Postgraduate Seminar
13:00		Vector fields on spheres
		Hicks Seminar Room J11
	Abstract: It is a classical result that any vector field on a even dimensional sphere vanishes. It is fairly easy to construct non-vanishing vector fields on odd dimensional spheres and one is naturally led to the question of what the largest number of linearly independent vector fields is. In this talk we will introduce Clifford algebras and see how they can be used to construct a lower bound for the number of linearly independent vector fields. We will also see a small part of how this relates to homotopy theory which allowed Frank Adams to show that this is the maximal number.
Mar 13	Wed	Xuesong Wu (Imperial)	Applied Mathematics Colloquium
14:00		Free-stream turbulence, streaks and bypass transition
		LT9
	Abstract: Bypass transition of boundary-layer flows occurs in the presence of relatively strong turbulence in the free stream, and the ensuing transition location depends directly on the turbulence level. It is generally accepted that free-stream turbulence penetrates into the boundary layer to generate streaks, which amplify downstream and become unstable thereby causing onset of turbulence. Therefore accounting for the entrainment of free-stream turbulence is a crucial step towards understanding and predicting bypass transition. A popular approach adopted in most previous studies, especially in DNS (direct numerical simulations), of bypass transition, is to use continuous spectra of the O-S and Squire operators. In this talk, I will argue that this approached is flawed by showing that continuous spectra and entrainment are fundamentally different. An alternative and appropriate mathematical approach, which describes in a self-consistent manner the entrainment, formation and instability of streaks, will be presented. This framework allows for, in principle, a physics-based prediction of bypass transition.
Mar 13	Wed	Milena Hering (Edinburgh)	Pure Maths Colloquium
16:00		The moduli space of points on the projective line and its ring of invariants
		Hicks Seminar Room J11
	Abstract: The ring of invariants for the action of the automorphism group of the projective line on the n-fold product of the projective line is a classical object of study. The generators of this ring were determined by Kempe in the 19th century. However, the ideal of relations has been only understood recently in work of Howard, Millson, Snowden and Vakil. They prove that for n>6, the ideal of relations is generated by quadratic equations using a degeneration to a toric variety. I will report on joint work with Benjamin Howard where we compute the Hilbert functions of these rings of invariants, and further study the toric varieties arising in this degeneration. As an application we show that the second Veronese subring of the ring of invariants admits a presentation whose ideal admits a quadratic Gröbner basis.
Mar 14	Thu	Keith Worden (Sheffield - Mechanical Engineering)	Statistics Seminar
14:00		Applications of Probability and Statistics in Structural Dynamics
		LT C
	Abstract: Probability and statistics are vital tools in the modern analysis of structural dynamic systems. This is partly because many of the forces which excite the structures we are interested in are random and partly because many of the measurements and processes we study are (sometimes extremely) uncertain. This talk will present some applications of probability and statistics made in the Dynamics Research Group in Sheffield in recent years. Topics covered may include the design of damage detection systems based on statistical pattern recognition; removal of artefacts from data using concepts from econometric time series analysis; Bayesian sensitivity analysis of large nonlinear models and modelling of nonlinear dynamical systems using Markov Chain Monte Carlo methods.
Mar 14	Thu	Reiner Lauterbach (University of Hamburg)	Topology Seminar
15:00		Equivariant Bifurcation and Ize Conjecture
		Hicks Seminar Room J11
Mar 15	Fri	Stuart Mumford (Sheffield)	SP2RC seminar
13:00		3D Simulations of MHD Waves in Flux Tubes Driven by Photospheric Vortex Motions
		LT 9
	Abstract: This talk will present results of very recent 3D simulations of magnetic structures in the low solar atmosphere. Modern observations and simulations have revealed the many types of motions present in inter-granular lanes in the photosphere, here discussion of these results and how they are used to seed oscillations in the magnetic structures will precede the results of the simulations showing how different drivers excite a different spectrum of MHD modes in magnetic structures and how the different types of wave modes excited change the amount of energy flux transmitted vertically through the solar atmosphere.
Mar 21	Thu	John Stevens (ScHaRR)	Statistics Seminar
14:00		Health Technology Assessment: A Day in the Life of a HEDS Statistician
		K14
	Abstract: Health technology assessment (HTA) typically involves comparing the population mean costs and benefits of two or more interventions. The assessment is done using a decision analytic model over a lifetime horizon which gives rise to structural and parameter uncertainty. After introducing the current decision rule based on the incremental costeffectiveness ratio, we will discuss some of the statistical issues involved in an HTA such as making comparisons between treatments that have not been compared in randomised controlled trials (RCTs); the extrapolation of evidence beyond the duration of a trial to estimate population mean survival; modelling non-fatal events such as development of Type 2 diabetes; modelling bivariate outcomes such as progression-free survival and death. In some cases, methods are available that are not well known in the health economic literature, whilst others depend on the format of the data and the amount of data that is available.
Mar 22	Fri	Sacha Brun (CEA-Saclay, Service d'Astrophysique (France). )	SP2RC seminar
13:00		What's new under the Sun?
		LT 9
	Abstract: We will discuss our recent progress to model in 3-D the solar global interior dynamics using the anelastic spherical harmonic (ASH) code. We will show that the nonlinear mechanical and thermal coupling between a turbulent convective envelope and a stable radiative interior yields realistic rotation profile, with a differentially rotating convective envelope and a tachocline of shear at its base. We will further investigate the excitation and propagation of internal waves in the deep radiative interior. Thanks to the use of a realistic seismically calibrated stratification (i.e solar-like Brunt-Väisälä frequency), we observe a large spectrum of internal waves in our simulation. These modes are excited by the continuous pummeling of convective plumes. When comparing with asymptotic formulations and an adiabatic oscillation code we find a good overall agreement and confirm that those waves are indeed gravity waves. We then discuss their properties and visibility at the surface and compare with recent observations.
Mar 25	Mon	Julia Goedecke (Cambridge University)	94th Peripatetic Seminar on Sheaves and Logic
09:30		The fundamental group functor as a Kan extension
		Hicks F24
	Slides
Mar 25	Mon	John Huerta (Instituto Superior Técnico, Lisbon)	94th Peripatetic Seminar on Sheaves and Logic
10:00		The categorified Poincaré supergroup
		Hicks F24
	Slides
Mar 25	Mon	Andrew Hawkins (Glasgow)	Non-commutative Geometry, Analysis and Groups
11:00		A twisted spectral triple on the Cuntz algebra
		Hicks, LT4
	Abstract: The non-existence of a finite trace on the Cuntz algebra prevents the possibility of constructing spectral triples with good summability properties. On the other hand, Connes and Moscovici present an abstract definition of a twisted spectral triple for which the resultant Dixmier functional satisfies a natural KMS condition. When the Cuntz algebra is viewed as an Exel crossed product of a subshift space by an endomorphism, the twisting can be interpreted as a scaling factor associated to the shift action. We suggest one possible way of writing down a twisted spectral triple for a large class of Cuntz-Krieger algebras using these ideas.
Mar 25	Mon	Thomas Athorne (Sheffield)	94th Peripatetic Seminar on Sheaves and Logic
11:00		When is the nerve-realisation adjunction comonadic?
		Hicks F24
Mar 25	Mon	Alexander Premet (Univesrity of Manchester)	BMC Joint ARTIN-BLOC Meeting
11:15		Derived subalgebras of centralizers and multiplicity-free primitive ideals.
	Abstract: Let $\mathfrak{g}$ be a finite dimensional simple Lie algebra over an algebraically closed field of characteristic 0. In my talk, based on a joint work with Lewis Topley, I am going to discuss a way to classify the primitive ideals $I$ of $U(\mathfrak{g})$ whose associated variety occurs with multiplicity 1 in the associated cycle $AC(I)$. The classification is based on the detailed study of the abelian quotients $\mathfrak{g}_e/[\mathfrak{g}_e,\mathfrak{g}_e]$ where $\mathfrak{g}_e$ is the centraliser of a nilpotent element $e$ in $\mathfrak{g}$.
Mar 25	Mon	Christina Vasilakopoulou (Cambridge)	94th Peripatetic Seminar on Sheaves and Logic
11:30		Enrichment of Categories of Algebras and Modules
		Hicks F24
	Slides
Mar 25	Mon	Sinead Lyle (East Anglia)	BMC Joint ARTIN-BLOC Meeting
12:00		Graded homomorphisms between Specht modules for KLR algebras of type A
		Hicks LT6
	Abstract: The Khovanov-Lauda-Rouquier algebras, or cyclotomic quiver Hecke algebras, are certain Z-graded algebras which depend on an oriented quiver. Remarkably, it has been shown by Brundan and Kleshchev that the cyclotomic quiver Hecke algebras of type A are isomorphic to the cyclotomic Hecke algebras of type G(r,1,n), also known as the Ariki-Koike algebras. These algebras include as special cases the Hecke algebras of type A and type B and hence also the symmetric group algebra. Thus one application of Brundan and Kleshchev's result is that it defines a Z-grading on the symmetric group algebra. A further result of Brundan, Kleshchev and Wang shows that the Specht modules are graded. It therefore makes sense to talk about graded decomposition numbers and graded homomorphisms between Specht modules. This talk will introduce the KLR algebras of type A and discuss some of the established results concerning these algebras. We will then discuss some joint work with Andrew Mathas on graded homomorphisms between certain pairs of Specht modules.
Mar 25	Mon	David O'Sullivan (Sheffield)	Non-commutative Geometry, Analysis and Groups
13:00		C*-categories
		Hicks, LT4
	Abstract: A C*-category is a categorification of a C*-algebra in the same sense that a groupoid is a generalisation of a group. C*-categories occur naturally when analytic assembly maps are studied - in particular one can associate to a discrete groupoid a C*-category that is in some sense more natural than the groupoid C*-algebras of Renault. In this introductory talk I will outline some of the basic theory of C*-categories, and show how a number of C*-algebraic results generalise to the level of categories. I will also outline the construction of the so-called groupoid C*-categories.
Mar 25	Mon	Peter Johnstone (Cambridge)	94th Peripatetic Seminar on Sheaves and Logic
13:00		Hyland + Gleason = Herbrand
		Hicks F24
Mar 25	Mon	Paul Taylor	94th Peripatetic Seminar on Sheaves and Logic
13:30		Overt subspaces of metric spaces
		Hicks F24
Mar 25	Mon	Simon Wadsley (Cambridge)	BMC Joint ARTIN-BLOC Meeting
14:00		Finite dimensional p-adic representations of compact p-adic groups
		Hicks LT6
	Abstract: The finite dimensional complex representation theory of compact p-adic Lie groups is well understood. We will discuss the finite-dimensional p-adic representation theory of these groups.
Mar 25	Mon	John Baez (University of California, Riverside)	94th Peripatetic Seminar on Sheaves and Logic
14:00		Bicategories and Tricategories of Spans
		Hicks F24
Mar 25	Mon	Nadia Gheith (Sheffield)	Non-commutative Geometry, Analysis and Groups
14:30		The Coarse Cofibration Category
		Hicks, LT4
	Abstract: Baues introduced a notion of cofibration category as a generalisation of a Quillen model category. He defined it to be a category together with two classes of morphisms called cofibrations and weak equivalences such that specific axioms are satisfied. In this talk I will introduce a notion of closeness equivalence classes of coarse maps- these are maps between spaces preserving the large scale structure. And prove that the category of spaces and closeness equivalence classes with two classes of morphisms called coarse cofibration classes and coarse homotopy equivalence classes satisfy the cofibration category axioms. This category will be called the coarse cofibration category.
Mar 25	Mon	Xiuping Su ( Bath)	BMC Joint ARTIN-BLOC Meeting
14:45		0-Schur algebras and 0-Hecke algebras
		Hicks LT6
	Abstract: In this talk I will give a geometric construction of 0-Schur and 0-Hecke algebras and discuss their structure.
Mar 28	Thu	Michael Moreels (Catholic Univeristy of Leuven (Belgium))	SP2RC seminar
13:00		Phase relations for seismology of photospheric flux tubes
		LT 9
	Abstract: We assess the possibility of photospheric seismology with the use of magnethydrodynamic waves. Recently MHD waves have been observed in the photosphere using the Solar Optical Telescope (Fujimura and Tsuneta 2009), the Rapid Oscillations in the Solar Atmosphere instrument (Morton et al. 2011 and Jess et al. 2012) and the Swedish Solar Telescope (Jess et al. 2009). Here we investigate if these observations allow us to calculate non-observable quantities of the flux tubes in the photosphere, such as the vertical wave number. We use a straight cylinder as a model for the flux tube. The plasma is uniform both inside and outside the flux tube with a possible jump at the boundary, the magnetic field is directed along the flux tube. We calculate analytic expressions for the velocity, intensity and magnetic field perturbations for both propagating and standing waves in the flux tube. We also calculate analytic expressions for the cross-sectional area variation and the total intensity variation. Using these analytic expressions we can calculate the phase differences between the cross-sectional area, the intensity variations, the velocity, and the magnetic field. These can then be used to identify the type of magnetohydrodynamic waves in the photosphere. The amplitude ratios of the velocity, the intensity and the magnetic field can be used to seismologically determine physical parameters of the photospheric flux tube.
Apr 9	Tue	Lassina Dembele (Warwick)	Number Theory seminar
15:00		Examples of abelian surfaces with everywhere good reduction
		Hicks LTD
	Abstract: In this talk, we will present explicit examples of abelian surfaces with everywhere good reduction. One class of examples is connected with the Paramodularity Conjecture of Brumer-Kramer, which will be discussed in the process. This is joint work with Abhinav Kumar.
Apr 10	Wed	Gordon Ogilvie (DAMTP, Cambridge)	Applied Mathematics Colloquium
14:00		Local dynamics and hydrodynamic instability of warped astrophysical discs
		LT9
	Abstract: Astrophysical discs, which include circumstellar discs in which planets are formed and high-energy accretion discs around black holes, consist of a continuous distribution of material in orbital motion around a central massive body. In a general Keplerian disc, this orbital motion can have variable eccentricity and inclination. A warped disc is one in which the orbital plane varies with radius and possibly with time. There is strong theoretical and observation motivation for considering warped discs in several situations. Current interest, for example, focuses on black holes in galactic nuclei, which grow by accreting gas that is supplied in different orientations, and protoplanetary systems, where spin-orbit misalignments have been discovered, suggesting that a warped disc may have been involved. We introduce a new local model for the study of warped astrophysical discs. This generalizes the shearing sheet of Goldreich & Lynden-Bell (1965) by imposing the local curvature of the orbital plane in addition to shear and rotation. The simplest hydrodynamic solutions in the local model are horizontally uniform laminar flows that oscillate at the orbital frequency. These determine the large-scale evolution of the shape and mass distribution of the disc through their hydrodynamic stresses. We present a simpler and independent derivation of the basic equations for warped discs obtained by Ogilvie (1999). We also analyse the hydrodynamic stability of the laminar flows and find widespread instability deriving from parametric resonances of inertial waves. Very small warps in nearly Keplerian discs of low viscosity can be expected to generate hydrodynamic turbulence by this mechanism. As well as modifying the dynamics of the warp, this could have important consequences for planet formation.
Apr 10	Wed	Charudatta Hajarnavis (Warwick)	Pure Maths Colloquium
16:00		The Artin-Rees property
		Hicks Seminar Room J11
	Abstract: (Joint work with A.Braun) An ideal $I$ of a ring $R$ is said to have the right Artin-Rees (AR) property if for every right ideal $E$ of $R$ there exists a positive integer $n$ such that $E \cap I^n \subseteq EI$. Unlike in the commutative case, the AR property does not hold universally for all ideals of a non-commutative Noetherian ring. For instance, for prime ideals (some form of) the AR property is intimately related to their localisability. We discuss the longstanding problem of whether the Jacobson radical of a prime Noetherian ring has the AR property.
Apr 11	Thu	Heather Battey (Bristol)	Statistics Seminar
14:00		Nonparametric estimation of a multidimensional density: some recent theory and methodology.
		K14
	Abstract: Density estimation is one of the most actively studied challenges in statistics. Whilst fully agnostic estimators can be appealing in low dimensions, the performance of such estimators deteriorates rapidly for a fixed sample size as the number of dimensions grows. This provides motivation for estimating within a restricted subset of the set of all p-dimensional Lebesgue densities, thereby reducing estimation error, even if this produces some approximation error when the constraint is not satisfied. In the first half of the talk, I will consider the restriction to the class of p-dimensional elliptic densities and, within this framework, present a two-stage nonparametric estimator for the Lebesgue density based on Gaussian mixture sieves. Under the on-line Exponentiated Gradient (EG) algorithm of Helmbold et al. (1997) and without restricting the mixing measure to have compact support, the estimator produces estimates converging uniformly in probability to the true elliptic density at a rate that is independent of the dimension of the problem. The rate performance (and optimal tuning parameter) associated with our estimator depends on the tail behaviour of the underlying density rather than on smoothness properties, and we provide a rule of thumb for estimating the relevant quantity based on observables. Although the rule of thumb is based on a particular member of the elliptic class, simulations indicate that the procedure generalises to other members of this class. In the second half of the talk, I will present some ongoing work on multidimensional density estimation. I will introduce a new class of procedures that are attractive in that they offer both flexibility and the possibility of incorporating constraints, whilst possessing a succinct representation which may be stored and evaluated easily. The latter property is of paramount importance when dealing with large datasets, which are now commonplace in many application areas. In a simulation study, we show that our approach is universally unintimidated across a range of data generating mechanisms, and can often outperform popular nonparametric estimators. Moreover, its performance is shown to be robust to the choice of tuning parameters, which is an important practical advantage of our procedure. The estimator is implemented in a binary classification task arising in medical statistics.
Apr 11	Thu	John Greenlees (Sheffield)	Topology Seminar
15:00		THH and the Gorenstein condition
		Hicks Seminar Room J11
	Abstract: Calculations of Boekstedt and Ausoni give examples showing that with suitable coefficients $THH(R)$ has strong duality properties. The talk will describe how to establish these duality properties without a complete calculation, showing that THH of ring spectra has Gorenstein duality remarkably often. The context is the notion of Gorenstein ring spectra studied with Dwyer and Iyengar, and the talk will include a suitable summary.
Apr 12	Fri	Dr Giuseppe Nistico (Warwick University)	SP2RC seminar
13:00		Decaying and decayless features in kink oscillations of coronal loops
		LT 9
	Abstract: Kink oscillations of coronal loops in active regions are among the most observed wave-like phenomena in the solar corona, detected in telescope images on board space missions (e.g. SoHO, TRACE, STEREO) at extreme ultra violet (EUV) wavelengths. They are seen to be triggered by impulsive release of energy in the form of flares or coronal mass ejections (CMEs), causing transverse movements whose amplitude decays rapidly in time within some minutes. The interest in kink oscillations comes from their use as a seismological coronal probe as well, in order to estimate the absolute values of the coronal magnetic field. Nowadays, the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) spacecraft launched in 2010, is able to capture the dynamics of the solar corona at high spatial and temporal resolution, better than any other past instruments. We present observations of kink oscillations in coronal loops, characterised to have two different behaviours: large-amplitude oscillations decaying in time and small-amplitude oscillations with decayless features. We explain the event in term of a damped linear oscillator excited by a continuous low-amplitude harmonic driver plus an impulsive high-amplitude driver, and compare it with those described in the literature.
Apr 16	Tue	Samuel Dean (Sheffield)	Pure Maths Postgraduate Seminar
13:00		Coherence for monoidal categories
		Hicks Seminar Room J11
	Abstract: There are many canonical constructions in mathematics which behave essentially like a multiplication, to the extent that we feel able to treat them as such without much need for caution, e.g. Cartesian products, tensor products, wedges of spaces, free products, and more. Why is this valid? Monoidal categories provide a framework for studying these familiar examples. A monoidal category is a category with a notion of multiplication. In strict monoidal categories the associative law and unital law holding on the nose. But this is too strict to model the above examples, so we need a weakened notion: weak monoidal categories.
Apr 16	Tue	Samuel Dean (Sheffield)	Pure Maths Postgraduate Seminar
13:00		Coherence for monoidal categories
		Hicks Seminar Room J11
	Abstract: There are many canonical constructions in mathematics which behave like a multiplication, to the extent that we feel able to treat them as such without much need for caution, e.g. Cartesian products, tensor products, wedges of spaces, free products, and more. Monoidal categories provide a framework for studying these examples. A monoidal category is a category with a notion of multiplication. In a strict monoidal category the associative law and unital law holding on-the-nose. But this is too strict to model the above examples, so we need a weakened notion. Since the familiar examples of weak monoidal categories can be incautiously treated like strict ones, we expect this to be true of weak monoidal categories in general. The coherence theorem formalises this. In this talk I will introduce the notion of monoidal category and explain the idea of coherence. I will explain why one apparently obvious method of proving the coherence theorem is wrong in although it carries through in some cases, and sketch a correct proof for a general monoidal category.
Apr 16	Tue	Abhishek Saha (Bristol)	Number Theory seminar
15:00		Yoshida lifts of arbitrary level and ratios of Petersson norms
		Hicks F41
	Abstract: I will give a representation-theoretic account of Yoshida lifts with respect to arbitrary congruence subgroups. Briefly, a Yoshida lift is a scalar valued holomorphic Siegel cusp form of degree 2 whose global L-parameter is the sum of two modular L-parameters. I will also prove an algebraicity property for the ratio of Petersson norms attached to these lifts. This is in line with a general phenomenon, whereby the ratio of Petersson norms of functorially related automorphic forms on different Shimura varieties are algebraic and Aut(C)-equivariant.
Apr 17	Wed	Stephane Launois (Kent)	Pure Maths Colloquium
16:00		On totally nonnegative matrices
		Hicks Seminar Room J11
	Abstract: In this talk, I will explain how one can use tools develop to study prime ideals of noncommutative algebras in order to study totally nonnegative matrices.
Apr 18	Thu	Jochen Einbeck (Durham)	Statistics Seminar
14:00		Principal curves and surfaces: Data visualization, compression, and beyond
		K14
	Abstract: Principal curves and surfaces have been proposed about two decades ago as a tool for nonlinear dimension reduction. Descriptively, they can be defined as smooth objects (of dimension 1 and 2, respectively) capturing the "middle" of a (potentially high-dimensional) data cloud. Though a relatively large amount of literature has discussed methods and algorithms for the estimation of principal curves and surfaces, most of this research stops here, and does not consider exploiting the fitted curve or surface once it is established. One may find this surprising, as the parametric analogue, linear principal component analysis, is rarely used as an end in itself, but unfolds is power only when used as an integrated data compression step for some high- dimensional, say, regression or classification problem. One reason for this reluctance may be that several rather cumbersome technicalities, such as the computation of distances or projection indexes, need to be solved before a fitted principal curve or surface can be used for further inferential purposes such as regression or classification. In this talk, we describe briefly how such problems can be resolved, and give some examples, stemming from current collaborative work, which illustrate how "local" principal curves and surfaces can be efficiently used as a nonparametric dimension reduction tool, enabling further statistical analysis based on the fitted principal object. We will focus on a case study involving the compression of the thermochemical state space of chemical combustion systems.
Apr 18	Thu	Simon Covez (University of Luxembourg)	Topology Seminar
15:00		On the conjectural Leibniz homology for groups
		Hicks Seminar Room J11
	Abstract: Twenty years ago Jean-Louis Loday has introduced and studied Leibniz algebras and their homology theory. Following this discovery, he has conjectured the existence of a conjectural Leibniz homology for groups and some of its properties, such as the existence of an algebraic structure on this conjectural homology or the existence of a natural morphism from this conjectural homology to the usual homology theory of groups. In this talk we will see that the homology theory of racks satisfies most of these properties and, therefore, should be this conjectural Leibniz homology theory.
Apr 19	Fri	Prof. Komandur Rangarajan (Indian Institute of Astrophysics (Bangalore))	SP2RC seminar
13:00		India's National Large Solar Telescope (NLST)
		LT 9
	Abstract: The Indian National Large Solar Telescope NLST will be a state-of-the-art 2-m class telescope. The main science goals of NLST include: a) Magnetic field generation and the solar cycle; b) Dynamics of magnetized regions; c) Local Helioseismology; d) Long term variability; e) Energetic phenomena and Activity; and f) Night time astronomy. The optical design of the telescope is optimized for high optical throughput and uses a minimum number of optical elements. A high order adaptive optics system is integrated as part of the design that works with a modest Fried's parameter of 7-cm to give diffraction limited performance. The telescope will be equipped with a suite of post-focus instruments including a high resolution spectrograph and a polarimeter. NLST will also be used for carrying out stellar observations during the night. A site characterization programme carried over several years has established the existence of suitable sites in the Ladakh region. After its completion, currently planned for 2017, NLST will fill a gap in longitude between the major solar facilities in the world.
Apr 23	Tue	Christopher Fish (Sheffield)	Pure Maths Postgraduate Seminar
13:00		Auslander-Gorenstein rings
		Hicks Seminar Room J11
	Abstract: In non-commutative algebra one often takes a definition from commutative algebra and then tries to adapt it to the non-commutative setting. Often one has to change the definition to make it work - the first example of this is the concept of "prime ideal". In commutative algebra a ring is said to be Gorenstein if it has finite injective dimension as a module over itself; such rings are both common, and have nice geometric and homological properties. The non-commutative generalisation is called Auslander-Gorenstein, where one adds to self-injectivity a condition on the Ext-modules which is a consequence of self-injectivity in the commutative case. In this talk I will give the various definitions involved, give some examples of rings that are AG, and give a nice consequence in terms of dimension which has an analog in the commutative case.
Apr 24	Wed	Kevin Buzzard (Imperial College, London)	Pure Maths Colloquium
16:00		$L$-functions
		Hicks Seminar Room J11
	Abstract: The Riemann zeta function can be defined first as an infinite sum, and then (by analytic continuation) as a function on the whole complex plane, with a pole at $s=1$. Facts about the zeta function sometimes imply facts about prime numbers and arithmetic, and if we knew the Riemann Hypothesis we would know even more about prime numbers than we do now. The zeta function is an inherently interesting object, and it is not unsurprising that there are now many generalisations of it, encoding other secrets about mathematics. I'll talk about it and its generalisations, so-called $L$-functions, and try to give some idea about what we know and what we want to know about them.
Apr 25	Thu	Alex Mijatovic (Imperial)	Statistics Seminar
14:00		A new look at short-term implied volatility in asset price models with jumps
		K14
	Abstract: This talk discusses the implied volatility smile for options close to expiry in the exponential Lévy class of asset price models with jumps. We introduce a new renormalisation of the strike variable with the property that the implied volatility converges to a non-constant limiting shape, which is a function of both the diffusion component of the process and the jump activity (Blumenthal-Getoor) index of the jump component. Our limiting implied volatility formula relates the jump activity of the underlying asset price process to the short end of the implied volatility surface and sheds new light on the difference between finite and infinite variation jumps from the viewpoint of option prices: in the latter, the wings of the limiting smile are determined by the jump activity indices of the positive and negative jumps, whereas in the former, the wings have a constant model-independent slope. This result gives a theoretical justification for the preference of the infinite variation Lévy models over the finite variation ones in the calibration based on the short-maturity option prices.
Apr 30	Tue	Alex Corner (Sheffield)	Pure Maths Postgraduate Seminar
13:00		Topological Quantum Field Theories
		Hicks Seminar Room J11
	Abstract: Modern theoretical physics relies on inherently pure mathematical ideas and techniques. Increasingly, categories are finding a place in the framework, nowhere more apparent than in the ideas behind quantum field theories. These are extensions of the classical field theories found in physics, used to describe interactions between phenomena such as gravity, electricity and magnetism, whilst taking into account the laws governing the quantum world. Topological quantum field theories spring out of these ideas and are profoundly interesting as mathematical objects in their own right. I will introduce mathematical ideas such as manifolds, cobordisms and categories and give an idea of how they relate to physical concepts. This will lead to a description of the basic ideas of physical fields and of spacetime in terms of algebra. The algebra we use will be monoidal categories and Frobenius algebras. Finally we will characterise topological quantum field theories and some low-dimensional examples, using this algebra.
May 2	Thu	Christopher Hunter (Sheffield - Chemisty)	Statistics Seminar
14:00
		K14
May 2	Thu	Oscar Randal-Williams (Cambridge)	Topology Seminar
15:00		Infinite loop spaces and positive scalar curvature
		Hicks Seminar Room J11
	Abstract: It is well known that there are topological obstructions to a manifold $M$ admitting a Riemannian metric of everywhere positive scalar curvature (psc): if $M$ is Spin and admits a psc metric, the Lichnerowicz–Weitzenböck formula implies that the Dirac operator of $M$ is invertible, so the vanishing of the $\hat{A}$ genus is a necessary topological condition for such a manifold to admit a psc metric. If $M$ is simply-connected as well as Spin, then deep work of Gromov--Lawson, Schoen--Yau, and Stolz implies that the vanishing of (a small refinement of) the $\hat{A}$ genus is a sufficient condition for admitting a psc metric. For non-simply-connected manifolds, sufficient conditions for a manifold to admit a psc metric are not yet understood, and are a topic of much current research. I will discuss a related but somewhat different problem: if $M$ does admit a psc metric, what is the topology of the space $\mathcal{R}^+(M)$ of all psc metrics on it? Recent work of V. Chernysh and M. Walsh shows that this problem is unchanged when modifying $M$ by certain surgeries, and I will explain how this can be used along with work of Galatius and the speaker to show that the algebraic topology of $\mathcal{R}^+(M)$ for $M$ of dimension at least 6 is as complicated as can possibly be detected by index-theory. This is joint work with Boris Botvinnik and Johannes Ebert.
May 3	Fri	Dr Youra Taroyan (Aberystwyth University)	SP2RC seminar
13:00		Implications of EUV Doppler shifts on models of solar coronal heating
		LT 9
	Abstract: Spectroscopic observations of different regions of the Sun often show blue shifts for emission lines with temperatures above 1 million degrees Kelvin and red shifts for lines below 1 million degrees Kelvin. These simultaneous blue and red shifts in EUV lines have been puzzling solar physicists since the first high resolution spectral observations of the Sun became available. A clear answer to the problem could provide important clues to the heating processes in the solar atmosphere. Recent observations with the Japanese Hinode/EIS insrtument show that the blue and red shifts are concentrated near the footpoints of loop-like structures that extend high into the atmosphere of the Sun. The Doppler shifts may last for days or weeks. The implications of these observations are addressed through numerical modeling of loop dynamics. The obtained results provide important constraints on models of solar coronal heating.
May 8	Wed	Jingsong He (Ningbo)	Applied Mathematics Colloquium
14:00
		LT10
May 8	Wed	Jacob Rasmussen (Cambridge)	Pure Maths Colloquium
16:00		Genus minimizing surfaces
		Hicks Seminar Room J11
	Abstract: Suppose M is a 3 or 4 dimensional manifold, and that x is an element of H_2(M). What is the minimal genus of an embedded orientable surface representing x? I'll discuss what we know and don't know about this question, and what it can tell us about topology in dimensions 3 and 4.
May 9	Thu	Idris Eckley (Lancaster)	Statistics Seminar
14:00		Coherence analysis of multivariate time series
		K14
	Abstract: Data collection systems are widely used within our everyday lives. For example within the energy sector they are used to record process activity within energy generations sites. These loggers are capable of sampling data at high rates, at a number of locations and recording multiple process aspects at each location. Such series are typically non-stationary in nature, with potentially time-varying dependence between the various series components. In this talk we consider the problem of modelling and estimating the coherence structure within such time series. In particular we focus on the challenge of identifying whether the dependence between a pair of components is direct or indirectly driven by other components of the series, illustrating our approach using examples taken from neuroimaging and wind energy.
May 9	Thu	Simon Willerton (Sheffield)	Topology Seminar
15:00		Integral transforms, correspondences and profunctors
		Hicks Seminar Room J11
May 10	Fri	Prof. Siraj Hasan (Indian Institue for Astrophysics (Bangalore, India))	SP2RC seminar
13:00		Solar Physics reseach in India: Current trends and future programmes
		LT 9
	Abstract: TBA
May 14	Tue	Daniel Fretwell (Sheffield)	Number Theory seminar
11:15		Algebraic modular forms
		Hicks Seminar Room J11
May 14	Tue	Thomas Sutton (Sheffield)	Pure Maths Postgraduate Seminar
13:00		An introduction to rational homotopy theory
		Hicks Seminar Room J11
	Abstract: Homotopy theory often assigns discrete objects to spaces which are invariant under homotopy equivalence. The purpose is usually to distinguish two spaces, or to attempt to give a simple classification of certain spaces. Perhaps the easiest to define of these invariants are the homotopy groups of a space. Despite this ease, they are, in general, notoriously hard to compute, and effectively no known general techniques exist for calculating them even when the spaces in question are "nice" (for example, spheres). Thus, homotopy theorists have often worked under certain simplications, for example stable homotopy theory, or rational homotopy theory. This talk will introduce the latter, where hte idea is to focus only on the rank of the homotopy groups. I will give an exposition of a general framework for rational homotopy theory, and conditions under which the theory is equivalent to a category of differential graded algebras. Finally, using the described equivalence and theorems relating to it, I will say how we can actually compute the rational homotopy of a large class of spaces, and do so for some examples.
May 15	Wed	Ben Wright (Harrison Goddard Foote)	Applied Mathematics Colloquium
14:00		[*Seminar has been postponed*] Overview of intellectual property
		LT10
May 16	Thu	Shahla Kaka Hama (Sheffield)	Pure Maths Postgraduate Seminar
13:00		Which topological spaces admit the structure of a topological group?
		Hicks Seminar Room J11
	Abstract: Every group (G,*) can be trivially made into a topological space by defining a discrete topology on it. A natural question arises from this: Is every topological space (X,T) a group? In this talk, I am going to talk about a topological groups and show that a fundamental group of every topological group is abelian. Finally, by using this theorem and some other facts I will answer the given question for some simple spaces including even-dimensional spheres.
May 16	Thu	Bruce Bartlett (Stellenbosch)	Pure Maths Colloquium
14:00		Three-dimensional TQFTs and modular categories
		Hicks Seminar Room J11
	Abstract: You know about representations of groups, and you've heard about representations of quivers. In this talk I will talk about representations of manifolds. Indeed, compact oriented manifolds of dimensions 1, 2 and 3 organize themselves into a structure known as a "bicategory", and an oriented 123 topological quantum field theory (TQFT) is a representation of this structure. They turn out to be classified by structures known as "anomaly-free modular categories". I will describe my recent work in this area, with examples. Along the way we will stumble across Morse theory, group cohomology and quadratic forms. Joint work with Jamie Vicary, Chris Schommer-Pries and Chris Douglas.
May 16	Thu	Peter Moerters (Bath)	Statistics Seminar
14:00		Clustering in spatial preferential attachment networks
		K14
	Abstract: I define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favouring short distances and high degrees. The competition of preferential attachment and spatial clustering gives this model a range of interesting properties. Empirical degree distributions converge to a limiting power law, and the average clustering coefficient of the networks converges to a positive limit. A phase transition occurs in the global clustering coefficients and empirical distribution of edge lengths. The talk is based on joint work with Emmanuel Jacob (ENS Lyon).
May 16	Thu	Mark Grant (Nottingham)	Topology Seminar
15:00		Topological complexity of braid groups
		Hicks Seminar Room J11
	Abstract: Topological complexity (TC) is a numerical homotopy invariant which quantifies the complexity of navigation in a topological space. Defined by Michael Farber in the early 21st century, it gives topological information about the motion planning problem in robotics. Briefly, TC(X) is the sectional category of the free path fibration on X. An interesting open problem is to determine TC of a K(G,1)-space algebraically in terms of the fundamental group G. After surveying this problem and related results, we will present an approach to finding lower bounds which is purely algebraic. We will then discuss how this can be applied to estimate the topological complexity of braid groups. This is joint work with Greg Lupton and John Oprea.
May 17	Fri	Dr Hannah Schunker (Max Planck Institute for Solar System Research (Katlenburg-Lindau, Germany))	SP2RC seminar
13:00		Prospects for inferring the subsurface structure of sunspots using helioseismology
		LT 9
	Abstract: > One goal of local helioseismology is to elicit three-dimensional information about the subsurface structure of sunspots. The physical quantities include sound-speed perturbations and magnetic fields. This information can be used to constrain sunspot models. Helioseismology involves solving both the forward and inverse problem. Traditionally, the inverse problem is solved assuming a linear relationship between the magnitude of the subsurface perturbation and the effect on the waves. We use three-dimensional numerical MHD simulations of wave propagation to explore the seismic effect of various perturbations to a reference sunspot model. These perturbations include modifications to the Wilson depression, subsurface sound-speed enhancements, and subsurface magnetic field changes. We comment on the possibility of measuring such perturbations on the Sun, and on the validity of using linear inversions.
May 21	Tue	Tao Lu (Sheffield)	Pure Maths Postgraduate Seminar
13:00		Invariants of Lie Algebras
		Hicks Seminar Room J11
	Abstract: The determination of invariants of Lie algebras is motivated by the important role played by these elements in Physics and in representation theory. For semisimple Lie algebras, the invariants were determined long ago. But for non-semisimple Lie algebras, invariants have only been determined when the dimensions are low. Let g be a finite dimensional Lie algebra. Our interest is the centre of the enveloping algebra U(g), which has a close relation with the invariant subalgebra of the symmetric algebra S(g). In this talk I will give the definition of Lie algebras, enveloping algebras, and the invariants. Then we recall the classical results for semisimple Lie algebras, and introduce the Duflo iosmorphism, giving a relationship between the invariants of S(g) and U(g). Finally I will introduce a method to compute the invariants by giving examples, and give some comments and criteria on the polynomiality of the centre of U(g).
May 22	Wed	Alan Zinober (Sheffield)	Applied Mathematics Colloquium
14:00		A Brief History of Optimal Variational Problems and Some Recent Research
		LT9
	Abstract: The Calculus of Variations was initiated in the 17th Century and forms a basic foundation of modern optimal (maximising or minimising) variational problems, nowadays often called optimal control. An introduction to the Calculus of Variations with some sample examples will be presented. This will include the Euler-Lagrange and Hamiltonian formulation together with the associated final boundary value conditions. A numerical shooting method can be used to solve the resulting Two Point Boundary Value Problem (TPBVP), a set of differential equations. There are many interesting applications including the optimal spending of capital, reservoir control, maintenance and replacement policy of vehicles and machinery, optimal delivery of medicines, drug bust strategies, study for examinations and optimal presentation of a lecture like this one. A new non-classical class of variational problems has been motivated by research on the non-linear revenue problem in the field of economics. This class of problem can be set up as a maximising problem in the Calculus of Variations (CoV) or Optimal Control. However, the state value at the final fixed time, $y(T)$, is {em a priori} unknown and the integrand to be maximised is also a function of the unknown $y(T)$. This is a non-standard CoV problem that has not been studied before. New final value costate boundary conditions will be presented for this CoV problem and some results will be shown.
May 31	Fri	Shanta Laishram (Indian Statistical Institute, Delhi)	Number Theory seminar
16:00		Irreducibility of generalized Hermite-Laguerre Polynomials
		Hicks Seminar Room J11
	Abstract: Schur's irreducibility result of 1929 has been generalized by many authors using p-adic methods of Coleman and Filaseta. In this talk, I will give a survey of some earlier results and state a number of results on the irreducibility of family of generalized Hermite-Laguerre polynomials. The proof of these results involve combining p-adic methods with the greatest prime factor of the product of consecutive terms of an arithmetic progression and results from prime number theory and solving some diophantine equations. This is a joint work with T. N. Shorey.
Jun 18	Tue	Daniela Cadamuro (York)
16:00		A quantum energy inequality for the massive Ising model
		Hicks F28
	Abstract: We derive a Quantum Energy Inequality (QEI) for the massive Ising model, giving a state-independent lower bound on suitable averages of the energy density; the first QEI to be established for an interacting quantum field theory with nontrivial $S$-matrix. Also, we show that - in contrast to a free Bose field - the Ising model has one-particle states with locally negative energy densities, and that the energy density operator is not additive with respect to combination of one-particle states into multi-particle configurations.
Jul 16	Tue	Nora Ganter (Melbourne)
15:30		Representations and characters of 2-groups
		Hicks Seminar Room J11
Jul 18	Thu	Alex Ghitza (Melbourne)	Number Theory seminar
14:00		Lifting Siegel modular forms (mod p) to characteristic zero
		Hicks Seminar Room J11
Aug 6	Tue	Alex Ghitza (Melbourne)	Number Theory seminar
14:00		A theta operator for Siegel modular forms (mod p)
		Hicks Seminar Room J11
Oct 2	Wed	Gabriel Lord (Heriot-Watt)	Applied Mathematics Colloquium
14:00		Computing Stochastic Travelling Waves
		LT9
	Abstract: This talk will introduce stochastic differential equations from scratch and develop from there to discuss stochastic partial differential equations (SPDEs). From there we will discuss how to compute travelling waves for SPDEs and discuss a technique that freezes the wave and stops it from moving.
Oct 2	Wed	Jayanta Manoharmayum (Sheffield)	Pure Maths Colloquium
16:00		Universal deformation rings and subgroups of $GL_n$
		Hicks Seminar Room J11
	Abstract: A good way of understanding groups is to look at its representations into the group of invertible n by n invertible matrices. One can organise such representations into families by first fixing a representation into $GL_n$ of a finite field and then lifting it to `bigger' rings. By a theorem of Mazur, under certain hypothesis the liftings fit into a nice universal family. I will discuss the inverse problem of realizing rings as the coefficient rings of such a universal family and results in this direction (joint work with Tim Eardley).
Oct 3	Thu	Stephen Connor (York)	Statistics Seminar
14:00		Mixing time for a random walk on a ring
	Abstract: We consider a variant of a process used in random number generation, and previously studied by Chung, Diaconis and Graham. This a random walk on the integers mod n (n odd), which at each step either increments by 1 or doubles its value, but where the probability of doubling is a decreasing function of n. We use a mixture of representation theory and probability to show that the total variation distance for this process exhibits a cutoff phenomenon. This is joint work with Michael Bate (York).
Oct 3	Thu	Katherine Reynolds (Teach First)
16:00
		Hicks Building LT6
Oct 3	Thu	Paul Mitchener (Sheffield)	Topology Seminar
16:00		Discrete homotopy and homology
		Hicks Seminar Room J11
	Abstract: In this article we introduce discrete analogues of homotopy and homology groups on a particular scale, and state and maybe prove some analogues of some of the classic theorems of algebraic topology. We also make an attempt to compare what happens in the limit as the scale gets larger and larger with some of the corresponding groups in coarse geometry.
Oct 3	Thu	Katherine Reynolds (Teach First)	Careers Talks
16:00		Teach First
		Hicks Building LT7
	Abstract: Maths is one of the subjects where we have the greatest need for inspirational teachers. A staggering 58% of pupils who are eligible for Free School Meals fail to get a maths GCSE at grade A*-C. There is substantial evidence that low numeracy skills are associated with poor outcomes for many people – and society as a whole. E.g. people with poor numeracy skills are more than twice as likely to be unemployed as those competent in numeracy and a quarter of young people in custody have a numeracy level below that expected of a seven-year-old. Becoming a teacher is a great way to use your degree and Katherine will be telling you how she used her Maths degree to make a difference. Teach First are an education charity working with others to give every child the right to a decent education. We train people with leadership potential to be inspirational teachers in schools in low-income communities across the country. These leaders go on to work in different sectors of society towards a future where no child’s educational success is limited by their socio-economic background. Katherine will be discussing her experiences on the programme but for more information beforehand please see http://graduates.teachfirst.org.uk/
Oct 3	Thu	Chris Boswell (TPP-UK)	Careers Talks
16:00		TPP-UK Consulting
		Hicks Building LT7
	Abstract: TPP produces SystmOne clinical software, which fully supports the NHS vision for a ‘one patient, one record’ model of healthcare. Professionals are able to access a single source of information, detailing a patient’s contact with the health service across a lifetime. This record is accessible whatever the care setting, so any health professional can enter information. It documents every appointment, every medication, every allergy and every contact the patient has ever had. Established 16 years ago, TPP had our first SystmOne go live in 1999 and has consistently grown year on year. We now host around 30 million patient records and our software is used by over 5000 NHS organisations. As a software developer, I write and update the software, working alongside our analysts to ensure SystmOne is up to date and functioning well for our end users. I also work on transferring data from legacy systems across to SystmOne for any organisations which decide to move onto SystmOne. We only recruit bright people with a logical mindset, making this an ideal position for Maths graduates. Every day is different and offers fresh intellectual challenges and problems to solve, from deciphering obscure database formats to writing and architecting new modules of SystmOne.
Oct 8	Tue	Samir Siksek (Warwick)	Number Theory seminar
14:00		Elliptic Curves over Real Quadratic Fields are Modular
		LT11
	Abstract: We combine the latest advances in modularity lifting with a 3-5-7 modularity switching argument to prove the result of the title. We use this to prove that the exponent in the Fermat equation over $\mathbf{Q}(\sqrt{d})$ is effectively bounded with d =3 mod 4 or d=6 or 10 mod 16. This is based on joint work with Nuno Freitas and Bao Le Hung.
Oct 8	Tue	Jon Keating (Bristol)
15:00		Quantum Mechanics and Topology
		Hicks Seminar Room J11
Oct 9	Wed	Andreas Kyprianou (Bath)	Statistics Seminar
14:15		Censored Stable Processes
		LT6
	Abstract: We look at a general two-sided jumping strictly alpha-stable process where alpha is in (0,2). By censoring its path each time it enters the negative half line we show that the resulting process is a positive self-similar Markov Process. Using Lamperti's transformation we uncover an underlying driving Lévy process and, moreover, we are able to describe in surprisingly explicit detail the Wiener-Hopf factorization of the latter. Using this Wiener-Hopf factorization together with a series of spatial path transformations, it is now possible to produce an explicit formula for the law of the original stable processes as it first *enters* a finite interval, thereby generalizing a result of Blumenthal, Getoor and Ray for symmetric stable processes from 1961. This is joint work with Juan Carlos Pardo and Alex Watson.
Oct 9	Wed	Thomas Mikosch (Copenhagen)	Statistics Seminar
15:45		Power Law Tails in Applied Probability - Some Recent Developments. [The 2013 Applied Probability Trust Lecture]
	Abstract: For many decades, regular variation has been a useful tool in various areas of applied probability theory, including queuing, branching, renewal theory, stochastic networks, time series analysis, extreme value theory, insurance, and tails (i.e., distributions with power law tails) naturally appear as limits for normalized and centered maxima and sums of independent and identically distributed random variables or as domain of attraction condition for such limit laws. However, models whose components have power law tails are not always motivated by asymptotic theory; regular variation is a convenient way of describing unusually large values, for example, catastrophic claims in an insurance portfolio, large and long transmission times in the Internet, big losses/gains on the stock market, etc. Since the encyclopedia Regular Variation by N. Bingham, C. Goldie and J. Teugels (Cambridge UP) appeared in 1987, various extensions and modifications of regular variation have been successfully developed and applied. In this talk, we consider some newer developments. Those include the notion of a regularly varying time series (i.e., the finite-dimensional distributions of such a series have power law tails), functional regular variation of stochastic processes, random fields and random sets, and large deviations of regularly varying structures.
Oct 9	Wed	Arend Bayer (Edinburgh)	Pure Maths Colloquium
16:00		Positivity in algebraic geometry via the derived category
		Hicks Seminar Room J11
	Abstract: Over the last 10 years, the classification of algebraic varieties has seen dramatic progress via the success of the minimal model program (MMP). MMP in turn is based on notions of positivity (of divisors) that fundamentally characterize algebraic geometry. In the talk, I will describe a new approach towards understanding positivity of divisors via the derived category and Bridgeland stability conditions; this is based on joint with with Emanuele Macrì. Via this approach, we can make general MMP-existence results effective, and on the way answer many concrete questions on the geometry of Hilbert schemes of K3 surfaces.
Oct 10	Thu	Ziyad Alhussain (Sheffield)	Statistics Seminar
14:00		Eliciting beliefs about a variance parameter
		Hicks Seminar Room J11
	Abstract: In eliciting an expert's opinion, we ask the expert to report judgements about the observable quantity. Then we fit those judgements into a probability distribution that best describes the expert's beliefs. One of the challenges in elicitation is to make direct judgements about the variance parameter of the normal distribution. Hence, we aim to find an elicitation method that best fits the expert's opinion about the variance into a probability distribution. In this talk, I will present two elicitation methods that attempt to fit the expert's judgements about the variation of normally distributed data into a probability distribution. The first method depends on Bayes' theorem where the expert is asked to update the initial judgements given hypothetical data. We then illustrate that the expert may find difficulty in updating judgements using Bayes' theorem. Therefore, we propose an elicitation method that does not depend on Bayes' theorem, easier to use and works for the assumption of conjugate and non-conjugate prior distributions. We conclude by an interactive example using a proposed software tool.
Oct 10	Thu	Fatimah Aloef (Sheffield)	Statistics Seminar
14:00		Bayesian experimental design in health economics
		Hicks Seminar Room J11
	Abstract: In health economics, the concept of health care evaluation refers to identify, measure, value and compare the cost as well as the benefits of different health care innervations to allocate the limited health recourses wisely. Cost-Effectiveness Analysis (CEA) has been the most widely used method to derive such allocation decisions, especially for those at the National Institute for Health and Clinical Excellence (NICE) in the UK. This evaluation technique uses Quality Adjusted Life Years (QALYs) as an outcomes measure in order to be able to compare different health care interventions directly. There are different techniques to measure the "Q" part of this quantity which reflects the quality of life for health outcomes, namely utility. Recently, there has been an increase interest in using Discrete Choice Experiments (DCEs) to elicit health state utilities as an alternative for the cardinal methods. Utilities are required for all health states defined by a classification system. However, discrete choice data is collected to a subset of health states, and then a model fitted to estimate the utilities for any health state defined by the classification system. Thus, an optimal choice design is required to estimate the utilities within QALYs framework precisely. In this talk I will consider the problems of constructing choice design for health evaluation purpose. Particularly, anchoring health utility values produced by the DCE into 0-1(dead-full health) scale to be used within QALY framework, the dependency problem of optimum choice design on the unknown choice model's parameters, and simplifying the choice task and its effect on the design efficiency. The experimental design used in our work is illustrated through a pair-wise comparison of practical health example, AQL-5D classification system.
Oct 10	Thu	Fionntan Roukema (Sheffield)	Topology Seminar
16:00		Enumerating Exceptional Knot Complement Pairs
		Hicks Seminar Room J11
	Abstract: Enumerating exceptional pairs (cusped hyperbolic manifolds with distinct non-hyperbolic fillings) is a natural and well studied programme in the literature. In this talk we will restrict our attention to hyperbolic knot complements in S^3. We will see that this essentially reduces to the study of Berge knots, and we will think about an approach to performing a complete enumeration of exceptional pairs in this setting.
Oct 15	Tue	Tobias Berger (Sheffield)	Number Theory seminar
14:00		TBA
		LT9
Oct 16	Wed	Constanze Roitzheim (Kent)	Pure Maths Colloquium
16:00		Algebraic models in topology
		Hicks Seminar Room J11
	Abstract: A differential graded algebra is a chain complex with a multiplication that is compatible with the differentials. This means that its homology also carries an algebra structure. But how many differential graded algebras realise the same homology algebra? We explain why this question is relevant to topology and present an example from homotopy theory.
Oct 17	Thu	Dennis Prangle (Lancaster)	Statistics Seminar
14:00		Summary statistics for likelihood-free model choice
	Abstract: A central statistical goal is to choose between alternative explanatory models. This work is motivated by population genetic models, which are typically complicated stochastic processes whose likelihoods are numerically intractable. Hence it is not possible to use statistical methods based on evaluating likelihood functions. Approximate Bayesian computation (ABC) is a commonly used likelihood-free method for such situations. ABC simulates data for many parameter values under each model and compares these to the observed data. The comparison is based on vectors of summary statistics of the data. More weight is given to models which produce simulated vectors close to that for the observations. The choice of summaries turns out to be crucial to the efficiency and accuracy of the inference algorithm. This talk presents a method to select good summary statistics for ABC model choice. An application is also presented, choosing between demographic models of Campylobacter jejuni, a bacterial pathogen responsible for a large proportion of gastroenteritis cases.
Oct 17	Thu	Philipp Wruck (Sheffield)	Topology Seminar
16:00		Using tom Dieck functors to obtain global Tambara functors
		Hicks Seminar Room J11
	Abstract: Many equivariant homology theories are definable not just for a particular group but for every compact Lie group. Such theories can be represented by global spectra. For a fixed group $G$, an ordinary equivariant homology theory is essentially the same as a $G$-Mackey functor, and $\pi_0$ of a $G$-spectrum naturally carries the structure of a $G$-Mackey functor. Therefore it is resonable to ask for a global equivalent of Mackey functors with similar properties. An important question is in what way additional structure in the spectrum translates into properties of the Mackey functor, e.g. when the spectrum is a commutative ring spectrum. The resulting structure in this case is called a Tambara functor. For finite groups, this structure is well understood. For compact Lie groups, Schwede has recently provided some insight with his notion of global power functors. In this talk, we will give an overview of the basic ideas of the theory of Mackey functors, Tambara functors and their global equivalents. We will present an approach based on work of tom Dieck which circumvents the use of stable homotopy theory to define global functors for compact Lie groups. This recovers the results of Schwede when passing to a suitable quotient.
Oct 23	Wed	Monica Oliveira (Strathclyde)	Applied Mathematics Colloquium
14:00		Extensional flows of complex fluids at the micro-scale
		LT9
	Abstract: The non-linear rheological properties of complex fluids often impart a rich set of unusual characteristics to flow systems. When these fluid properties, such as viscoelasticity, are combined with the small scales of microfluidics, the non-linearities are enhanced and may dominate the flow dynamics. In this presentation, we will discuss some of our experimental and numerical investigation highlighting the elastic effects that arise in viscoelastic microfluidic flows with a strong extensional contribution, and the use and optimisation of microfluidic devices for rheometry purposes.
Oct 23	Wed	Gill Lancaster; Dawn Teare; Sandra Eldridge (Lancaster; Sheffield; Queen Mary, London)	RSS Seminar
14:00		Statistical Issues in the Design and Analysis of Pilot and Feasibility Studies
		ScHARR
	Abstract: Three talks followed by group discussion: (1) Feasibility/pilot studies in the design, conduct and evaluation of complex interventions (2) How large does a pilot study need to be to estimate the key design paramters for the future RCT? (3) Reporting of pilot/feasibility studies
Oct 23	Wed	Norbert Peyerimhoff (Durham)	Pure Maths Colloquium
16:00		On noncompact harmonic and asymptotically harmonic spaces
		Hicks Seminar Room J11
	Abstract: Harmonic spaces are Riemannian manifolds on which all harmonic functions satisfy the mean value property. The Lichnerowicz conjecture stated that all simply connected harmonic manifolds are flat or rank-1 symmetric spaces. Szabo proved this conjecture in the compact case in 1990. Shortly afterwards in 1992, there appeared non-compact nonsymmetric harmonic spaces - the so-called Damek-Ricci spaces - disproving the conjecture in the noncompact case. In this talk I will introduce harmonic spaces and the more general asymptotically harmonic spaces and discuss some recent results about these interesting manifolds.
Jan 1	Thu	Alex Corner (Sheffield)
838:5		Multicategories and operads
		Hicks Seminar Room J11
	Abstract: The most basic building blocks that we use in mathematics are sets. However, we need to also say how sets interact with each other, which is why we have functions. A category is the abstraction of this idea - it is a collection consisting of some objects, as well as the composable maps between them. The generality of category theory then allows us to describe phenomena that occur throughout mathematics. Sometimes the objects we want model have a different sort of map. A category with vector spaces as objects would notionally have linear maps as the morphisms between them. However, we can also consider multilinear maps between vector spaces. The structure of a category isn't quite general enough to account for such maps and so we are required to define multicategories. The second notion in the title, an operad, is a specific case of a multicategory which can be regarded as a collection of n-ary operations - these are often found to be useful to describe notions in topology or algebra. In this talk I will give some motivation for the study of category theory. I'll introduce the definition of a category, along with some examples of such, as well as giving the general idea of why such things are useful to study. I'll carry on to talk about multicategories and operads, again with examples, with an idea of what kind of structures they can express. Finally, I will talk about the notion of an algebra for a multicategory or an operad - akin to an algebra over a field or a ring. The structure of a multicategory or an operad allows us to express interesting objects as algebras, examples including loop spaces and monoid homomorphisms will be shown in the talk.
Oct 24	Thu	Lindsey Lee (School of Earth and Environment - Leeds University )	Statistics Seminar
14:00		Statistical Methods for Understanding Uncertainty in a Global Aerosol Model
		Hicks Seminar Room J11
	Abstract: Uncertainty is inherent in the modelling of complex processes associated with climate science. Model uncertainty arises in any computer model that is restricted in terms of computational power and current knowledge but can broadly be defined in terms of input, parametric and structural uncertainty. Structural uncertainty can be considered by comparing outputs from different computer models. A lot of progress has been made in quantifying the effect of structural uncertainty on aerosol model predictions through the AEROCOM project. We have made progress in the quantification and understanding of parametric and input uncertainty by application of statistical methods in the NERC AEROS project. In this talk I will explain the statistical methods that have been applied in the AEROS project to help us understand and quantify parametric uncertainty in the GLOMAP aerosol model. These methods include expert elicitation, experimental design, emulation and sensitivity analysis. I will then show some of the results we have from applying these methods to study 28 uncertain parameters (and emissions) and their effects on GLOMAP model predictions.
Oct 24	Thu	Pokman Cheung (Sheffield)	Topology Seminar
16:00		Factorisation algebras and factorisation homology
		Hicks Seminar Room J11
	Abstract: This talk will be an overview of the theory of factorisation algebras. Factorisation algebras provide a local-to-global machinery (like, but also unlike, sheaves) and arise in the study of e.g. homotopy commutative algebras, mapping spaces and quantum field theory. I will discuss some examples in topology, geometry and (perhaps) mathematical physics.
Oct 29	Tue	Lynne Walling (Bristol)	Number Theory seminar
14:00		The action of Hecke operators on Siegel-Eisenstein series
		I12
	Abstract: Siegel introduced generalised theta series to study the number of times a quadratic form on a lattice represents lower dimensional quadratic forms; these generalised theta series gave us the first examples of Siegel modular forms. Although these are rather natural generalisations of classical modular forms, many questions resolved long ago in the classical case remain unresolved in the case of Siegel modular forms. In this talk I will introduce Siegel modular forms, Hecke operators, and Siegel-Eisenstein series (of abitrary integral weight, level, character, and Siegel degree). I will describe how to evaluate the action of the Hecke operators on the Eisenstein series, and how to then diagonalise the space of Eisenstein series with respect to Hecke operators. I will briefly discuss how to extend this work to half-integral weight forms.
Oct 29	Tue	Sylvia Wiegand (University of Nebraska-Lincoln)	Algebra / Algebraic Geometry seminar
16:00		Formal fibers of prime ideals in polynomial rings (this is joint work with William Heinzer and Christel Rotthaus).
		K14
	Abstract: Let $(S, n)$ be a Noetherian local domain of dimension $n$ that is essentially finitely generated over a field k; that is, $S$ is a localization of a finitely generated $k$-algebra. The generic formal fiber of $S$ is the set of prime ideals $Q$ of the $n$-adic completion $\hat{S}$ of $S$ such $Q\cap S = (0)$. Matsumura has shown that $n-1$ is the maximum of all the heights of prime ideals $Q$ in the generic formal fiber of $S$. We show that every prime ideal $Q$ of $\hat{S}$ that is maximal with respect to $Q\cap S = (0)$ has height $n-1$. The proof uses our 2006 theorem that, for a polynomial ring in indeterminates $x_1,\cdots, x_n$, $R = k[x_1,\cdots,x_n](x_1,\cdots,x_n)$, every prime ideal $P$ of $\hat{S} = k[[x_1,\cdots,x_n]]$ that is maximal with respect to $P\cap R = (0)$ has height $n-1$. A new "Generic Fiber Extension" Theorem yields that the extension $(R,m)\hookrightarrow (S, n)$ is such that the generic formal bers of R corresponds to those of $S$. We discuss these concepts, our motivation, and related results, past and current, regarding formal bers, and we give some of the proof.
Oct 30	Wed	Roger Wiegand (University of Nebraska)	Algebra / Algebraic Geometry seminar
13:00		Torsion in tensor products and vanishing of Tor
		K14
	Abstract: Let $M$ and $N$ be non-zero finitely generated modules over a local integral domain $R$. When studying depth properties of $M\otimes_{R}N$, such as whether or not the tensor product is torsion-free, one is led naturally to questions concerning vanishing of Tor. For example, if $R$ is a complete intersection $\text{and} \ \ Tor\,_{i}^{R}\,(M,N) \, = \, 0 \ \ \text{for all} \ \ i\,>\,0$, one has the "Depth Formula": $$\quad \,depth\ M +\,depth\ N =\,depth\ R +\,depth\ M\otimes_{R}N $$ Thus one seeks conditions that force the vanishing of all higher Tors. I will survey results on vanishing of Tor and related questions on the existence of torsion in tensor products. The following conjecture is of particular interest, due to its relation to other celebrated conjectures in representation theory: $$ \text{Conjecture:}\qquad\qquad\text{If} \ \ M\otimes_{R}\,Hom_{R}(M,R) \ \ \text{is maximal Cohen-Macaulay, then } \ M \ \text{is free}.\qquad\qquad\qquad $$ The conjecture is open even for one-dimensional complete intersections of codimension two. A substantial part of the talk will deal with recent joint work in progress with O Celikbas, C Huneke, S Iyengar, and G Piepmeyer.
Oct 30	Wed	Rainer Hollerbach (Leeds)	Applied Mathematics Colloquium
14:00		Magnetorotational Instabilities in Taylor-Couette Flow
		LT9
	Abstract: [APW: The flow in accretion discs has been observed to be turbulent, but according to the Rayleigh Criterion, hydrodynamic Kepler flows should be linearly stable. The existence of a subcritical nonlinear is debated, but appears to be unlikely. That turbulence in these flows originates via a magnetic instability looks more 'PROMISE'ing.]
Oct 30	Wed	John Cremona (Warwick)	Pure Maths Colloquium
16:00		The complex AGM, periods and elliptic logarithms of elliptic curves over $\mathbf{C}$
		Hicks Seminar Room J11
	Abstract: I will describe an efficient method for computing period lattices and elliptic logarithms for elliptic curves defined over C, using the complex Arithmetic-Geometric Mean (AGM) first studied by Gauss. Previous work has only considered the case of elliptic curves defined over the real numbers; here, the multi-valued nature of the complex AGM plays an important role, and modular forms make a cameo appearance. Joint work with Thotsaphon Thongjunthug.
Oct 31	Thu	Michael Salter-Townshend (University College Dublin)	Statistics Seminar
14:00		Modelling Multiple Social Relations
		Hicks Seminar Room J11
	Abstract: Social network analysis is the rapidly expanding field that deals with interactions between individuals or groups. The literature has tended to focus on single network views, i.e. networks comprised of a group of nodes with a single type of link between node pairs. However, nodes may interact in different ways with the same alters. For example, on twitter one user may retweet, follow, list or message another user. There are thus 4 separate networks to consider. Current approaches include examining all network views independently or aggregating the different views to a single super network. Neither of these approaches are satisfying as the interaction between relationship types across network views is not explored. We are motivated by an example consisting of the census of 75 villages in the Karnataka province in India. The data was collated for use by a microfinance company and 12 different link types are recorded. We develop a novel method for joint modelling of multiview networks as follows; we begin with the popular latent space model for social networks and then extend the model to multiview networks through the addition of a matrix of interaction terms. The theory behind this extension is due to emerging work on Multivariate Bernoulli models. We first present the theory behind our new model. We then explore the relationship between the interaction terms and the correlation of the links across network views and finally we present results for the Karnataka dataset. Inference is a challenge and we adopt the No-U-Turn sampler, a variant of Hamiltonian Monte Carlo for Bayesian inference.
Nov 6	Wed	Michele Bartuccelli (Surrey)	Applied Mathematics Colloquium
14:00		Obtaining estimates of the norm for solutions of dissipative partial differential equations
		LT9
	Abstract: In this talk we will address the problem of obtaining explicit and accurate estimates of the sup-norm for solutions of dissipative partial differential equations such as the Swift–Hohenberg Equation and the Navier-Stokes equations in one and two space dimensions. By using the best (so far) available estimates of the embedding constants which appear in the classical functional interpolation inequalities used in the study of solutions of dissipative partial differential equations, we will evaluate in an explicit manner the values of the sup-norm of the solutions of the PDE under investigation. In addition (time permitting) we will compute the so-called time-averaged dissipative length scale associated to the solutions of the PDE.
Nov 6	Wed	Leonid Chekhov (Loughborough)	Pure Maths Colloquium
16:00		Poisson and quantum algebras originated from bilinear forms
		Hicks Seminar Room J11
	Abstract: Bilinear forms with the transformation laws A->BAB^T manifest rich Poisson and quantum algebraic structures and admit a number of Poisson reductions among which are reductions to algebras of geodesic functions on Riemann surfaces. We describe the algebroid of bilinear forms, its reductions, the associated braid-group action, generalization to the affine case (joint papers with M.Mazzocco at Advances Math. and Comm.Math.Phys.) and present some new results on possible groupoid structures consistent with the transformation laws.
Nov 7	Thu	Peter Neal (Lancaster)	Statistics Seminar
14:00		MCMC for a birth-death-mutation (BDM) model
		Hicks Seminar Room J11
	Abstract: A birth-death-mutation (BDM) model has been used by a number of authors to model the evolution of a tuberculosis epidemic in San Francisco in the early 1990s. The observed data is assumed to be a cross-sectional study of the tuberculosis outbreak. It is impossible to write down the likelihood for the model without substantial, non-trivial data augmentation which prohibits the use of standard MCMC algorithms. However it is trivial to simulate a realisation of the BDM model and ABC algorithms have been used to estimate the parameters of the BDM model. Starting from the ABC perspective that simulation is straightforward, we construct an MCMC algorithm which uses simulation. Specifically we use a non-centered parameterisation which enables us to treat the simulation process as a data augmentation problem and takes similar amounts of time per iteration as the ABC algorithms. The MCMC algorithm is successfully applied to the San Francisco tuberculosis data.
Nov 7	Thu	Alexander Vishik (Nottingham)	Topology Seminar
16:00		Symmetric and Steenrod operations in algebraic cobordism
		Hicks Seminar Room J11
	Abstract: Symmetric operations are encoding all integral divisibilities of characteristic numbers of algebraic varieties. This permits to apply them to various questions related to torsion effects, getting more subtle results than what Landweber-Novikov operations would give. They also define natural obstructions for presenting a cobordism element by the class of an embedding. These operations are closely related to Steenrod operations in Algebraic Cobordism. There are two types of those: type of Quillen, and type of Tom Dieck. The latter are substantially more subtle, and were constructed only recently.
Nov 19	Tue	Paul-James White (Oxford)	Number Theory seminar
14:00		Studying L-functions via the trace formula
		LT11
	Abstract: Sarnak, following ideas of Langlands on "Beyond Endoscopy", gave a trace formula proof of the analytic continuation of the L-function associated to a holomorphic cusp form. Herman recently deduced the functional equation via the trace formula. We shall talk about a possible approach to studying base change $L$-functions via the trace formula.
Nov 20	Wed	Mohammed Afsar (Imperial)	Applied Mathematics Colloquium
14:00		Non-homogeneous Rapid-distortion theory on transversely sheared flows
		LT9
	Abstract: We are concerned with the small amplitude unsteady motion of an inviscid non-heat conducting compressible fluid on a transversely sheared mean flow. We show that the hydrodynamic component of the motion is determined by two arbitrary convected quantities in the absence of solid surfaces and hydrodynamic instabilities. These results can be used to specify appropriate upstream boundary conditions for unsteady surface interaction problems on transversely sheared mean flows in the same way that the vortical component of the Kovasznay (1953) decomposition is used to specify these conditions for surface interaction problems on uniform mean flows. But unlike Kovasznay’s (1953) result the arbitrary convected quantities no longer bear a simple relation to the physical variables. We complete the formalism developed in Goldstein (1978 & 1979) by obtaining the necessary relations between these quantities and the physically measurable flow variables. The results are important because they enable the complete extension of Non-homogeneous Rapid Distortion Theory to transversely sheared mean flows. We use these results to derive a generalization of the famous Ffowcs Williams and Hall (1970) formula for the sound produced by the interaction of turbulence with an edge that is frequently used as a starting point for predicting sound generation by turbulence/solid surface interactions. We illustrate the utility of this result by using it to calculate the sound radiation produced by the interaction of a two-dimensional jet with the downstream edge of a flat plate.
Nov 20	Wed	Vladimir Dokchitser (Warwick)	Pure Maths Colloquium
16:00		Ranks of elliptic curves
		Hicks Seminar Room J11
	Abstract: I will discuss elliptic curves from the classical number theoretic point of view of trying to solve Diophantine equations. The aim will be both to explain how we think about these creatures and to give an overview of what we can (and sometimes can't) prove about them, and to illustrate it with explicit examples. I will not try to describe the huge modern technical machine that has been developed to study elliptic curves, so most of the results will come as black boxes.
Nov 21	Thu	Axel Finke (Warwick)	Statistics Seminar
14:00		Static-parameter estimation in piecewise deterministic processes using particle Gibbs samplers
		Hicks Seminar Room J11
	Abstract: We give a brief introduction to recent advances in sequential Monte Carlo and pseudo-marginal MCMC methods as well as to piecewise deterministic processes (PDPs). The latter form a class of stochastic processes that jump randomly at a countable number of stopping times but otherwise evolve deterministically in continuous time. We then develop a particle Gibbs sampler for static-parameter estimation in PDPs that are observed only partially, noisily and in discrete time. We present a reformulation of the original particle filter for PDPs. This permits the use of a variance-reduction technique known as ancestor sampling that greatly improves mixing of the particle Gibbs chain. We compare our method with a particle Gibbs sampler based on the variable rate particle filter. Our approach is further illustrated on a shot-noise-Cox-process model that has applications in finance. This is joint work with Adam Johansen and Dario Spanò.
Nov 21	Thu	John Pullinger (House of Commons)	RSS Seminar
16:00		Statistics making an impact
		LT2
	Abstract: John Pullinger, President of the Royal Statistical Society, will give a reprise of his presidential lecture. He will explore how the role of statistics in society has changed with changes in the politics of decision-making. He will outline the Royal Statistical Society strategy for the next 4 years and consider how individual members of the RSS can play a part.
Nov 26	Tue	James Newton (Cambridge)	Number Theory seminar
14:00		Local-global compatibility for Galois representations associated to Hilbert modular forms of low weight
		I12
	Abstract: Generalising Deligne and Deligne-Serre's results in the elliptic modular case, Carayol, Taylor and Jarvis have explained how to construct Galois representations from cuspidal Hilbert modular eigenforms. In particular, Jarvis used congruences to construct these representations in the `low weight' cases (where some of the weights are equal to 1). Whenever one has a global Galois representation associated to an automorphic representation (e.g. the automorphic representation generated by a modular eigenform) one expects to recover the local Langlands correspondence when comparing the local Galois representations obtained by restricting to decomposition subgroups with the local factors of the automorphic representation - this statement is known as `local-global compatibility'. Jarvis already proved most cases of local-global compatibility for low weight Hilbert modular forms, but a few cases remain unknown. I will discuss an approach to proving local-global compatibility in at least some of these remaining cases, using tools from the p-adic Langlands programme (in particular, Emerton's completed cohomology and a generalisation, due to Kassaei, of Buzzard and Taylor's results on analytic continuation of overconvergent eigenforms).
Nov 27	Wed	Bill Chaplin (Birmingham)	Applied Mathematics Colloquium
14:00		Sounding stars and the search for exoplanets
		LT9
	Abstract: We are in a golden era for stellar physics driven by new satellite and telescope observations of unprecedented quality and scope. Thanks to the launch of the NASA Kepler Mission the past four years has seen dramatic progress in the study of other stellar systems in our galaxy. Kepler has revolutionized the field of asteroseismology, the study of stars by observation of their natural oscillations. In this seminar I will discuss the asteroseismic study of solar-type stars, including characterisation of exoplanet host stars which provides essential information for constraining the properties of the detected planets (including information on spin-orbit alignment of the systems). Finally, I will touch on what the future holds for Kepler (following the recent failure of a second of its reaction wheels).
Nov 27	Wed	Markus Rosenkranz (Kent)	Pure Maths Colloquium
16:00		Algebraic Boundary Problems: Abstract and Concrete
		Hicks Seminar Room J11
	Abstract: We give an overview of the algebraic structures underlying linear boundary problems, both in the vector space setting (abstract boundary problems) and in the integro-differential setting (concrete boundary problems). We outline the construction of the polynomial and free objects in the category of integro-differential algebras. The associated ring of integro-differential operators is compared to a generalized Weyl algebra for one variable. We conclude with some remarks on partial integro-differential operators with linear substitutions.
Nov 28	Thu	Marton Balazs (Bristol)	Statistics Seminar
14:00		Anomalous fluctuations in one dimensional interacting systems
		Hicks Seminar Room J11
	Abstract: I will describe a family of one dimensional interacting particle systems that contains the simple exclusion and the zero range processes, and many more. In the stationary distribution the current fluctuations show anomalous scalings, I will sketch parts of the proof of this phenomenon for some of our models. Meanwhile I will try to make it clear how convexity of a function of central importance leads to such unusual behaviour. The technical point that prevents us from proving anomalous scaling in great generality will also be pointed out. Our methods work with probabilistic arguments and couplings, hence it might give more intuition than alternative existing techniques of heavy combinatorics and analysis.
Dec 3	Tue	Haluk Sengun (Warwick)	Number Theory seminar
14:00		Torsion homology of Bianchi Groups and Arithmetic
		LT11
	Abstract: Bianchi groups are groups of the form SL(2,R) where R is the ring of integers of an imaginary quadratic field. They form an important class of arithmetic Kleinian groups and moreover they hold a key role for the development of the Langlands program for GL(2) beyond totally real fields. In this talk, I will discuss several interesting questions related to the torsion in the homology of Bianchi groups. After discussing the importance of torsion from the perspective of number theory, I will talk on joint work with N.Bergeron and A.Venkatesh on the cycle complexity of arithmetic manifolds and asymptotics of torsion growth.
Dec 4	Wed	Tony Padilla (Nottingham)	Applied Mathematics Colloquium
14:00		Sequestering the Standard Model Vacuum Energy
		LT9
	Abstract: We propose a very simple reformulation of General Relativity, which completely sequesters from gravity all of the vacuum energy from a matter sector, including all loop corrections and renders all contributions from phase transitions automatically small. The idea is to make the dimensional parameters in the matter sector functionals of the 4-volume element of the universe. For them to be nonzero, the universe should be finite in spacetime. If this matter is the Standard Model of particle physics, our mechanism prevents any of its vacuum energy, classical or quantum, from sourcing the curvature of the universe. The mechanism is consistent with the large hierarchy between the Planck scale, electroweak scale and curvature scale, and early universe cosmology, including inflation. Consequences of our proposal are that the vacuum curvature of an old and large universe is not zero, but very small, that wDE≃−1 is a transient, and that the universe will collapse in the future.
Dec 4	Wed	David Applebaum (Sheffield)	Pure Maths Colloquium
16:00		Generalised spherical functions on Lie groups and symmetric spaces
		Hicks Seminar Room J11
	Abstract: One of the most important classes of probability measures are those that are infinitely divisible. In Euclidean space, these are characterised by means of their Fourier transform, and this leads to the celebrated Levy-Khintchine formula. In symmetric spaces, there is an analogous characterisation due to Ramesh Gangolli, where the Fourier transform is replaced by the spherical transform, but it only works for measures that are bi-invariant under the action of that subgroup of the isometry group that leaves some point fixed. The problem of obtaining a Levy-Khintchine formula in the general case, without any bi-invariance assumption, has recently been solved in joint work with Tony Dooley (UNSW, now Bath). A key step was finding out what to use instead of the spherical transform. This involves an extension of the concept of a spherical function.
Dec 5	Thu	Keith Harris (Sheffield)	Statistics Seminar
14:00		Bayesian hierarchical models for microbial metagenomics
		Hicks Seminar Room J11
	Abstract: In this talk, we will introduce Dirichlet multinomial mixtures (DMM) for the probabilistic modelling of microbial metagenomics data. This data can be represented as a frequency matrix giving the number of times each taxa is observed in each sample. The samples have different size, and the matrix is sparse, as communities are diverse and skewed to rare taxa. Most methods used previously to classify or cluster samples have ignored all these features. The Dirichlet mixture components cluster communities into distinct ‘metacommunities’, and, hence, determine envirotypes or enterotypes, groups of communities with a similar composition. We applied the DMM model to human gut microbe genera frequencies from Obese and Lean twins. Our results suggested that obesity is not associated with a distinct microbiota but instead increases the chance that an individual derives from a disturbed enterotype. We will also show how the Dirichlet multinomial framework for defining enterotypes can be adapted to develop a Bayesian approximation to the Unified Neutral Theory of Biodiversity in ecology, which has been proposed as a null model for the structure of microbial communities. The approximation was developed as the existing maximum likelihood based genealogical approach for fitting the multi-site UNTB is too computationally demanding for the large datasets typically encountered in microbiomics. The key to our strategy is the observation that the UNTB is, in the limit of large population sizes, equivalent to the hierarchical Dirichlet process (HDP) in statistics, which can be exploited to derive an efficient Gibbs sampler for the neutral model. We firstly validated this method by applying it to synthetic data and twenty-nine tropical tree plots from Panama that had already been shown to satisfy the neutral model. We then used it to determine the extent to which gut microbial communities are neutrally assembled.
Dec 10	Tue	Dan Fretwell (Sheffield)	Number Theory seminar
14:00		Level p paramodular congruences of Harder type
		F24
	Abstract: For a long time we have known about the existence of congruences between the Hecke eigenvalues of elliptic modular forms. Of course the most famous of these is the Ramanujan congruence for the tau function mod 691. Such congruences are important in describing, in some sense, the structure of Galois representations.... Around ten years ago, a well known paper by Harder exploited the cohomology of Siegel modular varieties in order to predict a far reaching generalization of Ramanujan's congruence. His conjecture describes a specific congruence between the Hecke eigenvalues of Siegel modular forms and elliptic modular forms. The original conjecture was for level 1 forms. In this talk I will motivate Harder's conjecture as well as giving a new paramodular version. Then using conjectural work of Ibukiyama I show how we may translate into the realms of algebraic modular forms via something akin to the Eichler/Jacquet-Langlands correspondence. In this setting I provide a strategy for collecting evidence for the new conjecture along with examples of my own.
Dec 11	Wed	Ines Henriques (Sheffield)	Pure Maths Colloquium
16:00		F-thresholds and Test ideals for determinantal ideals of maximal minors
		Hicks Seminar Room J11
	Abstract: Test ideals first appeared in the theory of tight closure, and reflect the singularities of a ring of positive characteristic. Motivated by their close connection to multiplier ideals in characteristic zero, N. Hara and K. Yoshida defined generalized test ideals as their characteristic p analogue. Whereas multiplier ideals are defined geometrically, using log resolutions, or even analytically, using integration, test ideals are defined algebraically using the Frobenius morphism. The generalized test ideals of an ideal I form a non-increasing, right continuous family, {τ(c . I)}, parametrized by a positive real parameter c. The points of discontinuity in this parametrization, are called F-thresholds of I and form a discrete subset of the rational numbers (work of Blickle-Mustaţă-Smith, Hara, Takagi-Takahashi, Schwede-Takagi, Katzman-Lyubeznik-Zhang). We consider ideals generated by maximal minors of a matrix of indeterminates, in its polynomial ring over a field of positive characteristic. Using an algebraic approach, we give a complete description of their F-thresholds and generalized test ideals.
Dec 12	Thu	Rocio Campos (Sheffield)	Statistics Seminar
14:00		Statistical approach to systems biology and human nutrition: building a novel biological network around metabolic programming of health outcomes influenced by nutrients during lactation
		Hicks Seminar Room J11
	Abstract: Human milk contains a host of bioactive factors including hormones, growth factors, neuropeptides, anti-inflammatory and immunomodulatory components, as well as multiple nutrients as minerals, vitamins, amino acids and fatty acids. In addition, milk contains known and unknown molecules with important metabolic regulatory functions. Basic milk composition has already been established in the 60s, but this knowledge can be improved thanks to novel analytical techniques and systems biology approaches. Now we propose a nutrigenomic-based characterization of milk composition in order to get a full comprehensive view of milk characteristics and its role in infant growth. Moreover, the recent finding of microRNAs, with gene regulatory functions, in human milk is one of the key points that will be studied in this project. Therefore, this proposal intends to define relationships between molecular milk components and the potential influence of maternal diet on both milk composition and infant growth. Specifically, we are going to focus on the first two years of life and try to define (according to experimental models already developed in our home groups) potential adulthood predisposition to metabolic diseases, in particular on obesity.
Dec 12	Thu	Martin Legarreta	Statistics Seminar
14:00		Mapping of badger territories from field data
		Hicks Seminar Room J11
	Abstract: European badgers are animals that defend their territories not only with direct aggression but also through the use of detectable signs such as latrines. The aim of the research is to reconstruct maps of badger territories from data collected through bait-marking, where plastic markers placed in bait have been recovered after excretion and the spatial locations of latrines recorded. Latrines can be classified into three types: hinterland, boundary and outliers i.e. those from extraterritorial excursions. We have developed a Conditional Outlier Prediction Model which uses logistic regression to estimate the probability that a latrine is an outlier, based on its location, the types of other latrines in the same direction and other covariate information. This research extends previous work by estimating joint probabilities that multiple latrines are outliers and, combined with the Minimum Convex Polygon method, allowing the reconstruction of boundaries and quantifying the uncertainty in the reconstruction of a territory.
Jan 27	Mon	Madeleine Jotz Lean (Sheffield)
15:30		The infinitesimal description of Poisson and Dirac Lie groups
		Hicks Seminar Room J11
	Abstract: I will first give a quick introduction to Poisson Lie groups and Dirac manifolds. Drinfel'd proved classifications of Poisson Lie groups via Lie bialgebras, and of Poisson homogeneous spaces of a Poisson group via Dirac subspaces of its Lie bialgebra. This can be understood more naturally in the context of Dirac groups and their homogeneous spaces.
Feb 10	Mon	Theodore Voronov (Manchester)
15:30		On volumes of classical supermanifolds
		Hicks Seminar Room J11
	Abstract: As has been established in recent decades, constructions of algebra and geometry possess a natural self-consistent extension (some view it as "closure") in which the usual notion of commutativity is replaced by its ${\mathbb Z}_2$-graded analog. This is known as superalgebra and supergeometry and has its origins in unification of bosons and fermions in quantum field theory. In particular, supermanifolds are the corresponding generalizations of ordinary manifolds (differentiable or complex-analytic). The concept of volume in the super world may show unexpected features. For example, the total volume of a supermanifold may vanish. This is due to the fact that the underlying "Berezin integral" is not of the usual measure-theoretic nature, so considerations based in positivity are not applicable. A striking example is the superanalog of the unitary group, the unitary supergroup $U(n|m)$, whose total "Haar measure" is zero whenever $nm>0$ (Berezin, 1970s). Recently Witten raised a question as to whether the Liouville volume of every compact symplectic supermanifold is zero. The answer is negative, as is shown by a counterexample. As such one can take the superanalog of a complex projective space endowed with the analog of the classical Fubini--Study form. The explicit formula for the volume of this complex projective superspace ${\mathbb C}P^{n|m}$ is an analytic continuation of the corresponding formula for the ordinary complex projective space (up to a factor). Conjecturally, this is the case for other classical supermanifolds (such as the unitary supergroup). In the talk, I will explain how this all works. This is very much a work in progress and there remain open questions. There may be an interesting relation with recent works on "universal formulas" in Lie algebra theory by Mkrtchyan--Veselov.
Feb 11	Tue	Wansu Kim (Cambridge)	Number Theory seminar
14:00		Rapoport-Zink spaces of Hodge type and application to Shimura varieties
		F24
	Abstract: Rapoport-Zink spaces of (P)EL type are local analogues of Shimura varieties of PEL type. Examples include Lubin-Tate spaces and Drinfeld upper half spaces, and in general Rapoport-Zink spaces are the moduli spaces of p-divisible groups (up to certain rigidification) with extra structure analogous to the extra structure on abelian varieties that PEL Shimura varieties classify. As in Shimura varieties, the cohomology of Rapoport-Zink spaces is expected to realise the local Langlands and Jacquet-Langlands correspondences, which is verified in many cases. Furthermore, Rapoport-Zink spaces have a close relationship with p-adic geometry of Shimura varieties (by p-adic uniformisation), which should encode the local-global compatibility of Langlands correspondence. In this talk, we construct an "Hodge-type analogue" of Rapoport-Zink spaces under a certain unramifiedness hypothesis. This new spaces are constructed as moduli spaces of p-divisible groups with some "crystalline Tate cycles" (the p-adic analogues of Hodge cycles), and can be viewed as a local analogue of Shimura varieties of Hodge type. We also obtain the p-adic uniformisation result for Shimura varieties of Hodge type (in the unramified case). The new examples that can be constructed this way are Spin and orthogonal Rapoport-Zink spaces (of arbitrary rank) -- local analogues of Spin and orthogonal Shimura varieties. If time permits, we will discuss some potential applications and generalisations.
Feb 12	Wed	Christopher Nelson; Schuyler Nicholson (Sheffield)	Applied Mathematics Colloquium
14:00		SN: Implications regarding statistical distances in non-equilibrium systems; CN: The formation of Ellerman bombs in the lower solar atmosphere.
		LT9
	Abstract: Implications regarding statistical distances in non-equilibrium systems Statistical mechanics seeks to use the small scale dynamics of a system to derive its large scale outcomes, for example the macroscopic observables such as temperature, energy or pressure. This goal is hampered for non-equilibrium systems using traditional Statistical mechanics, as fundamental quantities such as the work done, or the equation of motion for the system’s ensemble are not always well defined. As a useful tool in understanding non-equilibrium systems, we investigate the metric distance in probability space given by the Thermodynamic length (L). For a system represented by a probability distribution that is changing in time, L lends a notion of distance that the system travels in its evolution. By utilizing this measure we show how the Thermodynamic length is actually a measure of work done by the system in its evolution. This result is interesting because of the generality in which the thermodynamic length is defined. The Logistic map is then used to numerically illustrate the thermodynamic length. Here the system is shown to often take the path of minimum work. The unstable fixed points of the Logistic map are also identified using our methodology as the major drivers of the system towards equilibrium, i.e. they most efficiently use the available work of the system. The formation of Ellerman bombs in the lower solar atmosphere We discuss the solar phenomena known as Ellerman bombs. These small-scale events form in the photosphere and are thought to be observational evidence of magnetic reconnection. A basic overview of Ellerman bombs is presented highlighting the key traits which are widely linked to magnetic reconnection, before a brief discussion about the mathematical modelling of these events is undertaken.
Feb 12	Wed	Madeleine Jotz Lean (Sheffield)	Pure Maths Colloquium
16:00		Ideals in Lie algebroids
		Hicks Seminar Room J11
	Abstract: Lie algebras and tangent bundles are the corner cases of Lie algebroids. The notion of ideal in a Lie algebra is well-known, and the Bott connection associated to an involutive distribution can be seen as an ideal in the tangent bundle of a manifold. It is hence natural to ask for the definition of an ideal in a more general Lie algebroid. I will explain why the "old" definitions are not satisfactory. An ideal in a Lie algebra corresponds to a multiplicative distribution on the corresponding Lie group. We describe the counterpart in this spirit of multiplicative distributions on Lie groupoids. These have drawn some attention in connection to geometric quantization of Poisson manifolds, and in a modern approach to Cartan's work on Lie pseudogroups. We explain how the infinitesimal counterpart of multiplicative distributions gives rise to a new notion of ideal in a Lie algebroid.
Feb 13	Thu	Partha Dey (Warwick)	Statistics Seminar
14:00		Multiple phase transitions in long-range first-passage percolation on square lattices.
		Hicks Seminar Room J11
	Abstract: We consider a model of long-range first-passage percolation on the d-dimensional square lattice in which any two distinct vertices x, y are connected by an edge having exponentially distributed passage time with mean $|x-y|^s$, where $s>0$ is a fixed parameter and $|.|$ is the $l_1$--norm on $Z^d$. We analyze the asymptotic growth rate of the set $B_t$, which consists of all $x \in Z^d$ such that the first-passage time between the origin 0 and $x$ is at most $t$, as $t\to\infty$. We show that depending on the values of $s$ there are four growth regimes: instantaneous growth for $s < d$, stretched exponential growth for $s\in (d,2d)$, superlinear growth for $s\in (2d,2d+1)$ and finally linear growth for $s>2d+1$ like the nearest-neighbor first-passage percolation model corresponding to $s=\infty$. We find explicit growth rates and also analyze the behavior at the boundary values $s=d,2d,2d+1$. Based on joint work with Shirshendu Chatterjee.
Feb 13	Thu	Andrey Lazarev (Lancaster)	Topology Seminar
15:00		Derived localization of algebras and modules
		Hicks Seminar Room J11
	Abstract: The concept of localization permeates homotopy theory: homotopy categories are constructed by localizing closed model categories at weak equivalences. Localization of commutative rings and their modules is an exact functor and is well-understood. In contrast, localization of noncommutative algebras is a more subtle procedure since it needs to be derived to have good properties. In this talk I discuss the notion of derived localization of algebras and prove that it can be constructed as an appropriate Bousfield localization in the category of modules. As an application I obtain a very general version of the group completion theorem and a derived Riemann-Hilbert correspondence. This is joint work with Joe Chuang and Chris Braun.
Feb 17	Mon	Will Donovan (Edinburgh)
16:00		Mixed braid group actions and B-brane heuristics
		Hicks Seminar Room J11
	Abstract: I will speak about certain examples of braid group actions which appear in algebraic geometry, and explain some physical heuristics which show the topological origins of these actions. This will lead towards a sketch of a construction, joint with Ed Segal, of a system of varieties with associated mixed braid groups acting on their derived categories of coherent sheaves.
Feb 18	Tue	Mitsuaki Funakoshi (Kyoto)	Applied Mathematics Colloquium
14:00		The onset of thermal convection in a rectangular container
		LT2
	Abstract: The widely known problem of onset of thermal convection in a container is examined in detail with high accuracy. That is, the onset of three-dimensional thermal convection of a fluid in a rectangular cavity is examined for various values of its aspect ratios under the assumption of rigid walls with perfect thermal conductance. The critical Rayleigh number, at which a motionless state becomes unstable, and the flow patterns of most unstable modes are calculated numerically with high accuracy using a Galerkin spectral method. A few interesting results on the dependences of critical Rayleigh number and flow patterns of most unstable modes on the aspect ratios are reported in this talk.
Feb 19	Wed	EPSRC visit - no pure colloquium	Pure Maths Colloquium
00:00
		Hicks Seminar Room J11
Feb 20	Thu	Mohamed Shakandli (Sheffield)	Statistics Seminar
14:00		Particle filtering applied to medical time series
		Hicks Seminar Room J11
	Abstract: This talk concerns the set-up and application of particle filtering to medical time series. Considering count time series (such as number of asthma patients recorded over time) we discuss and propose non-linear and non-Gaussian state space models, in particular dynamic generalized linear models (DGLMs). Inference and forecasting is achieved by employing sequential Monte Carlo methods, also known as particle filters. These are simulation based methods that can be used for tracking and forecasting dynamical systems subject to both process and observation noise in non-linear and non-Gaussian models.
Feb 20	Thu	Thomas Cottrell (Sheffield)	Topology Seminar
15:00		Weak n-categories: algebraic versus non-algebraic definitions
		Hicks Seminar Room J11
	Abstract: An n-category is a type of higher-dimensional category which, as well as having objects and morphisms, has 2-morphisms between the morphisms, 3-morphisms between the 2-morphisms, and so on, up to n-morphisms for some fixed natural number n. In a strict n-category, composition of these morphisms is associative and unital. The strict case is well-understood, but strict n-categories are not suitable for describing situations in which composition is not associative and unital, such as concatenation of paths and homotopies. For this a notion of weak n-category is required, in which composition is only associative and unital up to some higher-dimensional cells. Weak n-categories share a close relationship with topology via the homotopy hypothesis of Grothendieck. Many definitions of weak n-category have been proposed, but the relationships between these definitions are not yet well understood. These definitions can be divided into two types: algebraic definitions and non-algebraic definitions. In this talk I will explain what these terms mean, and give two examples of definitions. The first of these is an algebraic definition, due to Penon, which uses the theory of monads; the second is a non-algebraic definition, due to Tamsamani and Simpson, which takes a simplicial approach. I will finish by describing some of my work towards comparing these two definitions.
Feb 25	Tue	Thanasis Bouganis (Durham)	Number Theory seminar
14:00		On special L-values of Siegel and Hermitian modular forms
		Hicks Seminar Room J11
	Abstract: In this talk we will discuss algebraic and p-adic properties of special values of (standard) L-function attached to Siegel and Hermitian modular forms. We will start by presenting a result of Shimura on the algebraicity of these special values, and then discuss a refinement in some cases of his results. Namely, Shimura proves, in a very general situation, that the special values of the standard L-function attached to an eigenform $f$ (Siegel or Hermitian) is up to an algebraic number equal to some powers of $\pi$ times the Petersson inner product of $f$. We will present results which determine the field in which this algebraic number lies and some reciprocity laws for the action of the absolute Galois group. Then, depending on time, we will also discuss results on p-adic measures for Hermitian modular forms.
Feb 25	Tue	Thomas Sotiriou (Nottingham)
16:00		Black holes and Lorentz violations
		F35
	Abstract: I will discuss what happens to the notion of a black hole in gravity theories that exhibit violations of local Lorentz invariance. I will present black hole solutions in such theories, specifically Einstein-aether theory and the infrared limit of Horava gravity, as characteristic examples. I will then explain why these solution still deserve to be called black holes, even when there are excitation that propagate with arbitrarily high speed and can penetrate the usual horizons.
Feb 26	Wed	Examiner meeting- no pure colloquium	Pure Maths Colloquium
		Hicks Seminar Room J11
Mar 5	Wed	Silke Weinfurtner (Nottingham)	Applied Mathematics Colloquium
14:00		Measurement of Stimulated Hawking Emission in an Analogue System
		LT9
	Abstract: Hawking argued that black holes emit thermal radiation via a quantum spontaneous emission. To address this issue experimentally, we utilize the analogy between the propagation of fields around black holes and surface waves on moving water. By placing a streamlined obstacle into an open channel flow we create a region of high velocity over the obstacle that can include surface wave horizons. Long waves propagating upstream towards this region are blocked and converted into short (deep-water) waves. This is the analogue of the stimulated emission by a white hole (the time inverse of a black hole), and our measurements of the amplitudes of the converted waves demonstrate the thermal nature of the conversion process for this system. Given the close relationship between stimulated and spontaneous emission, our findings attest to the generality of the Hawking process.
Mar 5	Wed	Dustin Clausen (Copenhagen)	Pure Maths Colloquium
16:00		A topological perspective on quadratic reciprocity, and some applications
		Hicks Seminar Room J11
	Abstract: The quadratic reciprocity law is a special kind of theorem. It is simple to state but difficult to explain, and it points towards some important hidden structures in arithmetic. I'll talk about a new perspective on quadratic reciprocity, which lets one "see" why it holds as a consequence of some facts concerning the topology of tori. This topological perspective has applications beyond the quadratic reciprocity law. I'll also touch on some of these, namely: a new proof of the Artin reciprocity law, an explanation for Deligne's recent observations on the theory of half-integral weight modular forms (this represents work in progress), and, from the side of homotopy theory, an adelic perspective on the classical "image of J" elements of the stable homotopy groups of spheres.
Mar 6	Thu	Penny Watson (ScHaRR - University of Sheffield)	Statistics Seminar
14:00		The Use of Health Economic Methods in the Development of New Interventions for Systemic Lupus Erythematosus
		Hicks Seminar Room J11
	Abstract: I aim to evaluate alternative trial designs for a new intervention for systemic lupus erythematosus (SLE) from the perspective of a pharmaceutical company. The cost-effectiveness of new treatments for SLE can be evaluated in a cost-effectiveness simulation describing individual patient disease pathways and the costs and health outcomes associated with them. The CE model for SLE included using SLE registry data to describe long-term outcomes, and simulated Phase II trial outcomes to describe treatment efficacy. I developed a Bayesian Clinical Trial Simulation for a Phase III SLE trial to evaluate the value of trials with alternative design characteristics. I describe an analytic method to compare SLE Phase III RCTs with variable sample size and duration of follow-up. The BCTS was used to simulate trial datasets given a particular design specification. The trial data were combined with prior parameters of the CE model to estimate posterior densities for the CE model inputs and update the outcomes of the CE model. Initially Bayesian updating was completed using a traditional calculation using Markov Chain Monte Carlo Simulation (MCMC) in WinBUGS. However, this method would take years to generate results. An approximation method was used to speed up analysis time. I will present the outcomes of the analysis from 1,600 BCTS iterations and discuss the limitations of value of information analyses for complex diseases.
Mar 6	Thu	Moritz Groth (Nijmegen)	Topology Seminar
15:00		Grothendieck derivators (and tilting theory)
		Hicks Seminar Room J11
	Abstract: The theory of derivators (going back to Grothendieck, Heller, and others) provides an axiomatic approach to homotopy theory. It adresses the problem that the rather crude passage from model categories to homotopy categories results in a serious loss of information. In the stable context, the typical defects of triangulated categories (non-functoriality of cone construction, lack of homotopy colimits) can be seen as a reminiscent of this fact. The simple but surprisingly powerful idea behind a derivator is that instead one should form homotopy categories of various diagram categories and also keep track of the calculus of homotopy Kan extensions. In this talk I will give an introduction to derivators, indicating that stable derivators provide an enhancement of triangulated categories. If time permits, I will sketch some applications to tilting theory.
Mar 11	Tue	Jack Morrice (Sheffield)
16:00		Dark Matter as a Bose-Einstein Condensate
		TBA
Mar 12	Wed	Andy White (Heriot-Watt)	Applied Mathematics Colloquium
14:00		Disease-mediated replacement of native species: UK red/grey squirrels as a case study
		LT9
	Abstract: Since its introduction into the UK, c1900, the grey squirrel has replaced the native red squirrel throughout most of England and Wales, and in parts of Scotland and Ireland. There is strong evidence that grey squirrels are superior competitors in many habitats and also that a shared virus, squirrelpox, plays a critical role in red squirrel decline. ODE and PDE frameworks, parameterised to represent the red/grey/squirrelpox system, will be examined to understand the impact of squirrelpox on red and grey squirrel population dynamics and the spread of squirrelpox following grey invasion. Squirrelpox is endemic in grey populations in England and Wales but has only recently been reported in Southern Scotland. A spatial, individual based version of the model will be outlined and used to assess the spread of squirrelpox through squirrel populations in Southern Scotland. These findings are being used to inform current red squirrel conservation policy.
Mar 12	Wed	Brent Everitt (York)	Pure Maths Colloquium
16:00		Khovanov homology, higher limits and homotopy theory
		Hicks Seminar Room J11
	Abstract: The Khovanov homology of a knot categorifies the Jones polynomial and does a whole bunch of things the Jones polynomial can’t. So it’s a sexy thing. In this talk we will remember how Khovanov works and then reinterpret it via sheaf theory. This then allows us to bring in ideas from (stable) homotopy theory. This is joint work with Paul Turner (Geneva).
Mar 13	Thu	Jeremy Oakley (Sheffield)	Statistics Seminar
14:00		Bayesian calibration for computer models using likelihood emulation
		Hicks Seminar Room J11
	Abstract: I will start by giving a short overview of the field of "Uncertainty Quantification": a variety of problems related to uncertainty in mathematical models of physical systems. I will then present some recent work (in collaboration with Ben Youngman) on calibration: finding model inputs such that the model outputs fit physical observations. Our approach is motivated by a case study involving a natural history model for colorectal cancer patients. The model is stochastic and computationally expensive, which inhibits evaluation of the likelihood function. We use a history matching approach, where we first exclude regions of input space where we can easily identify poor fits. We then construct an "emulator" (a fast statistical approximation) of the likelihood, which is used within importance sampling to sample from the posterior distribution of the computer model inputs.
Mar 13	Thu	Ieke Moerdijk (Sheffield/Nijmegen)	Topology Seminar
15:00		The homotopy colimit functor as a Quillen equivalence
		Hicks Seminar Room J11
	Abstract: Let $A$ be a small category. I will present an elementary proof of the fact that the homotopy colimit functor from $A$-diagrams of spaces to spaces over the nerve of $A$ provides a left Quillen equivalence between appropriate model category structures (joint work with Gijs Heuts).
Mar 17	Mon	Madeleine Jotz Lean (Sheffield)
15:30		Dorfman connections and Courant algebroids
		Hicks Seminar Room J11
	Abstract: I will explain how linear connections are useful for the study of tangent spaces of vector bundles. I will then define Dorfman connections and explain how they arise naturally in the study of Courant algebroids, before explaining how a certain class of Dorfman connections can be used to describe the standard Courant algebroid over a vector bundle. (The standard Courant algebroid over a manifold is the direct sum of its tangent bundle with its cotangent bundle, equipped with a bracket extending the Lie bracket of vector fields on the tangent side.) This talk should be particularly accessible to postgraduate students.
Mar 18	Tue	David Loeffler (Warwick)	Number Theory seminar
00:00		Euler systems for Rankin--Selberg convolutions of modular forms
		F24
	Abstract: One special case of the Birch--Swinnerton-Dyer conjecture is the statement that if E is an elliptic curve over a number field, and the L-function of E does not vanish at s = 1, then E has only finitely many rational points and its Tate-Shafarevich group is finite. This is known to be true for elliptic curves over Q by a theorem of Kolyvagin. Kolyvagin's proof relies on an object called an 'Euler system' -- a system of elements of Galois cohomology groups -- in order to control the Tate-Shafarevich group. It has long been conjectured that Euler systems should exist in other contexts, and these should have similarly rich arithmetical applications; but only a very small number of examples have so far been found. In this talk I'll describe the construction of a new Euler system attached to pairs of elliptic curves -- or more generally pairs of modular forms -- and some of its arithmetical applications. This is joint work with Antonio Lei and Sarah Zerbes.
Mar 19	Wed	Lectureship candidates presentations- no pure colloquium	Pure Maths Colloquium
00:00
		Hicks Seminar Room J11
Mar 20	Thu	Marina Knight (York)	Statistics Seminar
14:00
		Hicks Seminar Room J11
Mar 24	Mon	Cesare Tronci (Surrey)
15:30		The geometry of collisionless kinetic theories
		Hicks Seminar Room J11
	Abstract: Kinetic theories of multiparticle systems are dynamical continuum models governing the evolution of a probability density function on phase space. These theories are well known to possess a Lie-Poisson structure on the Poisson algebra of Hamiltonian functions. Recently, the statistical method of moments has been shown to possesses momentum map features conferring moments the same Lie algebra structure as the symbols of differential operators. The geometry underlying these structures involves coadjoint orbits on the group of strict contactomorphisms (aka quantomorphisms) of the prequantization bundle. This talk reviews recent progress on these topics and shows how certain moment closures produce integrable systems such as the Camassa-Holm equation on the diffeomorphism group and Bloch-Iserles system on the Jacobi group.
Mar 25	Tue	Andrew Jones (Sheffield)	Number Theory seminar
14:00		Modular Forms over Number Fields
		F24
	Abstract: The Eichler-Shimura theorem from the classical theory of modular forms allows one to realise elliptic modular forms as classes in the cohomology of modular curves. The notions of cusp forms and Hecke operators transfer readily to this new setting, and so one can use new tools to compute the usual arithmetic data attached to cuspidal eigenforms (such as the method of modular symbols). The theorem generalizes to other examples. In particular, if we replace the group SL(2) of the classical setting with the reductive algebraic group G = Res(F/Q)(GL(2)), where F is an arbitrary number field and Res(F/Q) denotes the Weil restriction of scalars, then cuspidal automorphic forms associated to arithmetic subgroups of G can be identified in the cohomology of locally symmetric spaces for G. In this talk I will discuss a generalization of the modular symbols method (developed by Paul Gunnells and Dan Yasaki) which uses a reduction theory of Voronoi and Koecher for positive definite binary Hermitian forms over number fields to provide a finite model for the cohomology of such spaces, thus allowing one to compute Hecke eigenvalues of cuspidal forms. Combined with a recent result by C.P. Mok, which allows one to associate Galois representations to such forms over CM fields, it is possible to exhibit examples of modular elliptic curves over quartic CM fields.
Mar 26	Wed	Raf Bocklandt (Amsterdam)	GLEN Algebraic Geometry Seminar
12:00		Pants Decompositions and Stability conditions
		F20
Mar 26	Wed	Jon Pridham (Edinburgh)	GLEN Algebraic Geometry Seminar
13:45		Motives and Tannaka duality for dg categories
		F20
Mar 26	Wed	Shigeo Kida (Doshisha)	Applied Mathematics Colloquium
14:00		A new instability to Steady Flow in a Precessing Sphere
		LT9
	Abstract: We consider the flow structure and its stability in a rapidly rotating sphere with weak precession. This work is motivated by a recent laboratory experiment by Goto et al. (2011). They observed that the flow is unstable for $Po > O(Re−\alpha)$ with $\alpha = 0.8 \sim 0.9$ at large $Re$ (Reynolds number) and small $Po$ (Poincare number). However, this value of $\alpha$ is a bit surprising because it is long known (Greenspan 1968) that the decay rates of eigenmodes in a precessing sphere are proportional to $Re^{−0.5}$ and the precession, whose effects on the flow are proportional to $Po$, may destabilize the flow for $Po > O(Re^{−0.5})$. In fact we have shown by a linear stability analysis (Kida 2013) that the steady flow in a precessing sphere is unstable for $Po > 7.9\, Re^{−0.5}$ for the global disturbances (oscillating over the whole sphere) at $Re>>1$ and $Po<<1$. Since these unstable modes do not explain the experimental observation, we searched another mode and found that a local disturbance which is limited in the critical regions gives the stability curve $Po = 21.25\,Re^{−0.8}$. This curve agrees excellently with the above-mentioned laboratory experiment. Furthermore, it would be interesting to note that the stability curve for global disturbances coincides with that in a slightly oblate spheroid (Goto et al. 2011).
Mar 26	Wed	Balazs Szendroi (Oxford)	GLEN Algebraic Geometry Seminar
15:00		Quantum cluster positivity and cohomological Donaldson-Thomas theory
		F24
Mar 26	Wed	Ian Strachan (Glasgow)	Pure Maths Colloquium
16:00		Rational, Trigonometric and Elliptic Solutions to the WDVV equations
		Hicks Seminar Room J11
	Abstract: The Witten-Dijkgraaf-Verlinde-Verlinde equations first appear in the early '90s in two distinct settings: Topological Quantum Field Theory (where Gromov-Witten invariants are encoded with the structure of a field theory) and Seiberg-Witten theory (a low-energy effective field theory). Links with other areas of mathematics developed rapidly - for example, with singularity theory and integrable systems. The talk will review the three most elementary classes of solutions: rational, trigonometric and elliptic solutions, and discuss ideas of almost-duality and modular Frobenius manifolds.
Mar 27	Thu	Neil Strickland (Sheffield)	Topology Seminar
15:00		A large diagram in unstable homotopy theory
		Hicks Seminar Room J11
	Abstract: I will discuss a diagram involving an odd-primary analogue of the EHP sequence, the double suspension map and so on. Almost all ingredients appear in various places in the literature, but they are not combined into a single diagram. Moreover, many of the spaces and maps are constructed in a way that involves extensive choices. There are many issues about compatibility of choices that do not seem to be very clear. This talk will aim to explain some background and to describe a family of interesting problems; there will not be many actual results.
Mar 31	Mon	Elizabeth Mansfield (Kent)
15:30		Moving frames and the calculus of variations
		Hicks Seminar Room J11
	Abstract: The modern group-based definition of a moving frame allows for a symbolic invariant calculus that applies equally to discrete and smooth systems. In this talk I will present an introduction to these ideas and give an application to variational problems with a Lie group symmetry. Noether's Theorem guarantees such systems have conservation laws - typically conservation of energy and linear and angular momentum. I will show how the use of a moving frame adds information about the structure of the set of extremals and the conservation laws, in some cases yielding a complete solution.
Apr 2	Wed	Agata Smoktunowicz (Edinburgh)	Pure Maths Colloquium
16:00		Open questions in noncommutative ring theory
		Hicks Seminar Room J11
	Abstract: We will review some longstanding open questions from noncommutative algebra, namely: * Is a finitely generated algebraic algebra which is a domain finite dimensional? (The Kurosh conjecture on domains) * Does a finitely generated ring which is infinite and which is also a division ring exist? (Latyshev) * The Koethe conjecture on nil rings * The Jacobson conjecture on finitely presented algebras We will also look at the following, more recent questions: * Does a domain exist with a finite but non-integer Gelfand-Kirillov dimension? * Do finitely generated Noetherian algebras need to have polynomial growth? We will also consider some connections with other areas, such as group theory and noncommutative algebraic geometry, and look at some methods which are used in this area, for example the Golod-Shafarevich theorem, as well as some partial results which are known to be related to these questions.
Apr 3	Thu	Tom Stafford (Psychology, University of Sheffield)	Statistics Seminar
14:00		Measuring the learning curve (n= 854,064)
		Hicks Seminar Room J11
	Abstract: I will present the results of a study of learning in players of a simple online game. In contrast to the high-precision experimental tasks which are common in experimental psychology, this study leverages the statistical power gained by having a study population of 854,064 people. Use of game data allowed us to connect, for the first time, rich details of training history with measures of performance from participants engaged for a sustained amount of time in effortful practice. We showed that lawful relations exist between practice amount and subsequent performance, and between practice spacing and subsequent performance. Our methodology allowed an in situ confirmation of results long established in the experimental literature on skill acquisition. Additionally, we showed that greater initial variation in performance is linked to higher subsequent performance, a result we link to the exploration/exploitation trade-off from the computational framework of reinforcement learning. All the raw data and analysis code is available online, an example of "open science". Stafford, T. & Dewar, M. (2014). Tracing the trajectory of skill learning with a very large sample of online game players. Psychological Science, 25(2) 511-–518. http://pss.sagepub.com/content/25/2/511 Data and analysis code. https://github.com/tomstafford/axongame
Apr 3	Thu	Tobias Dyckerhoff (Oxford)	Topology Seminar
15:00		Triangulated surfaces in triangulated categories
		Hicks Seminar Room J11
	Abstract: Given a triangulated category $A$, equipped with a differential $\mathbb{Z}/2$-graded enhancement, and a triangulated oriented marked surface $S$, we explain how to define a space $X(S,A)$ which classifies systems of exact triangles in $A$ parametrized by the triangles of $S$. The space $X(S,A)$ is independent, up to essentially unique homotopy equivalence, of the choice of triangulation and is therefore acted upon by the mapping class group of the surface. We can describe the space $X(S,A)$ as a mapping space $Map(F(S),A)$, where $F(S)$ is the universal differential $\mathbb{Z}/2$-graded category of exact triangles parametrized by $S$. It turns out that $F(S)$ is a purely topological variant of the Fukaya category of $S$. Our construction of $F(S)$ can then be regarded as implementing a 2-dimensional instance of Kontsevich's proposal on localizing the Fukaya category along a singular Lagrangian spine. As we will see, these results arise as applications of a general theory of cyclic 2-Segal spaces. This talk is based on joint work with Mikhail Kapranov.
Apr 28	Mon	Elizaveta Vishnyakova (Luxembourg)
15:30		SEMINAR POSTPONED TO DATE TO BE FIXED DUE TO VISA DELAY. On $n$-ary analogue of Lie (super)algebras
		Hicks Seminar Room J11
	Abstract: A different reading of the standard Jacobi identity leads to various generalizations of the notion of Lie superalgebra for $n$-ary case. The most popular $n$-ary analogues were suggested by V.T.~Filippov, P.~Michor, A.~Vinogradov, M.~Vinogradov and others. For instance, A.~Vinogradov and M.~Vinogradov introduced a two parameter series of $n$-ary Lie superalgebras. The interesting fact here is that this series contains also commutative associative algebras. We will discuss the following: this theory in the context of quadratic $n$-ary Lie superalgebras using a "derived bracket" approach from Poisson Geometry; classification of simple $n$-ary Lie algebras and a decomposition of such algebras into elementary pieces.
Apr 30	Wed	Jonathan Pearson (Durham)	Applied Mathematics Colloquium
14:00		Constraining properties of the dark universe
		LT9
	Abstract: When recent observational evidence and the GR+FRW+CDM model are combined we obtain the result that the Universe is accelerating, where the acceleration is due to some not-yet-understood "dark sector". There has been a considerable number of theoretical models constructed in an attempt to provide an "understanding" of the dark sector: dark energy and modified gravity theories. The proliferation of modified gravity and dark energy models has brought to light the need to construct a "generic" way to parameterize the dark sector. I will discuss our way of approaching this problem: constructing equations of state for perturbations. Our approach is inspired by that taken in particle physics, where the most general modifications to the standard model are written down for a given field content that is compatible with some assumed symmetries. Our emphasis is on constructing a theoretically motivated toolkit which can be used to meaningfully transcribe from experimentally obtained observations into well defined statements about the allowed properties of the dark sector. It is key to use meaningful models of the perturbed universe when analysing data sets which are sensitive to the clustering of the dark sector. I will present our observational constraints (using e.g., Planck CMB temperature and lensing, CFHTLenS data) on the parameters in the equations of state for perturbations. If I get time, I shall briefly discuss “material models of dark energy”, where the theory of relativistic solids can be used to formulate a dark energy theory which can naturally be compared to data.
Apr 30	Wed	Jeffrey Giansiracusa (Swansea)	Topology Seminar
16:00		$G$-equivariant open-closed TCFTs
		Hicks Seminar Room J11
	Abstract: Open 2d TCFTs correspond to cyclic $A_\infty$ algebras, and Costello showed that any open theory has a universal extension to an open-closed theory in which the closed state space (the value of the functor on a circle) is the Hochschild homology of the open algebra. We will give a $G$-equivariant generalization of this theorem, meaning that the surfaces are now equipped with principal $G$-bundles. Equivariant Hochschild homology and a new ribbon graph decomposition of the moduli space of surfaces with $G$-bundles are the principal ingredients. This is joint work with Ramses Fernandez-Valencia.
May 1	Thu	Mark Meckes (Case Western)	Pure Maths Colloquium
15:00		The magnitude of metric spaces
		Hicks Seminar Room J11
	Abstract: How big is a geometric object? Of course, this question is ill-posed, with many possible answers. In this talk I'll discuss a notion of size, named "magnitude", introduced by Tom Leinster and Simon Willerton. As we'll see, magnitude, which was inspired by category theory, turns out to be related to a surprising array of fields, including integral geometry, potential theory, and even theoretical ecology.
May 6	Tue	Jennifer Balakrishnan (Oxford)	Number Theory seminar
00:00		p-adic heights and integral points on hyperelliptic curves
		TBC
	Abstract: We discuss explicit computations of p-adic line integrals (Coleman integrals) on hyperelliptic curves and some applications. In particular, we relate a formula for the component at p of the p-adic height pairing to a sum of iterated Coleman integrals. We use this to give a Chabauty-like method for computing p-adic approximations to integral points on such curves when the Mordell-Weil rank of the Jacobian equals the genus. This is joint work with Amnon Besser and Steffen Müller.
May 8	Thu	Chris Jackson (MRC Cambridge)	Statistics Seminar
14:00		Comparing structures of state-transition models for disease progression
		Hicks Seminar Room J11
	Abstract: Stochastic processes representing transitions between discrete states are often used to represent disease progression. Markov models are typical, and they may evolve in either discrete or continuous time. I will discuss the choice between models with different state-transition structures. The models will have some features in common, so that they can be used for the same purpose, such as estimating expected survival. For example, two adjacent states of disease severity could either be merged or separated, and we want to know which gives better estimates of survival. However, if the models are estimated from data at different levels of aggregation, standard likelihood-based model comparison methods do not apply since the likelihoods are on different scales. In one common situation, the transition probabilites or rates are estimated from a single longitudinal dataset consisting of observations of the states of a number of individuals over time. In this case, a modification of AIC or cross-validation can be used to compare the predictive ability of different models assessed on the data which they have in common. In the models used in health economic evaluations, however, the transition probabilities can typically only be estimated from data aggregated over individuals, or indirect data. In this case, models with split and merged states can often be compared by defining constraints on the parameters in the larger model. This produces a proxy for the merged model that can be compared against the larger one using standard methods. I will give examples from estimating the progression of health-related quality of life in psoriatic arthritis, and a health economic model for diagnostic tests for coronary artery disease.
May 12	Mon	John Rawnsley (Warwick)
15:30		Constructing central extensions of the real symplectic group
		Hicks Seminar Room J11
	Abstract: Let $(V,\Omega)$ be a finite dimensional real symplectic vector space. Its real symplectic group $Sp(V,\Omega)$ is the group of linear transformations of $V$ which preserve $\Omega$. The maximal compact subgroup of $Sp(V,\Omega)$ is isomorphic to a unitary group which can be constructed by taking a positive compatible complex structure $J$ on $V$. This means $J \in Sp(V,\Omega)$, $J^2 = -1$ and $\Omega(v,Jv) > 0$ for all $v\ne0$ in $V$ and the unitary subgroup is the centraliser of $J$. It follows that the fundamental group of $Sp(V,\Omega)$ is the integers. We are interested in two connected covering groups, the universal cover and the double cover. The latter, the metaplectic group, is the analogue of the spin group of a symmetric bilinear form. Unlike the spin case neither of these larger groups is linear making them awkward to work with. Similarly the automorphism group of the canonical commutation relations is a central extension of the symplectic group by a circle, the symplectic analogue of $Spin^c$, and is used in geometric quantisation to construct half-forms. We show how the above choice of a positive compatible $J$ gives a means to construct all these groups as well as a compatible construction of the Lagrangian Grassmannian useful in calculations with Maslov indices.
May 14	Wed	Chris Fewster (York)	Applied Mathematics Colloquium
14:00		Quantum Energy Inequalities
		LT9
	Abstract: Classical physics typically assumes that energy density is everywhere non-negative, as measured by any observer. This is responsible for the tendency of matter tends to collapse under its own gravity, which is the underlying physics of the famous singularity theorems of general relativity due to Hawking and Penrose. However, as I will describe, quantum theory is incompatible with the demand for everywhere-non-negative energy densities and even allows arbitrarily negative energy densities. Instead, classical positivity is replaced by Quantum Energy Inequalities (QEIs) which are lower bounds on local averages of the energy density. I will describe the status of QEIs and some of their consequences, including applications to the Casimir effect, and constraints on `designer spacetimes' containing wormholes or other exotic objects. I also describe related results in other parts of quantum theory, including the `backflow' phenomenon, in which state with momentum in one direction manges to reverse for a short while. The talk will also touch on (but not assume prior knowledge of) some of the mathematical tools used to investigate these ideas, which include microlocal analysis and sharp Gaarding inequalities.
May 15	Thu	Student seminar - Sujunya and Joe (Sheffield)	Statistics Seminar
14:00		Joe: Reconstructing the timescale of an ice-core Sujunya: Bayesian Semi-supervised Classification for Satellite Imagery
		Hicks Seminar Room J11
	Abstract: Joe's abstract: The concentrations of various chemicals, particles and gases in ice-cores hold a continuous record of climatic and environmental information dating back hundreds of thousands of years. These data are recorded as a depth series and in order to meaningfully interpret them we must first learn about their underlying, unobserved timescale. We present a fully Bayesian bivariate approach to obtaining a marginal posterior distribution for the time of year, as well as the date, at any given depth. Sujunya's abstract: The aim of our research is to develop a Bayesian classification model for combining the two data sources of multispectral satellite images and field survey data. It is motivated by a practical problem of remote sensing studies when we have a very small labelled sample from a ground survey and a substantial number of unlabelled-class pixels from satellite images. This problem can be solved according to a semi-supervised framework. We construct a semi-supervised model with mixture distributions as an incomplete-data problem, of which the unlabelled data are unknown classes. Then, we produce the Bayesian semi-supervised procedure by using two-step Gibbs sampling. To evaluate the proposed model, the experimental results of the real satellite images and the simulated data had been compared with the existing techniques, the ML supervised decision rule and the semi-supervised classification based on the EM algorithm. The numerical investigation has shown the benefits and the limitations of using the unlabelled data. In conclusion, I will discuss the strength and the weakness of semi-supervised techniques.
May 15	Thu	Frank Neumann (Leicester)	Topology Seminar
15:00		Étale homotopy theory of algebraic stacks
		Hicks Seminar Room J11
	Abstract: I will give an overview on étale homotopy theory à la Artin-Mazur of Deligne-Mumford stacks and discuss several examples including moduli stacks of algebraic curves and principally polarised abelian varieties and their compactifications. If time permits I will indicate how to extend the machinery to Artin stacks and how to apply it to the moduli stack of principal bundles over a curve.
May 19	Mon	Brent Pym (Oxford)
14:00		Categorified isomonodromic deformations via Lie groupoids ***This talk is only one hour in length.***
		Hicks Seminar Room J11
	Abstract: Given a meromorphic connection on a Riemann surface, one can seek deformations of the connection in which the locations of the poles are varied but the monodromy and Stokes data are held fixed. It is well known that this "isomonodromy" condition actually characterizes the deformation up to isomorphism, suggesting that it should be implemented by a functor. I will describe joint work in progress with Marco Gualtieri, in which we construct this functor as an instance of Morita equivalence between Lie groupoids. These Morita equivalences are themselves the solutions of an isomonodromic deformation problem, for which the initial condition is the meromorphic projective connection provided by the uniformization theorem.
May 20	Tue	Konstantinos Tsaltas (Sheffield)	Number Theory seminar
14:00		TBA
		F35
May 20	Tue	Rosona Eldred (Muenster)	Topology Seminar
15:00		Goodwillie calculus and nilpotence
		Hicks Seminar Room J11
	Abstract: The Goodwillie Taylor tower of a functor is a filtration with layers built from spectra. In particular, linear functors look roughly like (spectrum) $\wedge$ (input). Thinking of spectra as the abelianization of topological spaces, we can then ask how close this tower is to being a sort of nilpotent filtration for a functor, like the lower central series filtration of a group. I​ wi​ll give some background on the relationship between nilpotence and the Goodwillie tower and talk about my work tying in the partial-towers, ​formulated in terms of a decomposition involving adjoint functors.​
May 21	Wed	Jack Morrice (Sheffield)	Applied Mathematics Colloquium
14:00		Dark energy
		LT9
May 21	Wed	Diane Maclagan (Warwick)	Pure Maths Colloquium
16:00		Geometry of the moduli space of genus zero curves
		Hicks Seminar Room J11
	Abstract: The moduli space $\bar{M}_{0,n}$ of stable genus zero curves with n marked points is a beautiful space that has been intensively studied by algebraic geometers and topologists for over half a century. It arises from a simple geometric question ("How can we arrange n points on a sphere?"), but is the first nontrivial case of several interesting families of varieties (higher genus curves, stable maps, ...) and phenomena. Despite the long history there are still many mysteries about this variety. I will introduce this moduli space, and highlight some of the recent progress in understanding its geometry.
May 22	Thu	Enrico Scalas, Tusheng Zhang (Sussex)	Statistics Seminar
14:00		Enrico Scalas: On the compound fractional Poisson process Tusheng Zhang: Strong Convergence of Wong-Zakai Approximations of Reflected SDEs in A Multidimensional General Domain
		LT-4
	Abstract: Enrico Scalas: The compound fractional Poisson process (CFPP) is a random walk subordinated to a fractional Poisson process (FPP). The latter is a simple generalisation of the Poisson process where waiting times between events follow a Mittag–Leffler distribution. Several results on both CFPP and FPP will be presented related to applications in different fields of science. Tusheng Zhang: In this paper, we obtain the strong convergence of Wong-Zakai approximations of reflected stochastic differential equations in a general multidimensional domain giving an affirmative answer to a question posed by Evans and Stroock in their recent paper.
Jun 4	Wed	Elizaveta Vishnyakova (Luxembourg)
16:00		Quadratic symmetric $n$-ary superalgebras via a "derived bracket'' construction
		Hicks Seminar Room J11
	Abstract: An $n$-ary symmetric superalgebra is called quadratic if its multiplication is invariant with respect to a non-degenerate skew-symmetric form. Here one has to be careful with "skew-symmetric'' since we work in superspace! In superspace "skew-symmetric'' means that our form is skew-symmetric on the even part and symmetric on the odd part. Therefore, this class contains for example all Lie algebras with non-degenerate symmetric form, their $n$-ary generalizations and all commutative algebras with non-degenerate skew-symmetric form. The main observation here is that we can obtain all these algebras using a ``derived bracket'' approach from Poisson geometry. Our talk is devoted to a discussion of quadratic symmetric $n$-ary superalgebras and other applications of "derived brackets''.
Jul 2	Wed	Johan Andersson (Chalmers, Göteborg)	Applied Mathematics Colloquium
14:00		Statistical analysis and modeling of intermittent transport events in the tokamak SOL
		LT5
	Abstract: In the tokamak scrape-off layer (SOL), anomalous heat and particle transport arise as a consequence of a competition between particle and heat injection from the plasma core, perpendicular transport driven by turbulence, and plasma losses at the sheaths where the magnetic field lines intersect the vacuum vessel. Turbulent modes are ubiquitous in the SOL, and they are excited by a combination of effects, most notably the combination of unfavorable magnetic field curvature, a short pressure gradient scale $L_p=-p/\nabla p\sim 1$cm, and adiabaticity breaking through parallel dynamics effects. The resulting turbulent dynamics is characterized by the large fluctuations with a significant radial extension. In particular, both experimental measurements and non-linear simulations reveal the presence of radially propagating, coherent meso-scale modes, the so-called blobs, with amplitudes several times larger than the root-mean-square (RMS) fluctuation level. These intermittent plasma transport events manifests a patchy spatial and bursty temporal structure, pertaining to radially propagating coherent structures, and have been suggested to carry a significant fraction of the total transport. The likelihood of these intermittent events are described by probability density functions (PDFs) which significantly deviate from Gaussian predictions. In particular a major goal would be to control the edge heat flux loads, which depend on the instant amplitude of fluctuations, as opposed to the mean load, which can be calculated by quasilinear theory.
Sep 30	Tue	Ben Heredia (Granada)	Category Theory
14:00		Homotopy colimits and the Grothendieck construction
		Hicks Seminar Room J11
Oct 2	Thu	Chris Farmer (Oxford)	Statistics Seminar
14:00		Ensemble Variational Filters for Sequential Inverse Problems
		LT7
	Abstract: Given a model dynamical system, a model of any measuring instrument relating states to measurements, and a prior assessment of uncertainty, the probability density of subsequent system states, conditioned upon the history of the measurements, is of some practical interest. When measurements are made at discrete times, it is known that the evolving probability density is a solution of the discrete Bayesian filtering equations. This talk describes the difficulties in approximating the evolving probability density using a Gaussian mixture (i.e. a sum of Gaussian densities). In general this leads to a sequence of optimisation problems and high-dimensional integrals. Attention is given to the necessity of using a small number of densities in the mixture, the requirement to maintain sparsity of any matrices and the need to compute first and second derivatives of the misfit between predictions and measurements. Adjoint methods, Taylor expansions, Gaussian random fields and Newton's method can be combined to, possibly, provide a solution.
Oct 2	Thu	Tom Bridgeland (Sheffield)	Algebra / Algebraic Geometry seminar
15:00		Hall Algebras I
		Hicks Seminar Room J11
Oct 7	Tue	Evgeny Shinder (Sheffield)	Number Theory seminar
13:00		Mahler measure and modular forms.
		F38
	Abstract: I will talk about Mahler measure of polynomials and how the values of the Mahler measure is relate to L-values of modular forms.
Oct 7	Tue	Benjamin Heredia (Granada)	Category Theory
14:00		The Grothendieck construction and homotopy colimits
		Hicks Seminar Room J11
Oct 8	Wed	Haluk Sengun (Sheffield)	Pure Maths Colloquium
16:00		Asymptotics of Torsion Homology of Hyperbolic 3-Manifolds
		Hicks Seminar Room J11
	Abstract: Hyperbolic 3-manifolds have been studied intensely by topologists since the mid-1970's. When the fundamental group arises from a certain number theoretic construction (in this case, the manifold is called "arithmetic"), the manifold acquires extra features that lead to important connections with number theory. Accordingly, arithmetic hyperbolic 3-manifolds have been studied by number theorists (perhaps not as intensely as the topologists) with different motivations. Very recently, number theorists have started to study the torsion in the homology of arithmetic hyperbolic 3-manifolds. The aim of the first half of this introductory talk, where we will touch upon notions like "arithmeticity", "Hecke operators", will be to illustrate the importance of torsion from the perspective of number theory. In the second half, I will present new joint work with N.Bergeron and A.Venkatesh which relates the topological complexity of homology cycles to the asymptotic growth of torsion in the homology. I will especially focus on the interesting use of the celebrated "Cheeger-Mueller Theorem" from global analysis.
Oct 9	Thu	Peter Young (Lancaster)	Statistics Seminar
14:00		Refined Instrumental Variable Estimation: Maximum Likelihood Optimization of a Unified Box-Jenkins Model
		LT7
	Abstract: For many years, various methods for the identification and estimation of parameters in linear, discrete-time transfer function models have been available and implemented in widely available software environments, such as Matlab. This seminar considers a unified Refined Instrumental Variable (RIV) approach to the estimation of discrete and continuous-time transfer functions characterized by a unified operator that can be interpreted in terms of backward shift, derivative or delta operators. The paper shows that the resulting iterative RIV algorithm provides a reliable solution to the maximum likelihood optimization equations for an appropriately unified Box-Jenkins transfer function model and so its en bloc or recursive parameter estimates are optimal in maximum likelihood, prediction error minimization and instrumental variable terms. The backward shift and derivative operator versions of the algorithm are available as the RIVBJ and RIVCBJ routines in the freely available CAPTAIN Toolbox for Matlab and these have been used for Data-Based Mechanistic (DBM) modelling (see e.g Young, 2011) in areas ranging from engineering though economics and ecology to the environment. The seminar will describe a recent application where the RIVCBJ routine is used to identify and estimate a differential equation model of the latest globally averaged climate data. P. C. Young (2011). Recursive Estimation and Time-Series Analysis: An Introduction for the Student and Practitioner, Springer-Verlag, Berlin.
Oct 9	Thu	Jenny Freeman (Leeds / RSS Vice President)	RSS Seminar
16:15		Statistical Literacy: What do I need to know
		Hicks LT6
	Abstract: The ability to understand data and evidence is becoming increasingly important in today’s data-driven world. Jenny will discuss the elements of statistical literacy and what are the key questions to ask when presented with data and evidence.
Oct 13	Mon	Kirill Mackenzie (Sheffield)
15:00		Principal bundles and connections therein
		Hicks Seminar Room J11
	Abstract: This is the first of two or three talks in which I will give an introductory overview of principal bundles and their connection theory. The talks are designed for postgraduates but of course all interested are welcome. Note the time is now **3**pm, not 2pm.
Oct 14	Tue	Lloyd Kilford	Number Theory seminar
13:00		A Gentle Introduction to Overconvergent Modular Forms
		F38
	Abstract: In this talk we will give a general and gentle introduction to the subject of overconvergent modular forms, using explicit examples to motivate the theory and showcase some recent results.
Oct 14	Tue	Lukas Buhne (Hamburg)	Category Theory
14:00		Enriched monadicity
		Hicks Seminar Room J11
Oct 15	Wed	Vasilis Archontis (St. Andrews)	Applied Mathematics Colloquium
14:00		Magnetic flux emergence as a driver of solar dynamic events: jets, eruptions and flares
		LT B
	Abstract: We present a series of 3D MHD numerical simulations on magnetic flux emergence in the Sun. We focus on the onset of jets, eruptions and flares on various scales, after the emergence of magnetic flux from the solar interior into the highly stratified atmosphere of the Sun.
Oct 15	Wed	Paolo Cascini (Imperial)	Pure Maths Colloquium
16:00		On the Minimal Model Program
		Hicks Seminar Room J11
	Abstract: The aim of the Minimal Model Program is to generalize the classification of complex projective surfaces, known in the early 20th century, to higher dimensional varieties. Besides providing a historical introduction, we will discuss some recent results and new aspects of this Program.
Oct 16	Thu	Konstantin Shramov (Steklov Institute of Mathematics)	Algebra / Algebraic Geometry seminar
15:00		Automorphisms of Fano threefolds.
		Hicks Seminar Room J11
	Abstract: I will survey the results on automorphisms of Fano threefolds. In particular, I will speak about finiteness of automorphism groups (valid with a couple of explicitly described exceptions) and about the structure of Hilbert schemes of lines and conics that allows one to control the latter groups. Finally, I will describe some consequences for groups of birational automorphisms of rationally connected threefolds.
Oct 16	Thu	John Greenlees (Sheffield)	Topology Seminar
16:00		The localization theorem and algebraic models of rational equivariant cohomology theories
		Hicks Seminar Room J11
Oct 21	Tue	Chris Williams (Warwick)	Number Theory seminar
13:00		Overconvergent Bianchi modular symbols and p-adic L-functions
		F38
	Abstract: The theory of overconvergent modular symbols, developed by Rob Pollack and Glenn Stevens, gives a beautiful and effective construction of the p-adic L-function of a modular form. They define a 'specialisation map' from the space of overconvergent modular symbols to the space of classical symbols, and the crux of their theory is a 'control theorem' that says that this map is an isomorphism on the small slope subspace. This gives an analogue of Coleman's small slope theorem in the modular symbol setting. In this talk, I will describe their results, and then discuss an analogue of the theory for the case of modular forms over imaginary quadratic fields, for which similar results exist.
Oct 22	Wed	Takeshi Akinaga (Aston)	Applied Mathematics Colloquium
14:00		Sequential bifurcation approach for the transition of flow in the Taylor-Couette system
		LT B
	Abstract: We have studied transitions of flows to turbulence by sequential bifurcation approach, whereas multilateral researches are required in order to comprehend the structure of turbulence. Recently we utilised the approach to the Taylor-Couette system with two simplifications: narrow gap limit and co-rotation, as an extensional work of Weisshaar et al.[1]. The results will be shared and be compared with experimental results obtained by Hegseth et al.[2] in a consistent manner, as a connection between numerical and experimental studies. References: [1] E Weisshaar, FH Busse & M Nagata: Twist vortices and their instabilities in the Taylor-Couette system. J. Fluid Mech. 226 (1991), 549-564. [2] JJ Hegseth, GW Baxter & CD Andereck: Bifurcations from Taylor vortices between corotating concentric cylinders. Phys. Rev. E 53 (1996), 507-521. # This work is a collaboration between Dr Takeshi Akinaga, Dr Sotos Generalis (Aston) and Prof. Friedrich Busse (Bayreuth). ## FB is a Leverhulme Trust Visiting Professor and TA is a Marie Curie International Incoming Fellow.
Oct 22	Wed	Alexander Veselov (Loughborough)	Pure Maths Colloquium
16:00		From hyperplane arrangements to Deligne-Mumford moduli spaces: Kohno-Drinfeld way
		Hicks Seminar Room J11
	Abstract: Gaudin subalgebras are abelian Lie subalgebras of maximal dimension spanned by generators of the Kohno-Drinfeld Lie algebra $t_n$, associated to A-type hyperplane arrangement. It turns out that Gaudin subalgebras form a smooth algebraic variety isomorphic to the Deligne-Mumford moduli space $\bar M_{0,n+1}$ of stable genus zero curves with n+1 marked points. A real version of this result allows to describe the moduli space of the separation coordinates on the unit sphere in terms of the geometry of Stasheff polytope. A generalisation to Coxeter arrangements will also be discussed. The talk is based on joint work with L. Aguirre and G. Felder and with K. Schoebel.
Oct 23	Thu	Claudie Beaulieu (National Oceanography Centre Southampton)	Statistics Seminar
14:00		Detecting abrupt changes in the Earth’s climate system
		LTD
	Abstract: The Earth’s climate system and ecosystems exhibit abrupt changes and thresholds, which are especially challenging socio-economically due to the rapidity at which society has to adapt. Change-point detection techniques provide a valuable tool for the detection of abrupt changes in the climate and ecosystems. In this talk, the usefulness of change-point detection will be demonstrated through a range of applications. The possibility to anticipate abrupt changes will also be discussed.
Oct 23	Thu	Tom Bridgeland (Sheffield)	Algebra / Algebraic Geometry seminar
15:00		Hall Algebras, II
		Hicks Seminar Room J11
Oct 23	Thu	Magda Kedziorek (Sheffield)	Topology Seminar
16:00		tbc
		Hicks Seminar Room J11
Oct 28	Tue	Ayberk Zeytin (Istanbul)	Number Theory seminar
15:00		Class number problems and Lang conjectures
		F20
	Abstract: In this talk we are going to reinterpret class number problems of Gauss via Lang conjectures relating hyperbolicity and arithmetic of an algebraic variety. The connection in between is provided by a concept called "cark", an infinite ribbon graph (or a dessin of Grothendieck) of particular type. This work is supported by TUBITAK Career Grant 113R017.
Oct 29	Wed	Robert Poole (Liverpool)	Applied Mathematics Colloquium
14:00		Hibernating Turbulence
		LT B
	Abstract: The asymptotic upper limit of turbulent drag reduction with polymer additives – often termed Virk’s Maximum Drag Reduction (MDR) asymptote [1] – is a well-known phenomenon in the turbulent flow of complex fluids. One of the most intriguing features of MDR is its universality. Recent direct numerical simulations [2, 3] have identified time intervals showing key features of MDR. These intervals have been termed ‘hibernating turbulence.’ They are a weak turbulence state which is characterised by low wall-shear stress and extremely weak vortical flow structures. Here we report the results of an experimental investigation which appears to confirm that the streamwise velocity of a turbulent channel flow collapses to an MDR-like asymptote, even in the absence of a polymer additive, during intervals of hibernating turbulence. Our experiments are conducted in a fully developed turbulent channel flow of a Newtonian fluid at Reynolds numbers of Re_τ = u_τ h / ν = 70, 85, 100 and 120 where uτ is the friction velocity, h is channel half-height and ν is the kinematic viscosity. We measure the instantaneous wall-shear stress with a flush-mounted hot-film probe, which we use as an indicator for hibernating turbulence, whilst simultaneously sampling the streamwise velocity component with Laser Doppler Velocimetry. We also use stereoscopic Particle Image Velocimetry to probe the dynamics of individual hibernation events. [1] P.S. Virk, AIChE J. 21, 625 (1975) [2] L. Xi & M.D. Graham, PRL 108, 028310 (2012) [3] L. Xi & M.D. Graham, J. Fluid Mech., 693, 433-472 (2012)
Oct 29	Wed	Michael Wemyss (Edinburgh)	Pure Maths Colloquium
16:00		Noncommutative Approaches in Algebraic Geometry
		Hicks Seminar Room J11
	Abstract: I will discuss some recent work that associates and uses noncommutative structures to improve our understanding of algebraic geometry, specifically aspects of the three dimensional minimal model program. The majority of the talk will explain the motivating geometric problems, with lots of pictures, and I will try to motivate and explain why the new noncommutative structures are strictly necessary and should be expected. If time allows, I will discuss a homological method to jump between minimal models, and the newer applications this has to both birational geometry and derived categories.
Oct 30	Thu	Paul Johnson (Sheffield)	Algebra / Algebraic Geometry seminar
15:00		Topology of Hilbert Schemes of points in the plane
		Hicks Seminar Room J11
Oct 30	Thu	Neil Strickland (Sheffield)	Topology Seminar
16:00		An introduction to Homotopical Type Theory
		Hicks Seminar Room J11
	Abstract: I will give an introduction to Voevodsky's Homotopical Type Theory (HTT), and attempt to reconcile the following perspectives: HTT provides an intrinsic language for talking about homotopical phenomena, independent of any underlying geometric category or model category. HTT is a natural framework for thinking about computer representation of mathematical objects, propositions and proofs, where equality must usually be checked by a nontrivial computation.
Nov 3	Mon	Kirill Mackenzie (Sheffield)
15:00		Principal bundles and connections therein, 3
		Hicks Seminar Room J11
	Abstract: This is the third of three talks. I will describe the various formulations, and sketch the relationship between connections/curvature and the cohomology of Lie algebras and similar structures.
Nov 4	Tue	Sylvia Wiegand (University of Nebraska-Lincoln)	Algebra / Algebraic Geometry seminar
13:00		Prime ideals in Noetherian rings.
		LTA
Nov 4	Tue	Roger Wiegand (University of Nebraska-Lincoln)	Algebra / Algebraic Geometry seminar
14:00		Koszul modules over short graded Gorenstein rings
		LTA
Nov 5	Wed	Nick Gurski (Sheffield)	Pure Maths Colloquium
16:00		Generic automorphisms via operads
		Hicks Seminar Room J11
	Abstract: One should not expect to be able to say much about the group of automorphisms of an object without first knowing what that object is. But one can produce some automorphisms of cartesian powers of any object using merely the product structure. This is part of a general theory of monoidal categories of a certain form which are governed by special kinds of operads. Both of these structures boil down to a sequence of groups with additional prescribed maps between them, and families like the symmetric groups or braid groups are examples. I will discuss the general theory, some well-known and less-well-known examples, and then try to explain how this sheds light on invertible objects in these monoidal categories. Some of the work in this talk was done in conjunction with Alex Corner, and some of it is still in progress with Ed Prior.
Nov 6	Thu	Ziyu Zhang (Bath)	Algebra / Algebraic Geometry seminar
15:00		Holomorphic symplectic manifolds among moduli spaces of complexes on K3 surfaces (2:30 - 3:00: Pretalk in J11).
		Hicks Seminar Room J11
Nov 6	Thu	Dimitar Kodjabachev (Sheffield)	Topology Seminar
16:00		A strictly commutative model for E-infinity quasi-categories
		Hicks Seminar Room J11
	Abstract: I will show that E-infinity quasi-categories can be rigidified to strictly commutative objects in the larger category of diagrams of simplicial sets indexed by finite sets and injections. This complements earlier work on diagram spaces by Steffen Sagave and Christian Schlichtkrull.
Nov 10	Mon	Kirill Mackenzie (Sheffield)
15:00		Principal bundles and connections therein, IV.
		Hicks Seminar Room J11
	Abstract: Kirill will give the fourth of three lectures on principal bundles and connections therein. This will cover Chevalley-Eilenberg cohomology of Lie algebras, its resemblance to de Rham cohomology, and a unification which gives the standard identities for connections and curvature. These lectures are designed primarily for postgraduates, but all interested are welcome. (Note that the time is 3pm, not 2pm.)
Nov 13	Thu	Joao Domingos Scalon (Department of Exact Sciences – Federal University of Lavras – Brazil)	Statistics Seminar
14:00		Gibbs Point Processes for modelling spatial distribution of second-phase particles in composite materials
		LTD
	Abstract: Silicon carbide reinforced aluminium alloy composites are the typical candidates for engineering applications due to their enhanced mechanical properties over the corresponding aluminium alloys such as high strength and fatigue resistance. However, these mechanical properties can be highly sensitive to local variations in spatial distribution of reinforcement particles and, consequently, the analysis of such distribution is of prime importance in materials science. The aim of this seminar is to present Gibbs point processes as an intuitively appealing way for characterizing spatial patterns formed by the locations of second-phase particles in composite materials.
Nov 17	Mon	Madeleine Jotz Lean (Sheffield)
15:00		Degree 2 N-manifolds and metric double vector bundles, I
		F 38 --- nonstandard venue !!
	Abstract: This is the first of two or three lectures. In the first lecture, I plan to talk only about vector bundles and their equivalence to sheaves of locally finitely generated C^\infty(M)-modules.
Nov 18	Tue	Samuele Anni (Warwick)	Number Theory seminar
13:00		Residual Galois representations: a database
		F38
	Abstract: Let l be a prime number. To any mod l modular form, which is an eigenform for all Hecke operators, it is associated a 2-dimensional residual representation of the absolute Galois group of the rationals. Two different mod l modular forms can give rise to the same Galois representation: I will briefly address this problem, describing the "old subspace" in positive characteristic. Analogously, a residual modular Galois representation can arise as twist of a representation of lower conductor. In this talk, after a brief introduction on residual modular Galois representations and mod l modular forms, I will address these issues and outline an algorithm for computing the image of such representations.
Nov 19	Wed	Jonathan Potts (Sheffield)	Applied Mathematics Colloquium
14:00		The scale of animal movement decisions and consequences for continuum-limit modelling
		LT B
Nov 19	Wed	Matthew Daws (Leeds)	Pure Maths Colloquium
16:00		Fourier Algebras to Quantum Groups
		Hicks Seminar Room J11
	Abstract: This will be a gentle introduction to some elements of "non-commutative topology": in particular, using C*-algebras to study groups, or using groups to build interesting examples of C*-algebras, according to taste. I aim to introduce Gelfand duality, motivating how C*-algebras can be thought of as "non-commutative locally compact spaces". I'll then talk about locally compact groups, some functional analysis, and how to build various algebras, aiming to get to discuss the Fourier algebra. Time allowing, I hope to say a little about the theory of locally compact quantum groups.
Nov 20	Thu	Kamila Zychaluk (Liverpool)	Statistics Seminar
14:00		Semi-parametric models for coral reef dynamics
		LTD
	Abstract: There are many mathematical models for the dynamics of coral reefs. Typically, these models assume the functional relationships that are responsible for changes in the reef community but there is often little evidence on which to choose the functional relationships. Furthermore, the parameters of such models are difficult to estimate. Instead, we propose a statistical model based on many data but relatively few assumptions. We use a large database of repeated observations of the composition of coral communities to make predictions about the dynamics of reef composition. We use our model to estimate a regional dynamic equilibrium in reef composition. We have observations of the proportion of space occupied by three components (hard corals, macroalgae, and others). These observations were made in consecutive years at Caribbean, Kenyan and Great Barrier Reef sites. We assume that the state of the reef after one year follows a Dirichlet distribution with parameters dependent on the current state of the reef. These parameters are estimated using a local linear estimator with cross-validation bandwidth. These estimates are then used in a transition equation to obtain the stationary distribution of reef composition. The stationary distributions for the Caribbean and Great Barrier reef appear very different, in accordance with biological knowledge. These stationary distributions correspond to the dynamic equilibria for the two regions, if conditions remain as they are now. In addition to making predictions, our semi-parametric models provide a summary of the major features of reef dynamics, which more mechanistic models should be able to reproduce. Joint work with Matthew Spencer, Damian Clancy, John F. Bruno and Tim McClanahan
Nov 20	Thu	Paul Mitchener (Sheffield)	Topology Seminar
16:00		A menagerie of assembly maps
		Hicks Seminar Room J11
	Abstract: In geometric topology, a number of different maps are referred to as assembly maps, and various conjectures are present which assert that instances of these maps are injective. A theorem due to Weiss and Williams in the 1990s describes and characterises assembly in terms of spectra. In this talk, we look at a refinement of this machinery which lets us not just characterise assembly maps but give "universal" proofs of injectivity which apply to a number of different situations. We will conclude by talking about examples of the machinery, possibly including C*-algebra K-theory, L-theory, algebraic K-theory, and homotopy algebraic K-theory.
Nov 24	Mon	Madeleine Jotz Lean (Sheffield)
15:00		Degree 2 N-manifolds and metric double vector bundles, II
		Hicks Seminar Room J11
	Abstract: This is the second of two or three lectures. In the second lecture I plan to talk about N-manifolds, how degree 1 NQ-manifolds are Lie algebroids, how degree 2 N-manifolds are equivalent to metric DVB's.
Nov 25	Tue	Jonathan Crawford (Durham)	Number Theory seminar
13:00		A singular theta lift for higher weights
		F38
	Abstract: In this talk, we will discuss the construction and properties of a singular theta lift of harmonic weak Maass forms of weight 3/2-k (where k is a positive integer). Using this we obtain some automorphic objects of weight 2-2k, so-called "locally harmonic Maass forms", which are locally harmonic, but have singularities along certain geodesics. Via some natural differential operators we can relate the lift to the Shimura correspondence. For some kind of Poincare series, this lift was considered by Bringmann, Kane and Viazovska. My work generalizes work of Hövel for the case k=1 to higher weight.
Nov 26	Wed	Bogdan Hnat (Warwick)	Applied Mathematics Colloquium
14:00		Large scale flows in magnetically confined plasmas: Geodesic Acoustic Mode at the edge region of Mega Amp Spherical Tokamak.
		LT B
	Abstract: B. Hnat1, J. R. Robinson1, A. Kirk2, P. Tamain3, A. Thyagaraja4, K. G. McClements2, P. J. Knight2, and the MAST Team 1 Physics Department, University of Warwick, Coventry, CV4 7AL, UK. 2 EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon, OX14 3DB, UK. 3 Association Euratom/CEA, CEA Cadarache, F-13108 St. Paul-lez-Durance, France 4 University of Bristol, H.H. Wills Physics Laboratory, Bristol BS8 1TL. The development of magnetically confined fusion (MCF) plasma into a viable energy source rests on our ability to control the stability of a plasma heated to 200 million Kelvin. Hot plasmas are complex systems with dynamics driven by collective interactions of particles with the fields through a plethora of modes. Even when global-scale instabilities are eliminated, micro-instabilities drive turbulent plasma transport and this is the main obstacle in achieving self-sustained fusion reaction in a tokamak at the present time. Turbulent fluctuations can also self-organize through nonlinear processes into large-scale, linearly stable zonal flows, which act as a sink of energy for turbulence. A large body of evidence suggests that zonal flows are instrumental in achieving a high-confinement mode (H-mode): a basic operating scenario for ITER. In toroidal geometry, zonal flows couple to compressive modes, called Geodesic Acoustic Modes (GAM) and acquire a finite frequency, which allows for their identification in experimental data. We report recent observation of the GAM at the edge of the Mega Amp Spherical Tokamak (MAST). A shift in frequency with plasma rotation is found, and a rapid suppression of the mode is observed when magnetic configuration is modified. Non-linear coupling to high wave number turbulence is evident, and an increase in power of turbulence fluctuations is seen after suppression. The mode is then studied numerically using the two- fluid, global simulation CENTORI. We examine mode localisation and effects of magnetic geometry, given by aspect ratio, elongation and safety factor, on the observed frequency of the mode. An excellent agreement between simulations and experimental data is found for simulation plasma parameters matched to those of MAST.
Nov 26	Wed	Mark Pollicott (Warwick)	Pure Maths Colloquium
16:00		Counting circles in the Apollonian Circle Packing
		Hicks Seminar Room J11
	Abstract: The classical Apollonian circle packing is constructed by taking four mutually tangent circles in the unit plane and repeatly inscribing circles in the spaces between them. This results in infinitely many circles, whose radii tend to zero. There is a remarkably simple asymptotic formula due to Kontorich and Oh for the number of these circles with radii > r, as r tends to infinity. This talk will describe this and related results.
Nov 27	Thu	Duncan Lee (Glasgow)	Statistics Seminar
14:00		Cluster detection and risk estimation for spatio-temporal health data
		LTD
	Abstract: In epidemiological disease mapping one aims to estimate the spatio-temporal pattern in disease risk and identify high-risk clusters, allowing health interventions to be appropriately targeted. Bayesian spatio-temporal models are used to estimate smoothed risk surfaces, but this is contrary to the aim of identifying groups of areal units that exhibit elevated risks compared with their neighbours. Therefore, in this paper we propose a new Bayesian hierarchical modelling approach for simultaneously estimating disease risk and identifying high-risk clusters in space and time. Inference for this model is based on Markov chain Monte Carlo simulation, using the freely available R package CARBayesST that has been developed in conjunction with this paper. Our methodology is motivated by two case studies, the first of which assesses if there is a relationship between Public health Districts and colon cancer clusters in Georgia, while the second looks at the impact of the smoking ban in public places in England on cardiovascular disease clusters.
Nov 27	Thu	Rebecca Tramel (Edinburgh)	Algebra / Algebraic Geometry seminar
15:00		Bridgeland stability on surfaces with curves of negative self-intersection
		Hicks Seminar Room J11
Nov 27	Thu	Vesna Stojanoska (MPI Bonn)	Topology Seminar
16:00		Arithmetic duality for generalized cohomology theories
		Hicks Seminar Room J11
	Abstract: Poitou-Tate duality is a duality for the Galois cohomology of finite modules over the absolute Galois group of a global field. This arithmetic duality is reminiscent of Poincaré duality for manifolds familiar to topologists. In joint work with Tomer Schlank we upgrade it to a duality for generalized cohomology theories with action by such an absolute Galois group. We believe this upgraded duality should lead to a better understanding of rational points on algebraic varieties.
Nov 27	Thu	Catherine Edwards, Paul Ainsworth (Department for Work and Pensions)	RSS Seminar
16:00		Fraud and Error
		Hicks LT6
	Abstract: DWP has one of the largest budgets in Government: last year they paid nearly £170 billion in welfare benefits. But how accurate are those payments? How much fraud is in the system? How do they measure the loss because of errors? And how do they quantify and communicate uncertainty in their fraud and error estimates? Catherine Edwards from the Fraud and Error Measurement Analysis Team will explain the data collection, analysis and reporting routines of these National Statistics. Paul Ainsworth will also provide an introduction to bootstrapping - a statistical technique used to assign confidence intervals to the Department's fraud and error estimates.
Nov 28	Fri	Maxim Smirnov (ICTP)	Algebra / Algebraic Geometry seminar
13:00		Dubrovin's conjecture for IG(2,6)
		Hicks Seminar Room J11
	Abstract: For a smooth projective algebraic variety, according to a conjecture of Dubrovin, the semisimplicity of quantum cohomology is related to the existence of full exceptional collections in the derived category of coherent sheaves. I will start by giving a general introduction to quantum cohomology and, eventually, talk about a recent joint work with S. Galkin and A. Mellit on Dubrovin's conjecture for the symplectic isotropic Grassmannian IG(2,6). This appears to be the simplest case where one needs to work with the big quantum cohomology to formulate the conjecture.
Nov 28	Fri	Alessio Corti (ICL)	Algebra / Algebraic Geometry seminar
14:30		On the Fano/LG correspondence for surfaces
		Hicks Seminar Room J11
	Abstract: I will state two conjectures exploring mirror symmetry for surfaces and its implications for classification, and summarise the evidence available so far.
Nov 28	Fri	Alexander Kasprzyk (ICL)	Algebra / Algebraic Geometry seminar
16:00		Maximally-mutable Laurent polynomials
		Hicks Seminar Room J11
	Abstract: In this talk I will describe a special class of Laurent polynomials, which we call "maximally-mutable". These Laurent polynomials arise naturally in the study of Fano manifolds via mirror symmetry. In particular, I will explain why in dimension two, the rigid maximally-mutable Laurent polynomials correspond exactly, under mirror symmetry, with the 10 deformation families of smooth del Pezzo surfaces. A similar result holds in dimension 3, where the rigid maximally-mutable Laurent polynomials supported on a reflexive polytope correspond precisely with the 98 deformation families of smooth Fano 3-folds with very ample -K.
Dec 2	Tue	Srilakshmi Krishnamoorthy (Chennai)	Number Theory seminar
13:00		On sign changes for almost prime coefficients of half-integral weight modular forms
		F38
	Abstract: For a half-integral weight modular form f of weight k+1/2 on Γ_0(4) such that the Fourier coefficients a_f(n) are real, we prove that a_f(n), where n varies over almost r-primes, for some r, change signs infinitely often by using sieve theoretic methods.
Dec 3	Wed	Victor Ambrus (Sheffield)	Applied Mathematics Colloquium
14:00		Quadrature methods in lattice Boltzmann modelling
		LT B
Dec 3	Wed	Ivan Smith (Cambridge)	Pure Maths Colloquium
16:00		Homological algebra of symplectic topology
		Hicks Seminar Room J11
	Abstract: Symplectic manifolds arise naturally in dynamical systems, in Lie theory, and in algebraic geometry. Their study was revolutionised 30 years ago when Gromov and Floer introduced tools from holomorphic curve theory and partial differential equations into the subject; 20 years ago, the subject was revolutionised again by ideas of Fukaya and Kontsevich which suggested that the invariants arising from PDE should be packaged and manipulated via the algebra of A-infinity categories. This talk will give an overview of some of the current progress and problems in the theory.
Dec 4	Thu	John Moriarty (Manchester)	Statistics Seminar
14:00		A solvable two-dimensional degenerate singular stochastic control problem with non convex costs
		LTD
	Abstract: This optimisation problem is motivated by a storage-consumption model in an electricity market, and features a stochastic real-valued spot price modelled by Brownian motion. Although the possibility of negative prices makes the cost function neither convex nor concave, we show that the problem is nevertheless solvable and find analytical expressions for the value function, the optimal control and the boundaries of the action and inaction regions. Both boundaries may be interpreted as repelling, although interestingly the well known smooth fit condition holds at one boundary but not the other.
Dec 4	Thu	Martin Kalck (Edinburgh)	Algebra / Algebraic Geometry seminar
15:00		Relative singularity categories
		Hicks Seminar Room J11
	Abstract: (Relative) singularity categories are triangulated categories associated with (non-commutative resolutions of) singular varieties. I will explain these notions and their mutual relations focusing on the simplest examples - the singularities of type A_1, e.g. k[x|/x^2. For these examples, everything can be understood in a rather elementary way. In particular, familiarity with triangulated categories will NOT be necessary to follow the talk. In the end, I will mention what we know for ADE-singularities in general. This is based on joint work with Dong Yang.
Dec 4	Thu	Piotr Pstragowski (Sheffield)	Topology Seminar
16:00		On the Cobordism Hypothesis and the grammar of space
		Hicks Seminar Room J11
	Abstract: During the talk, I will explain the concept of an extended topological field theory and formulate the Cobordism Hypothesis, now a theorem of Jacob Lurie. I will give some examples of "grammar of space" phenomena, where a geometrically defined structure turns out to be universal in some strong algebraic sense.
Dec 9	Tue	Marc Masdeu (Warwick)	Number Theory seminar
13:00		Non-archimedean construction of elliptic curves and rational points
		F38
	Abstract: In this talk I will describe a non-archimedean conjectural construction of the Tate lattice of an elliptic curve E defined over an arbitrary-signature number field F. I will also provide analytic constructions of algebraic points on such curves, which generalize the so-called Stark--Heegner or Darmon points. One important feature of all these constructions is their explicitness, which allows for the numerical verification of the conjectures. This is joint work with Xavier Guitart and Mehmet H. Sengun.
Dec 9	Tue	Sarah Whitehouse (Sheffield)
17:00		Associativity from a topologist's point of view
		LT7
	Abstract: Many familiar algebraic operations, such as addition and multiplication of numbers, are associative. To a topologist, it is more natural to consider operations which are "associative up to homotopy" and I will discuss what this means. As soon as one does this, one is led to a rich structure with an infinite family of operations, known as an A-infinity structure. These structures have become important in many different areas of mathematics, including algebra, geometry and mathematical physics. One can play similar topological games with other algebraic conditions. This is a 50 year old story, with recent developments.
Dec 10	Wed	Aditi Sood (Sheffield)	Applied Mathematics Colloquium
14:00		MHD
		LT B
Dec 10	Wed	Marianne Johnson (Manchester)	Pure Maths Colloquium
16:00		Idempotent tropical matrices
		Hicks Seminar Room J11
	Abstract: This talk concerns nxn matrices with entries from a certain 'tropical' semiring (the entries will be real numbers, however the addition and multiplication operations on this set are not the usual ones). One can consider subsets of R^n which are spanned (under our new operations) by the rows (or columns) of a given tropical matrix; such row and column spaces are called tropical polytopes. An exact characterisation of those tropical polytopes which arise as the column (or row) space of a (multiplicatively) idempotent tropical matrix can be given (joint work with Kambites and Izhakian). A particularly interesting class of tropical idempotents arises from finite (semi)-metric spaces. We garner some further information about the geometric structure of the corresponding tropical polytopes in these cases.
Dec 11	Thu	Marina Knight (York)	Statistics Seminar
14:00		Hurst exponent estimation for long-memory processes using wavelet lifting.
		LTD
	Abstract: Reliable estimation of long-range dependence (LRD) parameters, such as the Hurst exponent, is a well studied problem in the statistical literature. However, when the observed time series presents missingness or is naturally irregularly sampled, the current literature is sparse, with most approaches requiring heavy modifications. In this talk I shall present a technique for estimating the Hurst exponent of an LRD time series that naturally deals with the time domain irregularity. The method is based on a flexible wavelet transform built by means of the lifting scheme, and we shall demonstrate its performance.
Dec 16	Tue	Nuno Freitas (MPIM Bonn)	Number Theory seminar
13:00		From the Generalized Fermat Equation to Hilbert modular forms with prescribed inertia types
		F24
	Abstract: In this talk I will report on ongoing work with Lassina Dembele and John Voight. After the proof of Fermat's Last Theorem the modular method to solve Diophantine equations has been generalized by several mathematicians and used to attack many other equations. As a consequence of these efforts the Generalized Fermat Equation Ax^r + By^q = Cz^p, where A,B,C are pairwise coprime integers, became the new focus of attention. In an attempt to study the particular case case x^19 + y^19 = Cz^p, among other things, we are led to compute huge spaces of (Hilbert) modular forms. To complete this task, following a suggestions of Fred Diamond, we intend to split the space of modular forms into smaller ones by prescribing the inertia types. These smaller spaces should be amenable to computations.
Dec 18	Thu	Vincent Bonhomme (Sheffield)	Statistics Seminar
14:00
		LTD
Dec 19	Fri	Jingsong He (Ningbo)	Applied Mathematics Colloquium
13:00		Rogue waves
		LT 10
Jan 20	Tue	Josep Alvarez-Montaner (Universitat Politècnica de Catalunya)	Algebra / Algebraic Geometry seminar
14:00		Lyubeznik numbers of local rings and linear strands of graded ideals
		F41
	Abstract: The aim of these talks is to review the basics on Lyubeznik numbers and to introduce a new set of invariants associated to the linear strands of a minimal free resolution of a graded ideal in the polynomial ring. It turns out that these invariants satisfy some properties analogous to those of Lyubeznik numbers of local rings. For the case of squarefree monomial ideals we have a close relation between both invariants that allows to interpret Lyubeznik numbers of Stanley-Reisner rings as the obstruction to the acyclicity of the linear strands of their associated Alexander dual ideals. Finally, we prove that Lyubeznik numbers of Stanley-Reisner rings are not only an algebraic invariant but also a topological invariant, meaning that they depend on the homeomorphic class of the geometric realization of the associated simplicial complex and the characteristic of the base field. The non-expository parts of these talks are based on joint works with K.Yanagawa and A.Vahidi respectively.
Jan 21	Wed	Josep Alvarez-Montaner	Algebra / Algebraic Geometry seminar
11:00		Lyubeznik numbers of local rings and linear strands of graded ideals
		F41
	Abstract: The aim of these talks is to review the basics on Lyubeznik numbers and to introduce a new set of invariants associated to the linear strands of a minimal free resolution of a graded ideal in the polynomial ring. It turns out that these invariants satisfy some properties analogous to those of Lyubeznik numbers of local rings. For the case of squarefree monomial ideals we have a close relation between both invariants that allows to interpret Lyubeznik numbers of Stanley-Reisner rings as the obstruction to the acyclicity of the linear strands of their associated Alexander dual ideals. Finally, we prove that Lyubeznik numbers of Stanley-Reisner rings are not only an algebraic invariant but also a topological invariant, meaning that they depend on the homeomorphic class of the geometric realization of the associated simplicial complex and the characteristic of the base field. The non-expository parts of these talks are based on joint works with K.Yanagawa and A.Vahidi respectively.
Jan 29	Thu	Bram Mesland (University of Warwick)
15:00		Noncommutative Geometry and Dynamics
		Hicks Seminar Room J11
	Abstract: In this talk I will discuss concepts and examples from the field of noncommutative geometry.Ideas from Riemannian geometry are used in the realm of C*-algebras in order to describe quantum systems in a geometric way. Examples will come from ergodic group actions and shift spaces.
Feb 5	Thu	Matt Nunes (Lancaster)	Statistics Seminar
14:00		Analysis of time series observed on networks
		Hicks Seminar Room J11
	Abstract: In this talk we consider analysis problems for time series that are observed at nodes of a large network structure. Such problems commonly appear in a vast array of fields, such as environmental time series observed at different spatial locations or measurements from computer system monitoring. The time series observed on the network might exhibit different characteristics such as nonstationary behaviour or strong correlation, and the nodal series evolve according to the inherent spatial structure. The new methodology we develop hinges on reducing dimensionality of the original data through a change of basis. The basis we propose is a second generation wavelet basis which operates on spatial structures. As such, the (large) observed data is distilled down to key information on a reduced network topology. We discuss the potential of this dimension reduction method for time series analysis tasks. This is joint work with Marina Knight (University of York) and Guy Nason (University of Bristol).
Feb 9	Mon	Theodore Voronov (Manchester)
15:00		Microformal geometry: ``thick morphisms'' of supermanifolds, adjoints of nonlinear operators and homotopy algebras
		Hicks Seminar Room J11
	Abstract: We introduce a generalization of smooth maps of manifolds (or supermanifolds) called ``thick morphisms''. Such morphisms are defined via formal canonical relations between cotangent bundles and make a formal category, a ``thickening'' of the usual category of smooth manifolds with the same class of objects. They induce pullbacks of smooth functions, which are formal nonlinear mappings with remarkable properties. In particular, we shall explain how this new construction makes it possible to obtain an analog of the adjoint operator for the case when the initial operator is nonlinear. (We consider maps of vector spaces or fiberwise maps of vector bundles $\Phi:\, E_1\to E_2$.) This gives a ``nonlinear pushforward map'' of the spaces of functions on the dual bundles $\Phi_*:\, \mathbf{C}^{\infty}(E_1^*)\to \mathbf{C}^{\infty}(E_2^*)$. (Since the mapping of functions is itself nonlinear, the functions should be even or ``bosonic''; there is a parallel ``fermionic'' construction.) Time permitting, we shall give an application to homotopy Poisson algebras and homotopy Lie (bi)algebroids. (See preprints: 1409.6475 and 1411.6720.)
Feb 10	Tue	Simon Willerton (Sheffield)	Category Theory
15:00		Categorifying the magnitude of graphs
		Hicks Seminar Room J11
	Abstract: (with Richard Hepworth) Magnitude is a measure of the size of a metric space introduced by Tom Leinster. Whilst its origins lie in category theory, it has a very concrete definition and turns out to have connections with various aspects of mathematics, such as biodiversity measurement, integral geometry, potential theory and Minkowski dimension. A graph gives rise to a metric space by taking the shortest-path metric, thus a graph can be assigned a magnitude, and this, it transpires, can be considered as a formal power series with integer coefficients. Just as Khovanov homology has the Jones polynomial as its Euler characteristic, so it turns out that there is a homology theory of graphs that has graph magnitude as its Euler characteristic. I will explain the background and some properties of this magnitude homology of graphs.
Feb 11	Wed	Sylvain Laizet (Imperial)	Applied Mathematics Colloquium
14:00		Incompact3d: a high-­order flow solver to tackle turbulence problems using supercomputers
		LT 10
	Abstract: Simulating and understanding turbulent flows remains one of the most challenging problems in mechanics. Significant progress has been made recently using high performance computing, and computational fluid dynamics (CFD) is now a critical complement to experiments and theories in order to understand turbulent flows and how to apply them in various engineering contexts. Only very few codes for Direct and Large Eddy Simulations (DNS/LES) are capable of undertaking massive simulations with several billion mesh nodes on thousands of computational cores. Most of them are simulating idealized homogeneous, isotropic turbulence, using spectral methods with periodic boundary conditions in at least two spatial directions. Engineering problems have more complex geometries and full spectral approaches are not practical. In conventional CFD, especially in an industrial context, complex geometries are usually treated using non­structured element meshes, requiring low­order schemes and sophisticated tools for the generation of highly distorted meshes. The resulting accuracy is most of the time incompatible with a detailed analysis of engineering problems. Note that the spectral element method seems to be a very promising strategy to undertake complex problems with the spectral accuracy. However, using this technique on thousands of computational cores is a challenging task that requires important numerical developments to conciliate accuracy, efficiency and scalability. In this talk, I will present an innovative numerical method which can reconcile accuracy, efficiency, versatility and scalability using a Cartesian grid. Various examples will be shown in this talk such as fractal­-generated turbulence, gravity currents in an open basin, impinging jets on a heated plate and a micro­jet device to control a turbulent jet.
Feb 12	Thu	Gwilym Pryce (Sheffield Methods Institute)	RSS Seminar
16:00		Poverty in suburbia: An oxymoron coming to a city near you
		Hicks Room LT6
	Abstract: Gwilym Pryce will present research by Leo Kavanagh, Duncan Lee and Gwilym Pryce. The traditional view of poverty as an inner city phenomenon is being challenged. Recent analysis of American cities finds that suburbia is now “home to the largest and fastest-growing poor population in the country and more than half of the metropolitan poor” (Economist 17/1/2002). As a result, the rise of suburban poverty is being highlighted as one of the most significant trends that may come to characterise twenty-first century cities. Suburbanisation of poverty may pose particular challenges for welfare policy and regeneration frameworks which have historically been geared towards inner cities. Their research investigates whether there is any evidence of this trend emerging in the UK, particularly in Scottish cities. They have also sought to improve research methods in this field by developing a way of quantifying the uncertainty associated with decentralisation measurement. Their approach will help policy makers and researchers know whether or not an apparent change in the pattern of poverty is a real phenomenon and not just due to random variation in the data. Initial findings suggest that poverty has indeed become noticeably less centralised in Glasgow over the 2001 to 2011 period, both in terms of the location of Incapacity Benefits and Job Seekers Allowance claimants. For more information on this ongoing research project, see the following short article published in The Conversation: https://theconversation.com/poverty-is-moving-to-the-suburbs-the-question-is-what-to-do-about-it-35986 and the ESRC AQMEN Research Briefing Paper: https://www.aqmen.ac.uk/sites/default/files/RB5-poverty-suburbia.pdf
Feb 16	Mon	Yun Tao (UC Davis)	Mathematical Biology Seminar
15:00		Transient Movement Ecology: Methods and Applications.
		Hicks F24
	Abstract: Movement ecology is an emerging discipline that is essential to our understanding of the interplay between fine-scale movement mechanisms of individuals and their large-scale implications for population and communities. More importantly, theoretical development of non-equilibrium and complex adaptive movement systems such as animal home range are critical to the development of next-generation solutions to conservational challenges in a messy, interconnected, and highly variable world. The studies here present original analytical and numerical frameworks for modeling transient movement dynamics that often occur rapidly and quietly. Modal selection function, formulated from the basis of optimal foraging theory, aims to facilitate an ecologically integrated approach to predicting the seasonal expansion and collapse of animal home range. Meanwhile, a simulation platform that delivers time-varying solutions to partial differential equations is introduced as an effective remedy to the technical restrictions that have to date impeded transient movement analysis of interacting individuals. In real-world applications, the integration of transient numerical analysis with SIR model can align movement and epidemiological processes, an thus help us better understand the dynamical emergence of various zoonotic disease such as Rift Valley fever.
Feb 16	Mon	Sarah Whitehouse (Sheffield)	Topology Seminar
16:00		A-infinity algebras and spectral sequences
		Hicks Seminar Room J11
	Abstract: This will be an expository talk, on the connection between A-infinity algebras and multiplicative spectral sequences. Since the cohomology of a dga over a field has an A-infinity algebra structure, there must be some kind of A-infinity structure on the pages of a multiplicative spectral sequence. I will review some work of Lapin and Herscovich in this direction.
Feb 17	Tue	Haluk Sengun (Sheffield)	Number Theory seminar
13:00		Modular Forms and Elliptic Curves over Number Fields
		F28
	Abstract: The celebrated connection between elliptic curves and weight 2 newforms over the rationals has a conjectural extension to general number fields. For example, over odd degree totally real fields, one knows how to associate an elliptic curve to a weight 2 newform with integer Hecke eigenvalues. Beyond totally real fields, we are at a loss at associating elliptic curves to weight 2 newforms. The best one can do is to "search" for the elliptic curve. In joint work with X.Guitart (Essen) and M.Masdeu (Warwick), we generalize Darmon's conjectural construction of algebraic points on elliptic curves to general number fields and then use this conjectural construction to construct the elliptic curve starting from a weight 2 newform over a general number field from its p-adic periods, under some hypothesis. In the talk, I will start with a discussion of the first paragraph and then will sketch our method.
Feb 18	Wed	Chris Keylock (Civil Eng., Sheffield)	Applied Mathematics Colloquium
14:00		Velocity Increments in Turbulent Wakes
		LT 10
	Abstract: (with Joachim Peinke and Robert Stresing, University of Oldenburg) A traditional approach to studying turbulence is by linking the moments of the velocity increments to dissipation. This then leads to models such as those of Kolmogorov (1941,1962), Frisch et al. (1978) and She and Leveque (1994) for the scaling of the moments. An alternative approach was proposed by Peinke and co-workes in 1997 based on studying the full distribution function for the increments. If a Markovian property holds, a Fokker-Planck equation can be written for the evolution of the increment distribution function, parameterised by drift and diffusion coefficients. An issue of contemporary interest is the effect that multiple scales of forcing has on the structure of turbulence. Peinke, Stresing and Vassilicos published a paper in Physical Review Letters in 2010 arguing that the drift and diffusion coefficients behaved differently under multiscale forcing. Here we combine the Fokker-Planck approach with the data from the PRL paper, and a method we have developed for controlled randomisation of datasets (called Gradual Wavelet Reconstruction). We show using this technique that we can explore the higher order expansions of the diffusion coefficient to gain a richer understanding of turbulence from the perspective of the Fokker-Planck model. An explanation is proposed for the differing behaviour of wakes produced by forcing at single- and multiple-scales. The content of this talk is based on a paper accepted in Physics of Fluids
Feb 18	Wed	Ieke Moerdijk (Nijmegen and Sheffield)	Pure Maths Colloquium
16:00		Dendroidal topology
		Hicks Seminar Room J11
	Abstract: Simplicial topology is an effective theory for approximating topological spaces by spaces built up out of simplices, and since its early development the theory has played a dominant role in algebraic topology and its applications. In this lecture, I will try to sketch how a similar theory can be developed in which one replaces simplices by tree-like objects. This new theory strictly contains the older simplicial one, and forms an effective tool for the approximation of operads (mathematical objects used to encode algebraic structures on spaces) and of infinite loop spaces.
Feb 19	Thu	Hendrik Suess (Manchester)	Algebra / Algebraic Geometry seminar
16:00		Frobenius splittings on an algebraic variety with torus action
		Hicks Seminar Room J11
Feb 23	Mon	David O'Sullivan (Sheffield)	Topology Seminar
16:00		Bundles in Noncommutative Topology
		Hicks Seminar Room J11
	Abstract: In ordinary topology we are often interested in families of objects parametrized over some base space. Vector bundles and fibrations are the obvious examples. The same is true of bundles in noncommutative topology, where they play a central role in the representation theory of topological groupoids. In some senses our bundles are a lot more general, in that we are not bound by things like local triviality. We can therefore construct some very interesting and powerful bundle-like constructions. Perhaps the most general is the Fell bundle, which can be though of as a bundle of Banach spaces in which the base object is no longer a topological space but instead a topological groupoid. In this talk I will explain how Fell bundles are constructed and how they are used in representation theory. It turns out that this is best done using the language of C*-categories, but with a new internal construction in the category of topological spaces. Along the way I will give an overview of the established theory of Banach- and Hilbert- bundles. I will also say a little on how we can study Fell bundles using an existing topological invariant.
Feb 24	Tue	Tobias Berger (Sheffield)	Number Theory seminar
13:00		Bloch-Kato conjecture for Asai representation
		F28
	Abstract: I will explain the statement of the Bloch-Kato conjecture for the Asai (or tensor induction) representations and discuss how Ribet style constructions of non-split extensions can be used to prove one direction of this conjecture.
Feb 26	Thu	Sayan Banerjee (University of Warwick)	Statistics Seminar
14:00		Maximal couplings and geometry
		Hicks Seminar Room J11
	Abstract: Maximal couplings are couplings of Markov processes where the tail probabilities of the coupling time attain the total variation lower bound (Aldous bound) uniformly for all time. Markovian couplings are coupling strategies where neither process is allowed to look into the future of the other before making the next transition. These are easier to describe and play a fundamental role in many branches of probability and analysis. Hsu and Sturm proved that the reflection coupling of Brownian motion is the unique Markovian maximal coupling (MMC) of Brownian motions starting from two different points. Later, Kuwada proved that to have a MMC for Brownian motions on a Riemannian manifold, the manifold should have a reflection structure, and thus proved the first result connecting this purely probabilistic phenomenon (MMC) to the geometry of the underlying space. In this work, we investigate general elliptic diffusions on Riemannian manifolds, and show how the geometry (dimension of the isometry group and flows of isometries) plays a fundamental role in classifying the space and the generator of the diffusion for which an MMC exists. We also describe these diffusions in terms of Killing vector fields (generators of rigid motions on manifolds) and dilation vector fields around a point. This is joint work with W.S. Kendall.
Mar 2	Mon	Kirill Mackenzie (Sheffield)
13:00		Poisson Lie groups, I (rescheduled from 23/2)
		LT A (note unusual time and place)
	Abstract: This is the first of a series of two or three lectures on Poisson Lie groups and Lie bialgebras. The lectures are designed for postgraduates but all interested are welcome. This abstract outlines the series. A PLG $G$ is a Lie group equipped with a Poisson structure with respect to which the multiplication is a Poisson map. Compatibility conditions like this are very familiar but because Poisson structures are contravariant, there are unexpected consequences: group inversion is antiPoisson, not Poisson, and left- and right-translations are neither Poisson nor antiPoisson. In other words the standard actions of the group on itself are not by Poisson diffeomorphisms. When $G$ is linearized to its Lie algebra $\frak g$, the Poisson structure induces a Lie algebra structure on $\frak g^*$, the vector space dual. Together $\frak g$ and $\frak g^*$ form a Lie bialgebra. The relationship between them is embodied in the (classical) Drinfeld double: the direct sum $\frak g\oplus g^*$ has a Lie algebra structure for which $\frak g$ and $\frak g^*$ are Lie subalgebras. These ideas are the basis of several strands of current work. They are also used in work on integrable systems. I will start with Lie bialgebras and work backwards towards PLGs. The only background assumed is a slight acquaintance with Lie groups and Lie algebras.
Mar 3	Tue	Florin Stan (Sheffield)	Number Theory seminar
13:00		The Siegel norm, the length function and character values of finite groups
		F28
	Abstract: In this talk I will present some new results on the connection between the Siegel norm, the length function and irreducible character values of finite groups.
Mar 4	Wed	Jeremy Sakstein (Portsmouth)	Applied Mathematics Colloquium
14:00		Astrophysical tests of gravity
		LT 10
	Abstract: The puzzling nature of the late-time acceleration of the cosmological expansion has prompted a recent interest in alternate theories of gravity. Any theory that can drive the acceleration must include a mechanism that recovers GR in the solar system, a screening mechanism. In this talk I will describe how astrophysical objects such as stars and galaxies can act as new and novel probes of these theories.
Mar 4	Wed	Paul Johnson (Sheffield)	Pure Maths Colloquium
16:00		Lattice Points and Simultaneous Core Partitions
		Hicks Seminar Room J11
	Abstract: For an integer t, t-core partitions are a subclass of partitions that appear naturally in representation theory, number theory, and geometry. More recently, in connection to rational Catalan combinatorics there has been active study into partitions that are simultaneously a-core and b-core, for a, b relatively prime. After a gentle introduction to core partitions, we will explain our recent work connecting simultaneous core partitions with the geometry of lattice points, that in particular allows us to prove a conjecture of Armstrong about the average size of simultaneous core partitions.
Mar 5	Thu	Edd Codling (Essex)	Mathematical Biology Seminar
13:00		Beyond movement analysis: using movement and behavioural data to detect health and welfare status in dairy cows.
		Hicks F41
	Abstract: Dairy cow welfare is increasingly a subject of public concern. A major ongoing challenge is the development of methods for automating the detection of welfare problems. In this talk, I will explain how we are using automated data collection techniques to record patterns of space use, movement, and social interactions of dairy herds within a commercial barn. We are using a range of techniques and methods borrowed from the ecological modelling literature to analyse and predict the movement, behaviour and welfare status of cows within the herd. I will explain how we can use space utilisation methods to overcome noisy sensor data and determine the amount of time individual cows spend in specific locations within the barn. I will discuss how approaches such as hidden Markov models can be used to monitor behavioural states and highlight abnormal periods of behaviour that may be indicative of reduced welfare. Finally, I will explain how social network analysis techniques will allow us to determine the social hierarchy of the herd and how this may also be used to monitor welfare status.
Mar 5	Thu	Andreas Krug (Warwick)	Algebra / Algebraic Geometry seminar
16:00		On derived categories of symmetric quotient orbifolds
		Hicks Seminar Room J11
	Abstract: A central result in the theory of Hilbert schemes of points on surfaces is the identification of their cohomology with the Fock module over a Heisenberg algebra by means of the Nakajima operators. In this talk, I aim to present two constructions on the level of the derived categories of symmetric quotient stacks which are related to these operators.
Mar 5	Thu	Paul Trenell and Jo Daniels (DWP Social Justice Analysis)	RSS Seminar
16:00		Offending, Benefits and Employment - A Big Data Innovation
		Hicks Room LT6
	Abstract: DWP share their experience of conducting a three-way data share with the Ministry of Justice and HM Revenue and Customs to create a matched dataset covering the benefit and employment history of 4.3 million offenders. This work has been a key Big Data innovation in the public sector, with data-sharing increasingly being used by government departments to design and evaluate policies. The sheer scale of the data presented complex legal and analytical challenges, but the result is a powerful analytical resource. The merged data is already providing an insight in this key area of public policy, and has been used to inform policy changes such as the creation of a specialist prison leaver payment group for the Work Programme by DWP, and the recovery of court costs from offenders by Ministry of Justice.
Mar 9	Mon	Ian Marshall (Faculty of Mathematics, Higher School of Economics, Ulitsa Vavilova 7, Moscow)
14:00		A new model in the Calogero-Ruijsenaars family
		Hicks Seminar Room J11
	Abstract: Hamiltonian reduction is used to project a trivially integrable system on the Heisenberg double of $SU(n,n)$, to obtain a system of Ruijsenaars type on a suitable quotient space. This system possesses $BC_n$ symmetry and is shown to be equivalent to the standard three-parameter $BC_n$ hyperbolic Sutherland model in the cotangent bundle limit. NOTE: this talk may be moved to a spot later in the week
Mar 9	Mon	Tom Sutton (Sheffield)	Topology Seminar
16:00
		Hicks Seminar Room J11
Mar 11	Wed	Takashi Sakajo (Kyoto)	Applied Mathematics Colloquium
14:00		Word representations of structurally stable Hamiltonian flows in multiply connected domains and its applications
		LT 10
	Abstract: We are concerned with Hamiltonian vector fields with a dipole singularity satisfying the slip boundary condition in two-dimensional multiply connected domains. One example of such a Hamiltonian vector field is the incompressible and inviscid flow in an exterior multiply connected domain with a uniform flow whose Hamiltonian is called the stream function. They are regarded as mathematical models for biofluids such as insect flights and vertical descend of rotating plant seeds and for environmental flows in rivers and coastal flows. Here, we consider structurally stable Hamiltonian vector fields and their streamline topologies. We introduce an encoding procedure to assign a unique sequence of words to these patterns, owing to which one can identify every streamline pattern with its representing sequence of words. Based on the theory of word representations, we can determine all possible structurally stable streamline patterns in a combinatorial manner. Moreover, we describe transitions between two different structurally stable patterns only from their word representations without specifying the Hamiltonian. We also demonstrate how the present theory is applied to fluid flow problems with vortex structures.
Mar 11	Wed	Jan Grabowski (Lancaster)	Pure Maths Colloquium
16:00		Gradings on cluster algebras and associated combinatorics
		Hicks Seminar Room J11
	Abstract: When studying any class of rings or algebras, the existence of a grading often has a big impact on what can be said about the members of the class. In the few years since their inception, cluster algebras have been found in numerous places and have been shown to be responsible for a plethora of combinatorial patterns, but until very recently gradings on cluster algebras have not been considered in a systematic way. In this talk, we will introduce gradings on cluster algebras and show how the intricate structure and combinatorics associated to cluster algebras allows us to find and classify gradings. We will look at cluster algebras of finite type and examine the gradings they admit, making use of cluster categories. Conversely, the gradings bring out some beautiful combinatorics of their own, in the form of tropical frieze patterns.
Mar 12	Thu	Kevin Wilson (Strathclyde)	Statistics Seminar
14:00		Expert judgement informed reliability growth models and the allocation of reliability tasks
		Hicks Seminar Room J11
	Abstract: There are many mathematical models in the literature for how a system’s reliability grows during development as a result of the Test, Analyse and Fix (TAAF) cycle. Most are based on convenient parametric forms and are extensions of simple models such as Poisson Processes. Often we can find one of these parametric models which fits our data well. However, parameters in such models are typically not observable and so eliciting a subjective prior distribution, which is often desirable due to a lack of observed data, is a challenging task. Further, engineers can be rightly sceptical of models based on parameters with no physical interpretation. In this talk we present a model for a reliability growth programme developed with engineering experts in the aerospace industry. All of the model parameters can be elicited from observable quantities and so priors can be specified directly. The model is used to identify an optimal subset of reliability tasks from a large number based on targets for cost, time on test and system reliability. The optimal subset is identified by maximising the prior expectation of a multi-attribute utility function.
Mar 16	Mon	Arief Gusnato (Leeds)	Mathematical Biology Seminar
15:00		Statistical analysis of copy number alterations using next-generation sequence data.
		Hicks F28
	Abstract: The next-generation sequencing technology has advanced the way we interrogate genome in cancer studies. It produces mapped short sequences (called 'reads'). The distribution of the reads in genomic 'windows' enables identification of regions in the genome that exhibit abnormal copy number in an analysis of copy number alterations (CNA). Unfortunately, the pattern of reads is not directly interpretatble due to (1) error, (2) different number of reads recorded (sequencing coverage), (3) different size of tumour and normal genomes and (4) contamination by normal sample in the tumour sample. Furthermore, window size is also a critical parameter in the estimation of CNA, as this determines whether a CNA pattern can be identified or not. In this talk, I will describe how we deal with these challenges in the estimation of CNA profiles in cancer patients. I will also describe briefly how the CNA profiles can be utilised to make prediction on tumor's pathological subtype in lung and oral cancers.
Mar 16	Mon	Julie Bergner (UC Riverside)	Topology Seminar
16:00		Models for equivariant (\infty, 1)-categories
		Hicks Seminar Room J11
	Abstract: Recent results of Marc Stephan give conditions under which a cofibrantly generated model category has an equivariant analogue, where the objects have a group action and weak equivalences and fibrations are defined via fixed point objects. We apply his results to several models for (\infty, 1)-categories. For discrete groups, all models satisfy the required conditions. For simplicial or topological groups, we need to consider those models which have the additional structure of a simplicial or topological model category, respectively. We can also give an explicit description for equivariant complete Segal spaces, leading to examples from G-categories.
Mar 17	Tue	Bram Mesland (Warwick)	Number Theory seminar
13:00		Noncommutative Bianchi manifolds
		F28
	Abstract: We establish an explicit relation between the $K$-homology of boundary crossed product algebras associated to groups of hyperbolic isometries, and the cohomology of such groups. We show that the notion of Hecke operator for arithmetic groups has a natural definition in terms of Kasparov's $KK$-theory. In the case of Bianchi groups, we establish an explicit Hecke equivariant isomorphism between the first cohomology of $\Gamma$ and the first K-homology group of the boundary cross-product algebra associated to $\Gamma$. A similar result holds for cocompact arithmetic Kleinian groups as well. These results are achieved in the context of unbounded Fredholm modules, shedding light on noncommutative geometric aspects of the boundary crossed product. This is joint work with Haluk Sengun (Sheffield).
Mar 18	Wed	Zheng-Tong Xie (Southampton)	Applied Mathematics Colloquium
14:00		Fluids
		LT 10
Mar 18	Wed	Elijah Liflyand (Bar-Ilan)	Pure Maths Colloquium
16:00		Extending tests for convergence of number series
		Hicks Seminar Room J11
	Abstract: Analyzing several classical tests for convergence/divergence of number series, we relax the monotonicity assumption for the sequence of terms of the series. We verify the sharpness of the obtained results on corresponding classes of sequences and functions.
Mar 19	Thu	Gwilym Pryce (Sheffield Methods Institute)	Statistics Seminar
14:00		Urban Inequalities in Exposure to Crime and the Impact on Education
		Hicks Seminar Room J11
	Abstract: This seminar will set out two statistical problems. First, how to measure crime exposure for each residential address in a city, and in particular, how to ascertain the optimal distance decay function for the crime exposure measure. Second, how to estimate the impact on school performance controlling for other factors. Both questions have important applications. Being able to measure crime exposure for individual address potentially overcomes the modifiable aerial unit problem associated with using averages for administrative areas, and allows us to better understand nuances in the spatial variation in crime and how these change over time. Developing robust measures of crime exposure is also the first step in enabling researchers better understand the true cost of crime in terms of the impact on of a variety of social factors including educational performance, health, well-being, house prices, and other life outcomes. The seminar will set out the main methodological challenges as the basis for discussion on how to best to design an appropriate research strategy.
Mar 26	Thu	Lars Winther Christensen (Texas Tech University)	Algebra / Algebraic Geometry seminar
10:30		Avatars of Tate homology.
		Hicks Seminar Room J11
	Abstract: Tate homology and cohomology originated in the realm of group algebras, and the theories generalize to Iwanaga-Gorenstein rings in a straightforward manner. The cohomological theory has a more far-reaching generalization to the setting of associative rings; it is now called stable cohomology, and it agrees with Tate homology over Iwanaga-Gorenstein rings. On the homological side, the picture is not this clear. In the talk I will discuss recent work - joint with Olgur Celikbas, Li Liang, and Grep Piepmeyer - on that topic.
Apr 13	Mon	Arkady Vaintrob (Oregon)
14:00		Hidden supersymmetries of generalized geometries
		Hicks Seminar Room J11
	Abstract: Generalized complex structures, introduced by Hitchin as a common generalization of complex and symplectic structures on manifolds, found many applications in differential geometry and in physics. They also have some peculiar features, such as the the extended diffeomorphism group (the so-called B-field action), D-branes (submanifolds with additional structure), and several competing notions of a generalized holomorphic map. In my talk I will explain how to describe the generalized structures by introducing anti-commuting coordinates (i.e. in terms of geometry of supermanifolds) and how this description helps to elucidate the above peculiarities.
Apr 13	Mon	Andrew Tonks (Leicester)	Topology Seminar
16:00		A homotopical perturbation lemma
		Hicks Seminar Room J11
	Abstract: A cute 1961 paper of C.T.C. Wall shows that from free chain resolutions for groups N and Q one may construct, by a ‘twisted tensor product’, a resolution for any group extension of N by Q. More recently Brown and others have attempted, with some degree of success, to lift this construction from the category of chain complexes to that of crossed complexes, or of CW complexes. This non-abelian situation is considerably harder; one knows, for example, that there is no homological perturbation theory for crossed complexes. In this talk we will give an overview of the problem and present some new results obtained in collaboration with O.J. Gill and G. Ellis.
Apr 14	Tue	Donggeon Yhee (Sheffield)	Number Theory seminar
13:00		Gross-Zagier conjecture and a nontrivial Sha
		F28
	Abstract: For an elliptic curve E/Q, Birch and Swinnerton-Dyer conjecture predicts that the rank of Mordell-Weil group and the order of zero of L-function at s=1 are same. Gross-Zagier (1986) computed L'(E/K,1) for certain elliptic curve E and imaginary quadratic extension K/Q and proves rank E(K) ≥ 1 if L(E/K,s) has simple zero at s=1 : the equality is proven by Kolyvagin (1989). The value L'(E/K,1) is also predicted by BSD conjecture and the result of Gross-Zagier leads us new conjectural formula : the number of torsion points in E(Q) divides (the number of units in K up to ±1) (Manin constant) (Tamagawa number) (square root of the size of Sha). I want to discuss the formula. This may be an evidence for BSD. This is a joint work with Dongho Byeon and Taekyung Kim.
Apr 15	Wed	Xin Li (Queen Mary)	Pure Maths Colloquium
16:00		Cartan subalgebras in C*-algebras
		Hicks Seminar Room J11
	Abstract: This talk is about Cartan subalgebras in C*-algebras, and continuous orbit equivalence for topological dynamical systems. These two notions build bridges between operator algebras, topological dynamics, and geometric group theory. We explore rigidity phenomena for continuous orbit equivalence, and discuss how Cartan subalgebras help to understand C*-algebras attached to semigroups of number-theoretic origin.
Apr 16	Thu	Nicos Georgiou (Sussex)	Statistics Seminar
14:00		Geometric aspects of directed last passage percolation on the plane
		Hicks Seminar Room J11
	Abstract: In this talk we present the corner growth model -an infection spreading in an orderly way through the sites in the first quadrant- and explain certain geometric aspects of the infection spread. In particular, we are concerned with understanding the law of large numbers of the infection surface and the microscopic random infinite geodesics associated with the model. This talk is intended for a diverse audience.
Apr 16	Thu	Nicola Pagani (Liverpool)	Algebra / Algebraic Geometry seminar
16:00		Wall-crossing on the universal compactified Jacobian: the Theta divisor
		Hicks Seminar Room J11
	Abstract: The moduli space of line bundles on a curve can be non-compact even when the worst singularities of the curve are nodes. A natural compactification is obtained by adding stable rank-1 torsion-free sheaves: such compactification depends on the choice of a polarization on the nodal curve. Similarly, when compactifying the universal Jacobian over the moduli space of stable curves, one obtains a family of compact birational moduli spaces that depend on a polarization parameter. In this talk I will present a wall-crossing formula that describes how the theta divisor varies as a function of this parameter. This is a joint work with Jesse Kass (South Carolina).
Apr 20	Mon	Christian Blohmann (MPI Bonn)
14:00		Removable presymplectic singularities and the local splitting of Dirac manifolds
		Hicks Seminar Room J11
	Abstract: I call a singularity of a presymplectic form removable if its graph extends to a smooth Dirac structure over the singularity. The guiding example is the symplectic form of a magnetic monopole in 2 dimensions. The question whether a given singularity of a presymplectic or Poisson structure is removable in this sense is surprisingly subtle. For example, the singularity of a monopole in 3 dimensions is not removable. I will report on recent results that give a complete understanding of the structure of removable singularities. The key tool is a (new) local splitting theorem for Dirac manifolds. Finally, I will explain how this leads to the generalized prequantization of singular symplectic manifolds.
Apr 22	Wed	Sarah Zerbes (UCL)	Pure Maths Colloquium
16:00		The conjecture of Birch and Swinnerton Dyer
		Hicks Seminar Room J11
	Abstract: The talk will be aimed at a general mathematical audience, not necessarily number theorists.
Apr 23	Thu	Student seminar: Christian Fonseca Mora and Jian Wang (Sheffield)	Statistics Seminar
14:00		Christian: Stochastic partial differential equations with Lévy noise in some infinite dimensional spaces Jian: Multivariate Stochastic Volatility Estimation using Particle Filters
		Hicks Seminar Room J11
	Abstract: Christian: In this talk we consider stochastic evolution equations driven by Lévy noise in some infinite dimensional spaces. Such equations are important from a theoretical point of view and also because they have a wide range of applications. The spaces in which this equations take values are called duals of nuclear spaces and play an important role in different areas of mathematics as partial differential equations, harmonic analysis and probability in infinite dimensional spaces. The talk is intended to be an introduction to the subject and to the main results that we have obtained so far. Jian: This presentation considers a modelling framework for multivariate volatility in financial time series. The talk will briefly review particle filtering or sequential Monte Carlo methods. An overview of the multivariate volatility modelling literature will be given. As most financial returns exhibit heavy tails and skewness, we are considering a model for the returns based on the skew-t distribution, while the volatility is assumed to follow a Wishart autoregressive process. We define a new type of Wishart autoregressive process and highlight some of its properties and some of its advantages. Particle filter based inference for this model is discussed and a novel approach of estimating static parameters is provided. Furthermore, an alternative for estimating the higher dimension data will be given. The proposed methodology is illustrated with two data sets consisting of asset returns of the FTSE-100 stock exchange and the current exchange rate.
Apr 27	Mon	Jon Pitchford (York)	Mathematical Biology Seminar
15:00		Biological networks: Real, complex or imaginary?
		Hicks LT11
	Abstract: Models of complex systems with n components typically have order n^2 parameters, because each component can potentially interact with every other. It is usually impractical to measure these parameters directly, so as an alternative one might choose random parameter values and study the emergent statistical properties at the system level. In theoretical ecology this has led to some beautiful and influential results, but also to some uncomfortable peculiarities. I use a combination of empirical data and mathematical theory to try to understand what these randomisation methods are really doing, and will sketch some ideas which might lead to useful predictions of network dynamics.
Apr 27	Mon	Daniel Schappi (Sheffield)	Topology Seminar
16:00		Tannaka duality and Adams Hopf algebroids
		Hicks Seminar Room J11
	Abstract: Classical Tannaka duality is a duality between groups and their categories of representations. It answers two basic questions: can we recover the group from its category of representations, and can we characterize categories of representations abstractly? These are often called the reconstruction problem and the recognition problem. In the context of affine group schemes over a field, the recognition problem was solved by Saavedra and Deligne using the notion of a (neutral) Tannakian category. This can be generalized to the context of Adams Hopf algebroids and their categories of comodules. Using the language of stacks, this generalization gives a duality between Adams stacks and their categories of quasi-coherent sheaves. I will start with an overview of classical Tannaka duality and its generalization, and I will conclude my talk with an outline how this duality can be used to interpret various geometric constructions involving Adams stacks in terms of their associated categories.
Apr 28	Tue	Jens Funke (Durham)	Number Theory seminar
13:00		Cohomolgical aspects of weakly holomorphic modular forms and periods
		F28
	Abstract: In this talk we give a simple cohomological identity between a weakly holomorphic form and a cusp form both of weight k obtained by applying certain differential operators to a given harmonic Maass form of weight 2-k. We derive several consequences. In particular, we give a cohomological interpretation for the equality of periods of the two weight k forms in question.
Apr 29	Wed	Peter Schmid (Imperial)	Applied Mathematics Colloquium
14:00		Dynamic mode decomposition
		LT 10
Apr 29	Wed	Jack Thorne (Cambridge)	Pure Maths Colloquium
16:00		Invariant theory and arithmetic
		Hicks Seminar Room J11
	Abstract: The idea of using invariant theory to study arithmetic goes back to Gauss, who studied class groups of imaginary quadratic fields using binary quadratic forms. In recent years, Bhargava and others have revived this circle of ideas, proving striking theorems about the sets of rational points of elliptic and hyperelliptic curves. We will explain some of these ideas.
Apr 30	Thu	Janine Illian (University of St Andrews, St Andrews, UK and NTNU Trondheim, Norway)	Statistics Seminar
14:00		Developing complex spatial models for the real world – a multi-disciplinary symbiosis
		Hicks Seminar Room J11
	Abstract: Strongly motivated by interdisciplinary research substantial advances have been made in the development of practically relevant, spatial statistical methodology. In the context of spatial point process models, this has been the case, in particular, for log Gaussian Cox processes. Facilitated by the recent development of efficient and very accurate approximation methods for fitting models based on spatial random fields it has become possible to develop and apply flexible and realistically complex spatial models without prohibitive computational cost (Rue et al. 2009; Lindgren et al. 2011, Illian et al. 2012a and b). The R library R-INLA has been instrumental in making these methods available to non-specialist users and promote their usage in practice. This talk outlines the mutual benefits of developing both methodology and software as part of a continuing dialogue between method developers and ecologists. Highlights of this symbiosis and recent developments resulting from it are presented. We illustrate these with a number of applications from ecology and beyond.
Apr 30	Thu	Matthew Fayers (Queen Mary )	Algebra / Algebraic Geometry seminar
16:00		Representations of symmetric groups in characteristic p
		Hicks Seminar Room J11
	Abstract: Given a finite group G, a representation of G over the complex numbers and a prime p, one can define a representation of G in characteristic p by a process of modular reduction. A natural question to ask is which irreducible representations of G remain irreducible in characteristic p. I will talk about how this question is answered when G is a symmetric or alternating group, before going on to describe some work in progress on double covers of symmetric groups. I will try to keep the talk at a very introductory level.
May 1	Fri	Ed Morrissey (Cambridge)	Mathematical Biology Seminar
14:00		Stem cell dynamics in homoeostasis and cancer.
		Hicks LT3
	Abstract: The intestinal epithelium is characterised by rapid cellular turnover sustained by adult stem cells located at the base of glandular crypts. Based on expression of specific genes and cell location, several different crypt base sub-populations have been put forward as intestinal stem cells, making it unclear how this compartment works. In this talk I will describe how a novel mutationally-activated cell reporter gene in a mouse model combined with mathematical modelling, allows description of the behaviour of stem cells in homoeostasis and in adenomas. In addition, building on these quantitative behaviours in homoeostasis we were able to model and quantify the evolutionary advantages of stem cells harbouring oncogenic mutations, when competing against wild type cells.
May 5	Tue	Panagiotis Tsaknias (University of Luxembourg)	Number Theory seminar
13:00		Possible generalizations of Maeda's conjecture
		F28
	Abstract: I will report on joint work with L. Dieulefait, currently in progress, on generalizations of the Maeda conjecture. I will provide a precise generalized version of its weak form regarding the number of newform Galois orbits for arbitrary level and trivial nebentypus. I will also describe further ways to generalize the original conjecture (e.g. non-trivial nebentypus, Hilbert modular forms, strong form for arbitrary levels).
May 7	Thu	Daniel Williamson (Exeter)	Statistics Seminar
14:00		Posterior belief assessment: extracting meaningful subjective judgements from Bayesian analyses with complex statistical models
		Hicks Seminar Room J11
	Abstract: In a Bayesian analysis of any reasonable complexity, many, if not all of the prior and likelihood judgements we specify in order to make progress are not believed (or owned) by either analyst or subject expert. In what sense then, should we be able to attribute meaning to a large sample from the posterior distribution? Foundationally, is the posterior distribution a probability distribution at all and, if not, what is it and what can it be used for? In this talk I will present a methodology for extracting judgements for key quantities from a large Bayesian analysis. We call this Posterior Belief assessment and it is based on the idea that there are many other Bayesian analyses that you might have performed (where, for example, you used different prior/model forms for sub-components of the statistical model). We impose forms of exchangeability and co-exchangeability over key derived posterior quantities under each of these theoretical Bayesian analyses and use these, a handful of alternative analyses and temporal sure preference to derive posterior judgements that we show are closer to what de Finetti termed prevision than the corresponding judgements from your original analysis. We argue that posterior belief assessment is a tractable and powerful alternative to robust Bayesian analysis and illustrate with an example of calibrating an expensive ocean model in order to quantify uncertainty about global mean temperature in the real ocean.
May 7	Thu	Paul Johnson (Sheffield)	Algebra / Algebraic Geometry seminar
16:00		The n! Conjecture and all that: What did Haiman prove, anyway?
		Hicks Seminar Room J11
	Abstract: In a celebrated body of work, Mark Haiman set out to prove a combinatorial conjecture of Macdonald about his eponymous symmetric functions, and to do so wound up proving some geometric theorems about the Hilbert scheme of points in the plane. This will be a high-level and idiosyncratic overview of this work -- we won't assume any knowledge of symmetric functions, but we will assume basic knowledge of the Hilbert scheme of points on the level of my talks last semester.
May 8	Fri	Duncan Mackay (St. Andrews)	Applied Mathematics Colloquium
13:00		Data Driven Non-Linear Force-Free Models of the Sun’s Magnetic Field
		LT 10
	Abstract: The talk will discuss the application of both global and local data driven non-linear force-free models of the Suns magnetic field. The construction of the models will first be discussed. Following this the models will be tested against observations of solar filaments, Open Magnetic Flux and CMEs. It will be shown that the non-linear force-free models reproduce many features of the solar corona and can be used in future to predict and understand space weather events.
May 11	Mon	Kevin Gurney (Sheffield)	Mathematical Biology Seminar
15:00		Building models at different scales in neuroscience: a case study with the basal ganglia.
		Hicks LT11
May 11	Mon	Simona Paoli (Leicester)	Topology Seminar
16:00		Weak globularity in homotopy theory and higher category theory.
		Hicks Seminar Room J11
	Abstract: Spaces and homotopy theories are fundamental objects of study of algebraic topology. One way to study these objects is to break them into smaller components with the Postnikov decomposition. To describe such decomposition purely algebraically we need higher categorical structures. We describe one approach to modelling these structures based on a new paradigm to build weak higher categories, which is the notion of weak globularity. We describe some of their connections to both homotopy theory and higher category theory.
May 12	Tue	Konstantinos Tsaltas	Number Theory seminar
13:00		On congruences of modular forms over imaginary quadratic fields
		F28
	Abstract: In this talk, I will discuss joint work with Frazer Jarvis on congruences between Galois representations associated to automorphic representations over imaginary quadratic fields. This will be done subject to the existence of congruences for automorphic representations for GSp(4) over the rationals, which arise as global theta lifts.
May 13	Wed	Lucy Wyatt (Sheffield)	Applied Mathematics Colloquium
14:00		Fisheries, swimmers and a severed head - my Australian (radar) adventure
		LT 10
May 13	Wed	Nick Wright (Southampton)	Pure Maths Colloquium
16:00		Geometric Examples of the Baum-Connes conjecture and Langlands duality
		Hicks Seminar Room J11
	Abstract: The Baum-Connes conjecture asserts that two invariants of a group are isomorphic: the first is a geometric invariant, the K-homology of the classifying space; the second is an analytic invariant, the K-theory of the group C^*-algebra. In some (rare) examples the second invariant can also be viewed geometrically. In this talk I will show that even when the group C^*-algebra can be viewed geometrically, its geometry may be different to that of the classifying space. In the case of (extended) affine Weyl groups the geometries are linked by Langlands duality and the Baum-Connes assembly map can therefore be viewed as a form of Langlands duality.
May 14	Thu	Zdzislaw Brzezniak (York)	Statistics Seminar
14:00		Strong and weak solutions to stochastic Landau-Lifshitz equations
		Hicks Seminar Room J11
	Abstract: I will speak about the existence of weak solutions (and the existence and uniqueness of strong solutions) to the stochastic Landau-Lifshitz equations for multi (and one)-dimensional spatial domains. I will also describe the corresponding Large Deviations principle and it's applications to a ferromagnetic wire. The talk is based on a joint works with B. Goldys and T. Jegaraj.
May 14	Thu	Daniel Pomerleano (Imperial College London)	Algebra / Algebraic Geometry seminar
16:00		The non-commutative Hodge theory of quotient stacks
		Hicks Seminar Room J11
	Abstract: Non-commutative Hodge theory is the study of Hodge structures on the cyclic homology groups of dg-categories C. In this talk, we will study the case C= D^bCoh(X/G), where X is a projective-over-affine variety and G is an algebraic group. Using Halpern-Leistner's theory of derived Kirwan surjectivity, we prove the collapse of nc Hodge-to-de Rham spectral sequence in variety of situations for example when X is smooth, G is reductive and $\Gamma(X,\mathcal O_X)^G$ is finite dimensional. These results on the degeneration of the spectral sequence also extend to categories of singularities. Using homotopy theoretic methods, there is a Chern character from a topological version of algebraic K-theory to this periodic cyclic homology. We show that this map is an isomorphism, thereby putting an integral structure and ultimately a weight zero Hodge structure on the periodic cyclic homology. Along the way, we identify the periodic cyclic homology with a complexified version of equivariant K-homology in the sense of Atiyah and Segal. This is joint work with Dan Halpern-Leistner.
May 18	Mon	Kirill Mackenzie (Sheffield)
14:00		Poisson Lie groups, II
		Hicks Seminar Room J11
	Abstract: This is the second of three talks on Poisson Lie groups.
May 20	Wed	Anthony Yeates (Durham)	Applied Mathematics Colloquium
14:00		IMPACT OF MAGNETIC TOPOLOGY ON PLASMA DYNAMICS
		LT 10
	Abstract: How is a plasma's evolution affected by its global magnetic field structure? I will focus on trying to understand the self-organisation of turbulently relaxing plasma - a phenomenon observed in laboratory devices and hypothesised to occur in astrophysical plasmas such as stellar atmospheres. If these plasmas were perfect electrical conductors, their magnetic topology (linkage and connectivity of their magnetic field lines) would be perfectly frozen-in for all time. In reality, the turbulent flows lead to very sharp layers of electric current where even a very small resistivity allows for field-line reconnection. Nevertheless, it is well-known that the total magnetic helicity - an overall measure of the topology - remains a robust invariant. Thus the magnetic energy released during the relaxation may be limited by the conservation of total magnetic helicity. Our work goes further: we focus on the possible relevance of additional topological constraints beyond total magnetic helicity. In a turbulently relaxing plasma, we propose that the leading order behaviour is a re-organisation of field-line helicity, which in general will put additional constraints on the dynamics. If the region of turbulent reconnection is localised, one such constraint may be expressed as conservation of the topological degree of the magnetic field-line mapping. Joint work with Gunnar Hornig and Alexander Russell (University of Dundee).
May 20	Wed	Jason Levesley (York)	Pure Maths Colloquium
16:00		On the interface between number theory and wireless technology. (..or "Heard the one about the two number theorists in a loud, crowded bar?")
		Hicks Seminar Room J11
	Abstract: Recently a concept known as "interference alignment" has been proposed to increase the transmission capabilities of various wireless networks and ideas from Diophantine approximation, a branch of number theory, are playing a key role. In this talk I hope to give a brief taste of this surprising ,and potentially exciting, link between two seemingly disparate areas.
May 21	Thu	Kyoung-Seog Lee (KIAS)	Algebra / Algebraic Geometry seminar
16:00		Quasiphantom categories on some fake quadrics
		Hicks Seminar Room J11
	Abstract: We discuss constructions of quasiphantom categories on some fake quadrics in details
May 27	Wed	Dumitru Stamate (University of Bucharest and Institute of Mathematics of the Romanian Academy)	Algebra / Algebraic Geometry seminar
15:00		On the defining equations of tangent cones of numerical semigroup rings
		LT11
	Abstract: Let $H$ be a numerical semigroup minimally generated by $a_1 < dots< a_r$. We show that if we bound the width $wd(H):= a_r - a_1$, then the Betti numbers of the tangent cone $gr_{\mathfrak{m}}K[H]$ are bounded as well. We conjecture what these bounds are in terms of the width and we present evidence to support this. This is joint work with Juergen Herzog.
May 28	Thu	Rina Anno (University of Pittsburgh)	Algebra / Algebraic Geometry seminar
16:00		A-infinity functors arising from the 3rd axiom of triangulated categories
		Hicks Seminar Room J11
	Abstract: Let C be a pre-triangulated category. Its homotopy category H^0(C) is triangulated; in particular, a commutative square induces a morphism between the cones of its rows. I am going to show how an attempt to lift this morphism into the original pre-triangulated category C reveals a structure which is best described as the data of an A-infinity functor. This is based on a joint work with Timothy Logvinenko.
Jun 1	Mon	Ekaterina Shemyakova (SUNY, New Paltz)
14:00		Darboux Transformations for Differential Operators on the Superline
		Hicks Seminar Room J11
	Abstract: We give a full description of Darboux transformations of any order for arbitrary (nondegenerate) differential operators on the superline. We show that every Darboux transformation of such operators factorizes into elementary Darboux transformations of order one. Similar statement holds for operators on the ordinary line. (Joint work with Ted Voronov and my student Sean Hill.)
Jun 2	Tue	Sophie Whyte / Joanne Dalzell, Graeme Connor (ScHARR / DWP)	RSS Seminar
16:00		Health Analytics: use of Statistics and OR in a health context
		Hicks Room LT7
	Abstract: This joint event between the local groups of the RSS and the OR Society is designed to showcase and discuss the use of both Statistics and OR in a health context. There will be two talks followed by an opportunity to discuss how Statisticians and OR analysts can work more closely together to deliver improved health analytics. Sophie Whyte: Using mathematical modelling to inform policy making for bowel cancer early diagnosis Joanne Dalzell, Graeme Connor: Personal Independence Payment - using data to deliver a range of quality analyses and advice at pace
Jun 11	Thu	Roland Abuaf (ICL)	Algebra / Algebraic Geometry seminar
16:00		Holomorphically symplectic categories
		Hicks Seminar Room J11
	Abstract: In this talk I will introduce the notion of holomorphically symplectic category and discuss some of their basic properties. I will focus in particular on a 4 dimensional modular example whose Hochschild numbers reveal very interesting features.
Sep 22	Tue	Sudip Mandal (Indian Institute of Astrophysics (Bangalore))	SP2RC seminar
13:00		Propagating Disturbances along fan-like coronal loops in an active region
		LT 10
	Abstract: Propagating disturbances are often observed in active region fan-like coronal loops. They were thought to be due to slow mode MHD waves based on some of the ob- served properties. But the recent studies involving spectroscopy indicate that they could be due to high speed quasi-periodic upflows which are difficult to distinguish from up- ward propagating slow waves. In this context, we have studied a fan loop structure in the active region AR 11465 using simultaneous spectroscopic and imaging observations from Extreme-ultraviolet Imaging Spectrometer (EIS) on board Hinode and Atmospheric Imaging Assembly (AIA) on board SDO. Analysis of the data shows significant oscilla- tions at different locations. We explore the variations in different line parameters to de- termine whether the waves or flows could cause these oscillations to improve the current understanding on the nature of these disturbances.
Sep 24	Thu	Ivan Vasko (Space Research Institute of the Russian Academy of Sciences (Moscow))	SP2RC seminar
13:00		Thermal electron interaction with non-linear electrostatic structures in the outer radiation belt
		LT 10
	Abstract: TBA
Sep 24	Thu	Nic Freeman (Sheffield)	Statistics Seminar
14:15		Cluster growth in a forest fire model.
		LT7
	Abstract: I will discuss the limiting behaviour of a mean field forest fire model as the size of the model tends to infinity. The model is closely related to the dynamical Erdős–Rényi random graph. We study a particular regime in which the model displays self-organized criticality and produces clusters of heavy tailed size.
Sep 24	Thu	Remco van Hofstad (Eindhoven )	Statistics Seminar
15:45		Competition and diffusion in random graphs (The 2015 Applied Probability Trust Lecture)
		LT7
	Abstract: Empirical findings have shown that many real-world networks share fascinating features. Indeed, many real-world networks are small worlds, in the sense that typical distances are much smaller than the size of the network. Further, many real-world networks are scale-free in the sense that there is a high variability in the number of connections of the elements of the networks, making these networks highly inhomogeneous. Such networks are typically modeled using random graphs with power-law degree sequences. In this lecture, we will investigate the behavior of competition processes on scale-free random graphs with finite-mean, but infinite-variance degrees. Take two vertices uniformly at random, or at either side of an edge chosen uniformly at random, and place an individual of two distinct types at these two vertices. Equip the edges with traversal times, which could be different for the two types. Then let each of the two types invade the graph, such that any other vertex can only be occupied by the types that gets there first. Let the speed of the types be the inverse of the expected traversal times of an edge by that types. We distinguish two cases. When the traversal times are exponential, we see that one (not necessarily the faster) types will occupy almost all vertices, while the losing types only occupied a bounded number of vertices. This is reflected in the ABBA lyrics ``The winner takes it all, the loser's standing small''. In particular, no asymptotic coexistence can occur. Work in progress investigates whether this occurs more generally. On the other hand, for deterministic traversal times, the fastest types always gets the majority of the vertices, while the other occupies a subpolynomial number. When the speeds are the same, asymptotic coexistence (in the sense that both types occupy a positive proportion of the vertices) occurs with positive probability. This lecture is based on joint work with Mia Deijfen, Julia Komjathy and Enrico Baroni, and builds on earlier work with Gerard Hooghiemstra, Shankar Bhamidi and Dmitri Znamenski.
Sep 29	Tue	Nikon Kurnosov (Higher School of Economics (Moscow))	Algebra / Algebraic Geometry seminar
16:00		Betti numbers of hyperkahler manifolds
		Hicks Seminar Room J11
	Abstract: In this talk i will introduce known results on Beauville conjecture. In particular, i will explain boundary conditions for the second Betti number which follows from Rozansky-Witten invariants and so(4, b_2-2)-action on cohomology. Guan has proved that in dimension four there can exist only finite numbers of hyperkahler manifolds. In dimension six and more some results are obtained by Sawon and Kurnosov.
Oct 2	Fri	Alex Hamilton (Queen Mary University)	SP2RC seminar
13:00		Coronal Magnetic Field Extrapolation Using the Solar B Extrapolation SunPy Affiliated Package
		LT 10
	Abstract: The solar corona is an important area of research in solar physics as the conduit for the solar plasma and particle material heading to the earth and the outer solar system. From the effects on Earth's climate to the negative impacts on communication technology and astronauts we can clearly take advantage of better understanding of the structure of the corona. Unfortunately, due to its low density its line of sight integral, observations are not able to determine the 3D structure of the plasma and its magnetic fields. This is particularly unfortunate as it is widely thought that these magnetic fields are responsible for transporting a considerable of energy upwards from the photosphere. To determine the magnetic fields we turn to extrapolation techniques, using photospheric magnetograms as boundary data allowing us to infer the magnetic field structure above. This presentation aims to explain the landscape of these extrapolation routines used in the field and the principles common to all while demonstrating an API implemented in a SunPy affiliated package that is intended to help the workflow of scientists in this field.
Oct 6	Tue	Welcoming new PhD students	Number Theory seminar
13:00
		F30
Oct 6	Tue	Nick Phillips (Manchester)	Mathematical Biology Seminar
15:00
		Hicks F30
Oct 6	Tue	Tom Bridgeland (Sheffield)	Algebra / Algebraic Geometry seminar
16:00		Introduction to derived categories of coherent sheaves
		Hicks Seminar Room J11
Oct 7	Wed	Nikolay Nikolov (University of Oxford)	Pure Maths Colloquium
14:00		On the growth of torsion in homology
		Hicks Seminar Room J11
	Abstract: There is a lot of interest regarding the growth of invariants of chains of finite index subgroups, e.g. the growth of Betti numbers, rank, deficiency and so on. In this talk I will consider the growth of another invariant: the size of the torsion subgroup in homology. I will focus on two main classes of groups where there has been recent progress: amenable groups (joint with Kar and Kropholler) and right angled groups (joint work with Abert and Gelander). The main tools are from combinatorial group theory and the notion of combinatorial cost.
Oct 9	Fri	Chris Nelson (Sheffield)	SP2RC seminar
13:00		Probing Ellerman Bombs - How do we observe them and what do we know?
		LT 10
	Abstract: The capabilities of instruments designed to observe the Sun have increased at a remarkable rate over the past decades. Indeed, the spatial and temporal resolutions of modern instruments, such as Rapid Oscillations of the Solar Atmosphere (ROSA) and the CRisp Imaging SpectroPolarimeter (CRISP), allow researchers to probe the photosphere and chromosphere down to scales of tens of kilometers. This talk will introduce such instrumentation and the data which can be collected using them, before an example of analysis undertaken using such data, on the Ellerman Bomb phenomena, will be presented. We will introduce the audience to the physical properties of Ellerman Bombs (e.g., sizes, lifetimes, velocities), before covering attempts to model their formation mechanisms and their links to features observed in other regions of the solar atmosphere.
Oct 12	Mon	Tom Bridgeland	Algebra / Algebraic Geometry seminar
13:00		Introduction to derived categories of coherent sheaves
		Hicks Seminar Room J11
Oct 13	Tue	Neil Dummigan (Sheffield)	Number Theory seminar
13:00		Dedekind zeta functions
		F30
Oct 13	Tue	Johannes Nicaise (University of Leuven / ICL)	Algebra / Algebraic Geometry seminar
16:00		Poles of maximal order of Igusa zeta functions
		Hicks Seminar Room J11
	Abstract: Igusa’s p-adic zeta function Z(s) attached to a polynomial f in N variables is a meromorphic function on the complex plane that encodes the numbers of solutions of the equation f=0 modulo powers of a prime p. It is expressed as a p-adic integral, and Igusa proved that it is rational in p^{-s} using resolution of singularities and the change of variables formula. From this computation it is immediately clear that the order of a pole of Z(s) is at most N, the number of variables in f. In 1999, Wim Veys conjectured that the only possible pole of order N of the so-called topological zeta function of f is minus the log canonical threshold of f. I will explain a proof of this conjecture, which also applies to the p-adic and motivic zeta functions. The proof is inspired by non-archimedean geometry (Berkovich spaces) but the main technique that is used is the Minimal Model program in birational geometry. This talk is based on joint work with Chenyang Xu.
Oct 14	Wed	James Cranch (University of Sheffield)	Pure Maths Colloquium
14:00		A calculus for representing two-dimensional data
		Hicks Seminar Room J11
	Abstract: The story that led to this talk started with an attempt to understand how to do category theory using a computer. Proofs in category theory can often be represented as commutative diagrams, but how does one describe a commutative diagram in a brief, unique, canonical and helpful fashion? One simple idea turned out to be surprisingly fruitful: not only does it give a language for commutative diagrams, but it led to some new algorithms for a range of computational combinatorial enumeration problems, resulting in contributions to the Online Encyclopedia of Integer Sequences.
Oct 14	Wed	SURE students: Samuel Hayes, James Heseltine, Richard Molyneux, Janith Petangoda, Ashleigh Randall (SoMaS)	Applied Mathematics Colloquium
14:00
		Hicks, LT 11
Oct 16	Fri	Norbert Gyenge (Sheffield)	SP2RC seminar
13:00		Statistical study of spatio-temporal distribution of precursor flares before major solar flares
		LT 10
	Abstract: The aim of the talk is to study the spatio-temporal distribution of less energetic X-ray flares during a 24-hour time interval preceding a more energetic X-class or M-class larger flare. Information on flares occurring before this major eruption is provided by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) satellite, while the energetic flares are observed by the Geostationary Operational Environmental Satellite (GOES) satellites between 2002 and 2014. The results show that there are distinct evolutionary differences between the distributions of smaller flares depending on the type of the main flare event. Therefore, the statistical differences detected in the spatio-temporal distribution of less energetic flare events before a major flare may be a good indicator of sunspot group evolution and large-scale magnetic field reorganisation during a few hours before elapsing more energetic flares. Our results also imply that pre-flare activity can be interpreted at a much longer time interval (longer than 2 hours) than earlier and the type of the major flare may be predicted based on the distribution of preceding solar flares.
Oct 19	Mon	Tom Bridgeland (Sheffield)	Algebra / Algebraic Geometry seminar
13:00		Introduction to derived categories of coherent sheaves
		Hicks Seminar Room J11
Oct 19	Mon	Weiyi Zhang (Warwick)
14:00		Geometric structures, Gromov norm and Kodaira dimensions
		Hicks Seminar Room J11
	Abstract: Kodaira dimension provides a very successful classification scheme for complex manifolds. The notion was extended to symplectic 4-manifolds. In this talk, we will define the Kodaira dimension for 3-manifolds through Thurston’s eight geometries. It is compatible with the mapping order and other Kodaira dimensions in the sense of “additivity”. This idea could be extended to 4-dimensional geometric manifolds. Those with highest Kodaira dimension are distinguished by nonvanishing Gromov norm. Finally, we will see how it is sitting in a potential classification of 4-manifolds.
Oct 20	Tue	Dan Fretwell (Bristol)	Number Theory seminar
13:00		Integer valued polynomials, Polya fields and how little we know!
		F30
	Abstract: A natural question to ask is, "which rational polynomials always give integer values at integer inputs?". This problem has a very simple solution concerning polynomials created from binomial coefficients. However, the generalization to an arbitrary integral domain D is a much more mysterious question and recently many open problems have been posed in this area. One such problem asks about the existence of a "regular basis" for the module of integer valued polynomials on D (i.e. bases {f_0, f_1, ...} with deg(f_i) = i). This problem is surprisingly difficult and leads to the study of Polya fields. In this talk I will describe what is and isn't known when we take the ring of integers of a number field as our domain. Also I will classify Polya number fields of small degree as well as indicating questions and cases that I am currently studying in more detail.
Oct 20	Tue	Guillaume Salbreux (Crick Institute)	Mathematical Biology Seminar
15:00
		Hicks F30
Oct 20	Tue	No talk	Algebra / Algebraic Geometry seminar
16:00
		Hicks Seminar Room J11
Oct 21	Wed	Damiano Testa (University of Warwick)	Pure Maths Colloquium
14:00		Geometric influences on arithmetic problems
		Hicks Seminar Room J11
	Abstract: Geometric techniques and results can sometimes shed light on arithmetic problems. I will motivate this statement with a few examples: three elementary puzzles in number theory leading to the question of existence of integral or rational solutions to systems of polynomial equations. The space of complex solutions of these systems are related to surfaces of a very special kind, called K3 surfaces. I will show how common geometric features of these K3 surfaces can be used to obtain insight on the initial problems. The talk will be almost entirely self-contained.
Oct 22	Thu	Ignazio Cabras (Northumbria)	RSS Seminar
16:30		A pint of happiness: how pubs shape and foster community cohesion in rural England
		LT9
	Abstract: Pubs in England represent an important locus for regional development and rejuvenation, particularly in rural areas where they act as hubs for social aggregation and economic activity. Generally, village pubs are regarded as complementaries to other local services and amenities within the area, such as sporting events, volunteering and charity initiatives, as well as business activities. The evidence presented will provide empirical support for this proposition by estimating the impact of pubs on social and communal activities at a local level. Data and information about facilities and services for rural parishes have been used to elaborate a set of index measurements of community cohesion. The indexes, created from a range of discrete variables capturing multiple aspects of community living, used different econometric and statistical techniques to measure the role of pubs in shaping the levels of community cohesion in the English countryside. Findings identified a strong postive relationship between the presence of pubs and higher levels of community cohesion index in the examined parishes, indicating that the relationship is maintained in time. Results are discussed in light of the significant decline in the number of pubs in England and the UK in the last three decades, and explored with regard to possible policies and initiatives, which could help preserve the positive impact these businesses have on rural communities.
Oct 23	Fri	Tamas Sandor Kiss (Sheffield)	SP2RC seminar
13:00		New temporal property of macrospicules
		LT 10
	Abstract: The recently launched Solar Dynamics Observatory (SDO) satellite provides fantastic new oppurtunities for a better understanding of small-scale solar chromospheric jets, e.g. spicules and macrospicules (MSs). These plasma ejecta are collimated cool and dense magnetised solar material lift off the solar surface. Thanks to the uniquely available high spatial and temporal resolution observations -provided by the Atmospheric Imaging Assembly's (AIA) camera on-board SDO- we constructed an extensive macrospicule dataset covering the period of June 2010 and December 2014 detected at 30.4 nm wavelength. Several promising outcomes will be discussed such as e.g. the temporal variation of the maximum physical length of the MSs, which shows a nearly two-year long oscillation, or the trajectories of MSs and their relationship to several global phenomena.
Oct 26	Mon	John Greenlees (Sheffield)	Topological modular forms
00:00		An introduction to tmf.
		Hicks Seminar Room J11
Oct 26	Mon	Tom Bridgeland (Sheffield)	Algebra / Algebraic Geometry seminar
13:00		Introduction to derived categories of coherent sheaves
		Hicks Seminar Room J11
Oct 26	Mon	David Saunders (Ostrava, Milton Keynes)
14:00		Cartan geometries and Lie algebroids
		Hicks Seminar Room J11
	Abstract: “A Cartan geometry is a Klein geometry with curvature”: that is, given a Klein geometry as a homogeneous space G/H where G is a Lie group and H a closed Lie subgroup, a Cartan geometry is a smooth manifold M which locally is “like G/H”. A modern approach to Cartan geometry is given in a book by Sharpe, where the structure is given by a principal H-bundle over M and a “Cartan connection”, a 1-form on M taking values in the Lie algebra of G (rather than H). In this talk I shall describe an alternative approach to Cartan geometry using, rather than a principal bundle, a fibre bundle with standard fibre G/H. The morphisms of this structure form a Lie groupoid with a distinguished Lie subgroupoid, and the geometry is given by a path connection. The corresponding infinitesimal structures are Lie algebroids and an infinitesimal connection. An advantage of this approach is that the Lie algebroids obtained in this way can be identified with certain Lie algebroids of projectable vector fields on the fibre bundle. This gives a means of relating the present approach to those classical studies of projective and conformal geometry which used methods of tensor calculus.
Oct 27	Tue	Frazer Jarvis (Sheffield)	Number Theory seminar
13:00		L-functions of modular forms
		F30
Oct 27	Tue	Sam Dolan (Sheffield)	Cosmology, Relativity and Gravitation
15:00		On the Riemann tensor, Lorentz transformations and SO(3,C)
		LT5 Hicks
	Abstract: This is a pedagogical talk for researchers interested in Einstein's theory of General Relativity. I will highlight the isomorphism between $SO+(3,1,R)$ [the group of proper orthochronous Lorentz transformations] and $SO(3,C)$ [the group of complex 3x3 orthogonal matrices with unit determinant]. The latter representation arises naturally when considering Lorentz transformations of bivectors (two-forms). Using the Hodge dual, bivectors can be written as complex 3-vectors. We may then write the Riemann tensor as a 3x3 complex matrix; and the Weyl tensor as a traceless symmetric matrix. Considering the eigenproblem leads us to the Petrov classification, and the various ways that gravitational fields can affect (e.g.) Szekeres' gravitational compass.
	Slides
Oct 27	Tue	Jørgen Rennemo (Oxford)	Algebra / Algebraic Geometry seminar
16:00		Homological projective duality for Sym^2 P^n
		Hicks Seminar Room J11
	Abstract: In 2011, Hosono and Takagi constructed an interesting example of two derived equivalent, non-birational Calabi-Yau 3-folds. This example can be explained by phrasing it in terms of Kuznetsov's theory of homological projective duality. With this as motivation, we compute the homological projective dual of Sym^2 P^n, and by taking n = 4 we recover Hosono and Takagi's example. I will explain this result and its proof, which showcases a general technique for approaching HP duality, based on "gauged LG models and variation of GIT stability".
Oct 28	Wed	Matthew Juniper (Cambridge)	Applied Mathematics Colloquium
14:00		Nonlinear Thermoacoustics: flames on the edge of chaos
		Hicks, LT 11
	Abstract: Thermoacoustic oscillations occur in combustion chambers when heat release oscillations lock into pressure oscillations. They were first observed in lamps in the 18th century, in rockets in the 1930s, and are now one of the most serious problems facing gas turbine manufacturers. Most analysis of thermoacoustic oscillations has been linear and has considered the point at which the oscillations become unstable. Nonlinear studies have usually assumed that, once linearly unstable, a thermoacoustic system grows to limit cycle oscillations. Recent experiments, however, show that limit cycle oscillations in thermoacoustics are the exception rather than the rule. They also show that thermoacoustic oscillations can sometimes be triggered by little more than background noise. These experiments motivate the current study. In this study, a pre-mixed flame in a tube is modelled using a level-set approach. The flame dynamics is coupled to the acoustics. This system, although relatively simple, exhibits much of the elaborate nonlinear behaviour found in experiments, such as bi-periodic, quasi-periodic, multi-periodic and chaotic oscillations. This raises questions, and some answers, about how thermoacoustic oscillaions should be modelled in the nonlinear regime. This study also shows how triggering in thermoacoustics is related to bypass transition to turbulence in hydrodynamics.
Oct 29	Thu	Mathew Joseph (Sheffield)	Probability seminar
15:00		Longest increasing path within the critical strip
		LT 7
	Abstract: Consider the square $[0,n]^2$ with points from a Poisson point process of intensity 1 distributed within it. In a seminal work, Baik, Deift and Johansson proved that the number of points $L_n$ (length) on a maximal increasing path (an increasing path that contains the most number of points), when properly centered and scaled, converges to the Tracy-Widom distribution. Later Johansson showed that all maximal paths lie within the strip of width $n^{\frac{2}{3} +\epsilon}$ around the diagonal with probability tending to 1 as $n \to \infty$. We shall discuss recent work on the Gaussian behaviour of the length $L_n^{(\gamma)}$ of a maximal increasing path restricted to lie within a strip of width $n^{\gamma}, \gamma< \frac{2}{3}$.
Oct 30	Fri	Alexander Shukhobodskiy (Sheffield)	SP2RC seminar
13:00		Kink Oscillations of Coronal Loops
		LT 10
	Abstract: The first coronal loop oscillation was observed by TRACE in 1998 and reported by Aschwanden et al. (1999) and Nakarikov et al. (1999). The talk will discuss kink oscillations of coronal loops. Ruderman (2011) and Ruderman, Verth and Erdelyi (2008) models describing kink oscillations are briefly are briefly discussed. Introducing now more general model, by considering the straight magnetic flux tube with variable cross section, plasma density and background plasma flow parallel to the magnetic field in the presence of a dominant magnetic field. Other assumptions and equilibrium conditions of that model are presented. Linearized MHD equations describing the system behavior are presented. Considering Lagrangian particle, the closed system of equations describing the motion of the plasma are obtained.
Oct 30	Fri	Alex Shukhobodskiy (Sheffield)	SP2RC seminar
13:00		Kink Oscillations of Coronal Loops
		LT 10
	Abstract: The first coronal loop oscillation was observed by TRACE in 1998 and reported by Aschwanden et al. (1999) and Nakarikov et al. (1999). The talk will discuss kink oscillations of coronal loops. Ruderman (2011) and Ruderman, Verth and Erdelyi (2008) models describing kink oscillations are briefly are briefly discussed. Introducing now more general model, by considering the straight magnetic flux tube with variable cross section, plasma density and background plasma flow parallel to the magnetic field in the presence of a dominant magnetic field. Other assumptions and equilibrium conditions of that model are presented. Linearized MHD equations describing the system behavior are presented. Considering Lagrangian particle, the closed system of equations describing the motion of the plasma are obtained.
Nov 2	Mon	John Greenlees (Sheffield)	Topological modular forms
00:00		An introduction to tmf (continued).
		Hicks Seminar Room J11
Nov 2	Mon	Tom Bridgeland (Sheffield)	Algebra / Algebraic Geometry seminar
13:00		Introduction to derived categories of coherent sheaves
		Hicks Seminar Room J11
Nov 3	Tue	Haluk Sengun (Sheffield)	Number Theory seminar
13:00		Expository talk on elliptic cohomology
		Hicks Seminar Room J11
Nov 3	Tue	Luca Borger (Swansea)	Mathematical Biology Seminar
15:00
		Hicks F30
Nov 3	Tue	Jurgen Mifsud (Sheffield)	Cosmology, Relativity and Gravitation
15:00		The consequences of disformal couplings on the fine-structure constant
		LT5, Hicks
Nov 3	Tue	Vasily Golyshev (IITP RAS Moscow)	Algebra / Algebraic Geometry seminar
16:00		Fibered motives and motivic gammas
		Hicks Seminar Room J11
Nov 4	Wed	Haluk Sengun (Sheffield)	Number Theory Learning Seminar
11:00		Quaternion Algebras
		Hicks Seminar Room J11
	Abstract: We introduce quaternion algebras and discuss some their most basic properties.
Nov 4	Wed	Nansen Petrosyan (University of Southampton)	Pure Maths Colloquium
14:00		Dimensions of discrete groups and Brown's question
		Hicks Seminar Room J11
	Abstract: Today there are some very useful notions of a cohomological dimension of a group. Classically, for a torsion-free group, the ordinary cohomological dimension is equal to its geometric dimension provided the cohomological dimension is not two. For groups that contain torsion, the analogues of algebraic and geometric dimensions are less clear. This prompted K.S.Brown's question in 1977 which subsequently led to developments of new notions of cohomological dimensions. I will discuss the history of this topic and a recent joint work Ian Leary on Brown's question.
Nov 5	Thu	Mohammud Foondun (Loughborough)	Probability seminar
15:00		Approximations of a class of stochastic heat equations
		LT 7
	Abstract: In this talk, we are going to explore some results about approximations of a class of stochastic heat equations. To be more precise, we will indicate how one can approximate stochastic heat equation by infinitely dimensional interacting SDEs. From this, a lot of interesting properties of the heat equation follow
Nov 6	Fri	Andrew Leonard (Sheffield)	SP2RC seminar
13:00		Temperature and emission diagnostics of the solar corona
		LT 10
	Abstract: This talk presents a new software tool to quickly estimate coronal characteristics using AIA data. The method creates high-resolution temperature and emission measure maps of the whole solar disk within minutes. A slower but more thorough version was also developed as a comparison, and complimentary to, the main method. Both methods are tested extensively on synthetic data calculated from known temperature distributions and are then applied to real data. A prototype method for fast estimation of coronal line-of-sight emission distribution is also presented. A broad study investigates the characteristics of various coronal regions. The results are compared to previous works and found to be consistent, although the combination of values produced by the two methods reveals material cooler than that found by other studies, particularly at coronal hole boundaries. Another investigation applies the fast method to two sets of flaring active regions. A weak correlation exists between the flare size and mean temperature of the region for a small number of flares in one set. In the other set each region’s temperature variability over time is compared to a non-flaring region’s. The flaring regions’ mean temperatures are found to vary more than the non-flaring region’s - significantly more in several cases. This gives confidence in using such diagnostics as part of a future flare prediction method. The fast temperature map method presented here offers a significant speed advantage over similar methods, whilst maintaining robust results. This allows the maximum exploitation of AIA’s fine spatial and temporal resolution for temperature and emission measure studies.
Nov 9	Mon	Tom Bridgeland (Sheffield)	Algebra / Algebraic Geometry seminar
13:00		Introduction to derived categories of coherent sheaves
		Hicks Seminar Room J11
Nov 13	Fri	Rahul Sharma (Sheffield)	SP2RC seminar
13:00		Dynamical evolution of solar spicules: An overview
		LT 10
	Abstract: I will present an overview of dynamical behavior of solar spicules including my current work. Spicules are thin, long, jet-like magnetic features which populate the interface region between solar chromosphere and corona. In recent years, these structures had been in focus because of their possible role in transfer of energy and plasma. Waves were observed in spicules from both ground- and space-based observatories and is a subject of debate regarding the nature of observed waves. I will then discuss the 3D velocity-field reconstruction technique and how it can contribute to better interpretation of wave physics associated with spicules.
Nov 16	Mon	Simone Gutt (Bruxelles)
14:00		Symplectic analogues of spaces of constant curvature
		Hicks Seminar Room J11
	Abstract: We show how symplectic symmetric spaces with Ricci-type curvature are the symplectic analogues of space forms. The large number of their totally geodesic symplectic (or Lagrangian) submanifolds opens up the possibility of defining some Radon-type transform in a symplectic context.
Nov 16	Mon	Haluk Sengun (Sheffield)	Topological modular forms
15:00		Elliptic curves
		Hicks Seminar Room J11
	Abstract: We cover parts, that are necessary for the construction of tmf, of the theory of elliptic curves.
Nov 17	Tue	Tobias Berger (Sheffield)	Number Theory seminar
13:00		Algebraicity of critical values of L-functions
		Hicks Seminar Room J11
Nov 17	Tue	David Dempsey (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Analogue Black Holes and the Draining Bathtub Vortex
		LT5, Hicks
	Abstract: I introduce the draining bathtub vortex; an analogue model of a Kerr black hole which may be observed in a laboratory. Surface waves on water obey the same wave equation as a scalar field on curved spacetime with a certain effective metric. The system we consider has both an analogue event horizon and an analogue ergosphere. We consider the behaviour of a wave created by a Gaussian far from the vortex and investigate its interaction with the analogue black hole. The wavefront travels along null geodesics of the metric and its height is related to the Van Vleck determinant.
Nov 18	Wed	Haluk Sengun (Sheffield)	Number Theory Learning Seminar
11:00		Quaternion algebras. II.
		Hicks Seminar Room J11
	Abstract: We continue our discussion of quaternion algebras: QA's over local fields, ramification of QA's over number fields, discriminant.
Nov 18	Wed	Julia Wolf (University of Bristol)	Pure Maths Colloquium
14:00		From combinatorics to group theory (and back again)
		Hicks Seminar Room J11
	Abstract: An approximate group is a subset S of a group that is almost closed under the group operation (say multiplication), in the sense that the set of pairwise products of elements in S is not much larger than S itself. Evidently a true subgroup forms an approximate group, and much effort has gone into investigating to what extent sets satisfying the aforementioned relaxed closure condition resemble actual subgroups. The study of approximate groups in the abelian case goes back to the 1970s, but a strongly quantitative as well as a rich non-abelian theory have recently become available, the latter having applications to many other areas of mathematics where groups play a vital role. This talk will be entirely self-contained. We shall start from the abelian basics before surveying some of the more recent developments, illustrating the richness of the subject and highlighting some of the remaining challenges.
Nov 18	Wed	Alex Hague + Freddie Mather (SoMaS)	Applied Mathematics Colloquium
14:00		(Solar physics)
		Hicks, LT 11
	Abstract: Alex: Buoyancy-Driven Magnetohydrodynamic Waves in a Two-Layer Solar Atmosphere: In this talk we look at magnetohydrodynamic (MHD) waves in a gravitationally stratified plasma embedded in a vertical magnetic field. We consider waves where buoyancy plays a key role in the motion. In a non-magnetic model, such waves are internal gravity waves (IGWs). Using appropriate simplifying assumptions we show that the magnetic counterparts to IGWs are slow MHD waves. We will study propagating waves, standing waves in a one-layer cavity, and waves in a two-layer semi-infinite atmosphere. Freddy: Stability of Magnetohydrodynamic surface waves at a tangential discontinuity in a viscous plasma with shear flow: Background flows are ubiquitous in many physical plasma's. These flows can lead to Doppler shifting of MHD waves. Without a flow, in linear MHD, a surface wave can have a forward and backward propagating solution, traveling with equal phase speed but in opposite directions. With the addition of a strong enough shear flow, this backward wave can reverse it's direction of propagation. The addition of dissipation to a system leads to the loss of energy. This loss of energy can lead to damping of a wave. It has been shown, however, that this loss of energy can lead to the amplification of a surface wave over time while a shear flow is present. These types of waves are generally called negative energy waves. In this presentation we look at the stability of a tangential discontinuity in a system with a shear flow, magnetic field and stratified by a gravitational field. We first consider the problem with no viscosity (ideal MHD) and see that indeed a strong enough flow can cause backward propagating surface waves to reverse direction. We then look at the problem with a slightly viscous plasma. We see that damping occurs whilst the wave is still backwards propagating but when the direction of propagation is reversed the waves are indeed amplified over time.
Nov 19	Thu	Christian Andres Fonseca Mora (Sheffield)	Probability seminar
15:00		Stochastic integration with respect to Lévy processes in the dual of a nuclear space
		LT 7
	Abstract: Apart from Banach spaces, nuclear spaces and its strong duals are the most important classes of infinite dimensional spaces used in functional analysis. Among the most important examples are the classical spaces used in the theory of distributions $\mathcal{S}(\mathbb{R}^{d})$, $\mathcal{S}'(\mathbb{R}^{d})$, $\mathcal{D}(\mathbb{R}^{d})$ and $\mathcal{D}'(\mathbb{R}^{d})$. Motivated by the study of stochastic partial differential equations, in this talk we introduce a theory of stochastic integration for operator-valued processes taking values in the dual of a nuclear space with respect to some classes of martingale-valued measures. The stochastic integral is defined using some novel techniques. In particular, this theory allow us to define stochastic integrals with respect to Lévy processes via the Lévy-Itô decomposition. No prior knowledge on stochastic analysis in infinite dimensional spaces is assumed and all the necessary background will be provided within the talk.
Nov 20	Fri	Krishna Prasad (Queen's University, Belfast)	SP2RC seminar
13:00		Propagating slow magneto-acoustic waves in the solar atmosphere
		LT 10
Nov 23	Mon	Kirill Mackenzie (Sheffield)
14:00		The outlines of double Lie theory
		Hicks Seminar Room J11
	Abstract: Abstract: I will describe the main ideas of the Lie theory of double Lie groupoids. The talk is intended for a general pure mathematics audience. (The title may appear ungrammatical but it should become clear in the course of the talk.)
Nov 23	Mon	Haluk Sengun (Sheffield)	Topological modular forms
15:00		Modular forms
		Hicks Seminar Room J11
	Abstract: We cover parts, that are necessary for the construction of tmf, of the theory of modular forms.
Nov 24	Tue	Olivier Taïbi (Imperial)	Number Theory seminar
13:00		Arthur's multiplicity formula for automorphic representations of certain inner forms of special orthogonal and symplectic groups
		Hicks Seminar Room J11
	Abstract: I will explain the formulation and proof of Arthur's multiplicity formula for automorphic representations of certain special orthogonal groups and certain inner forms of symplectic groups G over a number field F. I work under an assumption that substantially simplifies the use of the stabilisation of the trace formula, namely that there exists a non-empty set S of real places of F such that G has discrete series at places in S and is quasi-split at places outside S, and by restricting to automorphic representations of G(AA_F) which have algebraic regular infinitesimal character at all places in S. In particular, I prove the general multiplicity formula for groups G such that F is totally real, G is compact at all real places of F and quasi-split at all finite places of F. Crucially, the formulation of Arthur's multiplicity formula is made possible by Kaletha's recent work on local and global Galois gerbes and their application to the normalisation of Kottwitz-Langlands-Shelstad transfer factors.
Nov 24	Tue	Jake Shipley (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Double-Black-Hole Solutions and Chaos in General Relativity
		LT5
	Abstract: In this talk I will present an overview of the relativistic problem of two fixed extremal Reissner-Nordstrom black holes, which is a special case of the Majumdar-Papapetrou solution to the Einstein-Maxwell theory. In particular, I will discuss the null geodesics, with a particular focus on the unstable eternal orbits around the two black holes. We find that the initial conditions corresponding to these eternal orbits form a Cantor set. I will highlight the fractal nature of this set and how the intricate mixing of initial conditions leads to chaos around the two black holes.
Nov 24	Tue	Jon Woolf (Liverpool)	Algebra / Algebraic Geometry seminar
16:00		Contractibility of spaces of stability conditions
		Hicks Seminar Room J11
	Abstract: To each triangulated category T one can associate a complex manifold Stab(T) of stability conditions on T. The expectation is that Stab(T) is always contractible, and this has been verified in many examples. In this talk, I will explain how to prove that any `finite-type' component of Stab(T) is contractible, by considering a cellular stratification of Stab(T) arising from the decomposition into regions in which the heart of the stability condition remains constant. I will use examples from the theory of quivers to illustrate the results, and, I hope, explain all the technical terms above. If there is time I will also discuss why the braid and spherical twist groups of a Dynkin quiver are isomorphic. This is joint work with Yu Qiu.
Nov 25	Wed	Haluk Sengun (Sheffield)	Number Theory Learning Seminar
11:00		Hyperbolic Spaces of Dimensions 2 and 3
		Hicks Seminar Room J11
	Abstract: We introduce basics of hyperbolic geometry and the groups of isometries in dimensions 2,3.
Nov 25	Wed	Richard Sharp (University of Warwick)	Pure Maths Colloquium
14:00		Growth and spectra on regular covers
		Hicks Seminar Room J11
	Abstract: Two natural numerical invariants that can be associated to a Riemannian manifold are the bottom of the spectrum of the Laplacian operator and, if the manifold are negatively curved, the exponential growth rate of closed geodesics. Suppose we have a regular cover of a compact manifold. Then, for each of these quantities, we might ask under what circumstances we have equality between the number associated to the cover and the number associated to the base. This question becomes non-trivial questions once the cover is infinite. It turns out that the question has a common answer in the two cases and this depends only on the covering group as an abstract group. For the Laplacian, this result was obtained by Robert Brooks in the 1980s, and Rhiannon Dougall and I have recently obtained the analogue for the growth of closed geodesics. I will discuss this work, relating it to random walks and a class of groups introduced by von Neumann in his study of the Banach-Tarski Paradox.
Nov 25	Wed	Richard Mann (Leeds)	Applied Mathematics Colloquium
14:00		Maximum Entropy Production in Collective Animal Behaviour
		Hicks, LT 11
	Abstract: Maximum Entropy Production (MEP) is a powerful tool for deriving steady-state flows in non-equilibrium physical systems, such as energy flows in the earth’s climate [1]. Flows of energy and material through the system are assumed to take values that maximise the production of entropy, much as in equilibrium systems are assumed to exist in a state of maximum entropy, subject to any known constraints. Recently the ‘causal entropic principle’ has been proposed as an analogous concept for intelligent systems [2]. In this talk I will discuss our application [3] of the causal entropic principle to collective decision-making and collective motion. Our analysis shows that agents in groups that are maximally entropic over their possible paths through future state-space must obey Weber's law interactions over discrete choices, and linearly additive social forces in continuous motion. This provides both a novel derivation of these commonly observed interactions and a new perspective on group-level behaviour. [1] R. K. Niven, Phys. Rev. E 80, 021113 (2009) [2] A. Wissner-Gross and C. Freer, Phys. Rev. Lett. 110, 168702 (2013) [3] R.P. Mann and R. Garnett, J. R. Soc. Interface 12, 20150037 (2015)
Nov 26	Thu	Jenny Saul (Sheffield, Department of Philosophy)	Equality and diversity discussions at lunch
12:00		Unconscious bias in teaching
		Hicks LT3
	Abstract: TBA (This talk will be about unconscious bias.)
Nov 26	Thu	Francisco Alejandro Díaz De la O (Liverpool)	Statistics Seminar
14:00		Subset Simulation for Bayesian Updating and Model Selection
		Lecture Theatre B
	Abstract: On the one hand, the problems of model updating and model selection can be tackled using a Bayesian approach: the model parameters to be identified are treated as uncertain and the inference is done in terms of their posterior distribution. On the other hand, the engineering structural reliability problem can be solved by advanced Monte Carlo simulation techniques such as Subset Simulation. Recently, a formulation that connects the Bayesian updating problem and the structural reliability problem has been established. This opens up the possibility of efficient model calibration and model selection using Subset Simulation. The formulation, called BUS (Bayesian Updating with Structural reliability methods), is based on a rejection principle. Its theoretical correctness and efficiency requires the prudent choice of a multiplier, which has remained an open question. Motivated by this problem, this talk presents a study of BUS. The discussion will lead to a revised formulation that allows Subset Simulation to be used for Bayesian updating and model selection without having to choose a multiplier in advance.
Nov 27	Fri	Peter Keys (Sheffield)	SP2RC seminar
13:00		Observations of surface and body modes in pores
		LT 10
	Abstract: MHD wave phenomena have been readily observed in recent years in various magnetic elements found within the solar atmosphere. They are often touted as a possible mechanism in channeling energy to the outer layers of the solar atmosphere. Recent advances in both observational techniques and instrumentation has gradually bridged the gap between observations and theory of these phenomena, as various wave modes have been identified and their properties studied across a wide range of structures. For example, numerous contemporary studies have identified and studied the properties associated with compressible sausage modes in different bandpasses, often employing magnetic pores as a test bed. However, the spatial structuring of the mode within the flux tube, that is the surface/body characteristics, has thus far been ignored in observational studies. We employed high spatial and temporal resolution observations from a combination of both ground- (ROSA) and space-based (SDO) instrumentation to study several pore datasets which were observed to support sausage modes. Using a range of techniques, we observed and were able to classify for the first time the surface and body characteristics for the wave modes observed within the pores. The most frequently occurring oscillation period in our observations was found to be ~300s, which is consistent with the p-mode spectrum. Estimates made for the energetics of these wave modes will also be discussed within the context of our results.
Nov 30	Mon	Eli Hawkins (York)
14:00		Compatibility between Metric and Poisson Tensors
		Hicks Seminar Room J11
	Abstract: If a compact Riemannian manifold can be smoothly deformed to a noncommutative geometry, then the deformation is characterized by a Poisson tensor that is locally a sum of wedge products of commuting Killing vectors. I will discuss elements of my proof. The full story involves the cotangent Lie algebroid, a contravariant connection, a higher curvature, symplectic realizations, foliations, cotangent geodesics, the Gauss-Codazzi equation, Kaluza-Klein geometry, and the secret life of Killing vectors.
Nov 30	Mon	Tom Bridgeland (Sheffield)	Topological modular forms
15:00		An introduction to stacks and the moduli stack of elliptic curves, Part 1
		Hicks Seminar Room J11
Dec 1	Tue	Lucio Guerberoff (UCL)	Number Theory seminar
13:00		Periods for automorphic motives attached to unitary groups
		Hicks Seminar Room J11
	Abstract: In this talk I will explain some results relating critical values of L-functions of cohomological automorphic representations of unitary groups over CM fields and periods. Roughly speaking these values are Petersson norms of holomorphic forms, and we explain the link with Deligne's conjecture on critical values, which predicts that these have a factorization in terms of quadratic periods, depending on the signature of the unitary group; these period relations would follow from Tate's conjecture.
Dec 1	Tue	TBA	Number Theory seminar
13:00
		Hicks Seminar Room J11
Dec 1	Tue	Christina Cobbold (Glasgow)	Mathematical Biology Seminar
15:00
		Hicks F30
Dec 1	Tue	Peter Dunsby (University of Cape Town)	Cosmology, Relativity and Gravitation
15:00		f(R) Theories of Gravity and the Emergence of Late Time Cosmological Acceleration
		LT5, Hicks
	Abstract: I will review various approaches to cosmological modelling in f(R) theories of gravity, using both top-down and bottom-up constructions. The top-down models are based on Robertson-Walker geometries and employ techniques such as Dynamical Systems methods and the reconstruction of the gravitational action from the expansion history of the Universe. The bottom-up constructions are built by patching together sub-horizon-sized regions of perturbed Minkowski space. The results obtained suggest that these theories do not provide a theoretically attractive alternative to the standard Concordance model of cosmology.
Dec 2	Wed	Haluk Sengun (Sheffield)	Number Theory Learning Seminar
11:00		Arithmetic manifolds associated to orders in quaternion algebras
		Hicks Seminar Room J11
	Abstract: We discuss arithmetic lattices arising from groups of norm one elements of orders in quaternion algebras over number fields and the associated manifolds.
Dec 2	Wed	Kay Magaard (University of Birmingham)	Pure Maths Colloquium
14:00		The lift invariant and the Conway Parker Theorem
		Hicks Seminar Room J11
	Abstract: It is a well known fact that the braid orbits on Nielsen tuples are in one to one correspondence with the connected components of Hurwitz spaces corresponding to curve covers of the Riemann sphere. The theorem of Conway and Parker asserts that if every element of the Schur multiplier of a group G is a commutator and if the ramification type is sufficiently general, then the corresponding Hurwitz space is connected. For many reasons it would be desirable to have effective versions of this theorem. In 2010 Fried showed that the lift invariant distinguishes components of Hurwitz spaces corresponding to alternating group covers whose ramification data consists entirely of three cycles.In particular the number of connected components of the corresponding Hurwitz space is never more than 2. In joint work with A. James and S.Shpectorov we show that the lift invariant distinguishes Hurwitz components of $A_5$ covers. Generalizations of this will also be discussed.
Dec 2	Wed	Miguel Teixeira (Reading)	Applied Mathematics Colloquium
14:00		Two mechanisms for free surface deformation over a flowing stream: subsurface turbulence and bottom topography
		Hicks, LT 11
	Abstract: The surface of a stream, particularly when this is shallow and flows fast, is characterized by deformations on a wide range of scales. Whereas in the deep ocean, such deformations are mostly free surface waves forced by the wind, in a fast shallow stream they result primarily from subsurface turbulence, which can generate both free and forced waves, and from bottom topography, which generates stationary waves. In this talk I will focus on these two mechanisms, showing some results from linear theories that capture essential aspects of each of them. The first theory is Rapid Distortion Theory (RDT), where the pressure disturbances that deform the free surface result from the interaction between the mean shear in the stream and subsurface turbulence. The second theory uses the fact that the stationary waves on the free surface are analogous to atmospheric waves trapped at a temperature inversion. The pressure disturbances that force them are thus due to interaction of the flow with bottom topography, and, for an isolated obstacle, produce a pattern reminiscent of Kelvin's ship waves.
Dec 3	Thu	Peter Diggle / Sheila Bird (RSS President / MRC Cambridge)	RSS Seminar
15:00		A celebration of 70 years of the Sheffield RSS Local Group
		LT2
	Abstract: The RSS Local Group in Sheffield was founded in 1945 and remains one of the longest running RSS local groups in the country. To commemorate this milestone, please join us at the University of Sheffield for an afternoon of seminars and statistical discussion. We are delighted to welcome Prof. Peter Diggle (RSS President) and Prof. Sheila Bird (Medical Research Council, Cambridge). Reminisce with friends and colleagues and share your experiences, memories and anecdotes. The presentations will be followed by a buffet and wine reception.
Dec 4	Fri	Stuart Mumford (Sheffield)	SP2RC seminar
13:00		Simulations of Magnetohydrodynamic Waves Driven by Photospheric Motions
		LT 10
	Abstract: This talk discusses the generation of MHD waves in the photosphere. A realistic magnetohydrodynamic model of the low-solar atmosphere is simulated using the Sheffield Advanced Code. MHD waves are driven in the domain by a series of velocity profiles based on physical motions in the photosphere. The simulations are analysed utilising a flux surface algorithm to decompose the velocity and wave energy flux into the reference frame of the magnetic field. This analysis enables the identification and quantification of the different MHD modes. We conclude that a horizontal driver excites almost exclusively slow mode perturbations, while, a vertical driver excites the fast mode. Further, we conclude that the velocity profile of the three studied torsional drivers does not have as much of an effect of the excited waves as the expansion factor of the spirals. Finally, the driving period is varied and found to have a minimal impact on the relative strengths of the excited wave modes.
Dec 7	Mon	David Applebaum (Sheffield)
14:00		The Ubiquitous Heat Kernel and the Hardy-Littlewood-Sobolev Inequality
		Hicks Seminar Room J11
	Abstract: In the first part of the talk, I will introduce the heat kernel on a manifold and discuss some of its properties. In the second half I will show how the heat kernel can be used to prove a generalisation of the classical Hardy-Littlewood-Sobolev inequality to Riemannian manifolds, and even more general metric measure spaces. Based on joint work with Rodrigo Banuelos (Purdue).
Dec 7	Mon	Tom Bridgeland (Sheffield)	Topological modular forms
15:00		An introduction to stacks and the moduli stack of elliptic curves, Part 2
		Hicks Seminar Room J11
Dec 8	Tue	Nigel Boston (University of Wisconsin - Madison)	Number Theory seminar
13:00		Non-Abelian Cohen-Lenstra Heuristics
		Hicks Seminar Room J11
	Abstract: In 1983, Cohen and Lenstra introduced a measure on the set of finite abelian p-groups (p odd) and conjectured that this gives the distribution of p-class groups of imaginary quadratic fields. Bush, Hajir, and I introduced a measure on the set of finitely generated pro-p groups (p odd) and conjecture (BBH) that this gives the distribution of p-class tower groups of imaginary quadratic fields. These heuristics can be succinctly rephrased in terms of moments as recently shown by Wood and me. We also prove some function field cases of the BBH conjecture.
Dec 8	Tue	Jack Morrice (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Topology & Large Scale Structure
		LT5, Hicks
	Abstract: On the scales of galaxy clusters, galaxies and below, the fundamental structures, or countable objects, are aggregations of matter. Galaxies and their clusters form disconnected regions of high density, surrounded by a connected low density sea. In contrast, the countable objects on the largest observable scales seem to be the voids, or absences of matter. Somewhere in between these scales, the topology of structure completely reverses. In this very open-ended talk I will discuss how topology can provide new insights into the formation and evolution of the largest known structures, and how this may uncover some big new challenges to the standard model of cosmology.
Dec 8	Tue	Joseph Karmazyn (Bath)	Algebra / Algebraic Geometry seminar
16:00		Knörrer periodicity and equivalences of singularity categories.
		Hicks Seminar Room J11
	Abstract: The singularity category is a homological invariant of a scheme that captures the singular information. The singularity category of the type A_n Kleinian surface singularity is equivalent to that of the finite dimensional algebra k[x]/(x^n), and this can be shown via Knörrer periodicity. I will discuss joint work with Martin Kalck that extends a similar phenomenon outside of the Kleinian case to produce an equivalence between the singularity category of a cyclic quotient surface singularity and a certain finite dimensional algebra. This equivalence is constructed geometrically by considering subcategories of the derived category of a surface containing a type A configuration of rational curves , and intriguingly the finite​ dimensional algebras produced are noncommutative in general.
Dec 9	Wed	Giovanni Rosso (Cambridge)	Number Theory seminar
11:00		Eigenvarieties for non-cuspidal Siegel modular forms
		Hicks Seminar Room J11
	Abstract: In a recent work Andreata, Iovita, and Pilloni constructed the eigenvariety for cuspidal Siegel modular forms. This eigenvariety has the expected dimension (the genus of the Siegel forms) but it parametrizes only cuspidal forms. We explain how to generalize the construction to the non-cuspidal case. To be precise, we introduce the notion of "degree of cuspidality" and we construct an eigenvariety that parametrizes forms of a given degree of cuspidability. The dimension of these eigenvarieties depends on the degree of cuspidality we want to consider: the more non-cuspidal the forms, the smaller the dimension. This is a joint work with Riccardo Brasca.
Dec 9	Wed	Nigel Boston (University of Wisconsin - Madison)	Pure Maths Colloquium
14:00		Group Inequalities, Information Inequalities, and the Entropy Region
		LT-2
	Abstract: Given a finite group G and subgroups G_1,...,G_n, for S a subset of {1,...,n} let h_S be the log of the index of the intersection of the G_i for i in S and let h = (h_S), a point in 2^n-dimensional real space. A fundamental question is to describe the conic closure of these points as G and its subgroups vary. This set arises in many fields- it has alternative definitions in terms of polymatroids or of joint entropies of discrete random variables. It interests engineers since finding network coding capacities is a convex optimization problem on the set. It is, however, only explicitly known for n=2 and 3. For n=4 its boundary is curved and I will describe work with Ting-Ting Nan that describes a little more about this mysterious region.
Dec 9	Wed	Amirul Khan (Leeds)	Applied Mathematics Colloquium
14:00		CFD-based optimisation of ventilation systems
		Hicks, LT 11
	Abstract: Airflow, contaminant concentration and temperature distribution in a multi-bed hospital ward represented by a simple model room with multiple inlet and outlet vents, have been studied using computational fluid dynamics (CFD). Our work is concerned with the development and implementation of a practical and robust response surface based multi-objective optimization (MOP) scheme, with the aim of assisting hospital ward designers and managers /operators to enhance infection control (i.e. reduce the risk of airborne transmission) without compromising patient comfort and environmental impact.
Dec 11	Fri	Marianna Korsos (Sheffield)	SP2RC seminar
13:00		Flare/CME prediction by photospheric data
		LT 10
	Abstract: We present new insights into pre-flare and Coronal Mass Ejection behavior and the evolution of the Active Regions (ARs) by analysing the SOHO/MDI-Debrecen Data (SDD) and the SDO/HMI - Debrecen Data (HMIDD) sunspot catalogues. Our method employs the weighted horizontal gradient of magnetic field (WG_M) defined between opposite polarity spot-groups at the polarity inversion line of ARs. This parameter give the important diagnostic information (i) about the accurate prediction of onset time, (ii) on the flare intensity and (iii) towards CME risk assessment from C class to the X class flare. We discuss additional two auxiliary parameters that guide us which AR be given attention for pre-flare and CME monitoring and further analysis.
Dec 15	Tue	Arend Bayer (Edinburgh)	Algebra / Algebraic Geometry seminar
14:00		Wall-crossing implies Brill-Noether
		Hicks Seminar Room J11
	Abstract: Wall-crossing for stability conditions on derived categories has, over the last few years, led to many new results purely within algebraic geometry. I will illustrate some of the methods behind these applications by reproving an old theorem, namely Lazarsfeld's Brill-Noether theorem for curves on K3 surfaces.
Dec 15	Tue	Andrew Economou (KCL / Crick Institute)	Mathematical Biology Seminar
15:00
		Hicks F30
Dec 16	Wed	Haluk Sengun (Sheffield)	Number Theory Learning Seminar
11:00		Modular curves and Shimura curves
		Hicks Seminar Room J11
	Abstract: We focus on modular and Shimura curves and their coarse moduli space interpretations.
Dec 16	Wed	Alina Vdovina (University of Newcastle)	Pure Maths Colloquium
14:00		Combinatorial structure of fake algebraic surfaces
		Hicks Seminar Room J11
	Abstract: In 1979, D.Mumford constructed a celebrated example of a fake projective plane, but the same paper contains an outline of a much more general construction of "fake" algebraic surfaces using groups acting on buildings. We'll discuss explicit constructions of such groups, old and new, and their connections with the algebraic surfaces. Main results are based on joint works with N.Boston, N.Barker, N.Peyerimhoff and J.Stix.
Dec 18	Fri	Nabil Freij (Sheffield)	SP2RC seminar
13:00		The identification and analysis of MHD waves in localised solar atmospheric wave guides
		LT 10
	Abstract: There has been ubiquitous observations of wave-like motions in the solar atmosphere for decades and the presence of magneto-acoustic waves in magnetic structures in the solar atmosphere is well-documented. The aim is to detect and identify magnetohydrodynamic (MHD) sausage waves in the lower solar atmosphere. In order to achieve this, high-resolution data is taken from numerous solar telescopes. The cross-sectional area and total intensity were measured through time, then these signals were analysed with two signal analysis methods, wavelets and Empirical Mode Decomposition. The oscillations found were identified as slow sausage MHD waves, as the phase difference between the cross-sectional area and total intensity was in-phase, which is the signature of the slow sausage MHD waves. Further, it was possible to determine several properties of these oscillations such as the radial velocity perturbation, magnetic field perturbation and vertical wavenumber using magneto-seismology. Finally was the analysis of Running Penumbral Waves (RPWs). Here, RPWs within a magnetic pore are observed for the first time and are interpreted as Upwardly Propagating Waves (UPWs) due to the lack of a penumbra that is required to support RPWs. These UPWs are also observed co-spatially and co-temporally within two elemental lines that sample the Transition Region and low corona. The estimated energy of the waves is around 150 W m^-2, which is on the lower bounds required to heat the quiet-Sun corona.
Jan 1	Thu	Rony Keppens (KU Leuven (Blegium))	SP2RC seminar
838:5		Parallel, block-adaptive MHD simulations for solar coronal dynamics.
		LT11
	Abstract: I present the open source MPI-AMRVAC simulation toolkit [Keppens et al.,2012, JCP 231, 718; Porth et al., 2014, ApJS 214, 4], with a focus on solar physical applications modeled by its magnetohydrodynamic module. Spatial discretizations available cover standard shock capturing finite volume algorithms, but also extensions to conservative high order finite difference schemes, both employing many flavors of limited reconstruction strategies. Multi-step explicit time stepping includes strong stability preserving high order Runge-Kutta steppers to obtain stable evolutions in multidimensional applications realizing up to fourth order accuracy in space and time. The parallel scaling of the code is discussed and we obtain excellent weak scaling up to 30000 processors allowing to exploit modern peta-scale infrastructure. Solar physics applications target the formation of flux rope topologies through boundary driven shearing of magnetic arcades, following the in situ condensation of prominences in radiatively controlled evolutions of arcades and flux ropes, and the enigmatic phenomenon of coronal rain, where small-scale condensations repeatedly form and rain down in thermodynamically structured magnetic arcades.
Jan 28	Thu	Andrey Soldatenkov (Bonn)	Algebra / Algebraic Geometry seminar
16:00		Irreducible holmorphic symplectic manifolds and sheaves on cubic 4-folds.
		Hicks Seminar Room J11
	Abstract: It is well known that the variety of lines on a cubic 4-fold X is an irreducible holomorphic symplectic (IHS) manifold. More recently Lehn et. al. have constructed another IHS manifold Z which is related to the variety of twisted cubics on X. We will discuss how to describe an open subset of this manifold in terms of moduli spaces of sheaves on X. We will see that the existence of symplectic form on Z is related to the structure of the derived category of X. The talk will be based on a joint work with E. Shinder.
Jan 29	Fri	Judith de Patoul (Exeter University)	SP2RC seminar
13:00		3D electron density distributions in the solar corona during solar minima: assessment for more realistic solar wind modelling
		LT 11
	Abstract: The distribution of the magnetic field generated in the solar interior and connected into the solar wind influences most coronal phenomena including large-scale and slowly evolving coronal structures. Knowledge of the electron density distribution in the solar corona can serve as a tracer of the configuration of the coronal magnetic field and provide constraints on the field configurations for coronal modelling as well as on initial conditions for solar wind modelling. We work with polarized SOHO/LASCO-C2 images from the last two recent minima of solar activity (1996-1997 and 2008-2010), devoid of coronal mass ejections. We derive the 4D electron density distributions in the corona by applying a newly developed time-dependent tomographic reconstruction method. First, we compare the results with both a polytropic and thermodynamic MHD models. Second, we study the temporal variation with the solar cycle in the polar and equatorial regions during the two solar minima. Finally, we focus on the highest-density structures and measure their differential rotation well above the surface. Such valuable information on 4D electron density distributions and large-scale structures could help to connect the sources of the solar wind to their in-situ counterparts in future missions such as Solar Orbiter and Solar Probe Plus.
Feb 4	Thu	Jessica Banks (Hull)	Topology Seminar
16:00
		Hicks Seminar Room J11
Feb 5	Fri	Sophie Murray (Met Office)	SP2RC seminar
13:00		Space Weather Operations and Research at the Met Office
		LT 11
	Abstract: Space weather has the potential to severely affect a range of vital technologies, which has led to its inclusion in the UK National Risk Register. To mitigate these impacts, it is crucial to have an ability to forecast severe events. The Met Office is the owner of this risk and has a growing role in space weather forecasting, which augments its expertise in numerical weather prediction and climate modelling. This seminar will outline the typical daily operations and services of the Met Office Space Weather Operational Centre. Current research and development activities will also be described, including the processes involved with transitioning basic science to operations.
Feb 9	Tue	Christos Aravanis (Sheffield)	Category Theory
13:00		Structures on monoidal categories
		LT11
	Abstract: This series of talks will be an introduction to certain monoidal categories with extra structure which are related to the construction of 3d-TQFTs. Among them, we will discuss fusion, pivotal and spherical categories, trying to motivate them appropriately and studying examples.
Feb 10	Wed	Karen Vogtmann (University of Warwick)	Pure Maths Colloquium
14:00		Cycles in moduli spaces of graphs
		Hicks Seminar Room J11
	Abstract: Finite metric graphs paramaterize many phenomena in mathematics and science, so we would like to understand spaces which parameterize such graphs, i.e. moduli spaces of graphs. Moduli space of graphs with a fixed number of loops and leaves often have interesting topology that is not at all well understood. For example, Euler characteristic calculations indicate a huge number of nontrivial homology classes, but only a very few have actually been found. I will discuss the structure of these moduli spaces, including recent progress on the hunt for homology based on joint work with Jim Conant, Allen Hatcher and Martin Kassabov.
Feb 10	Wed	Andrew Hillier (DAMTP, Cambridge)	Applied Mathematics Colloquium
14:00		Investigating MHD turbulence in solar prominences
		Hicks, LT 9
	Abstract: The motions of plasma in quiescent prominences, as revealed by Hinode observations, display highly complex flows across a wide range of spatial and temporal scales, and with the small diffusivity and viscosity of the system, it is no surprise that prominences host turbulence. In this talk I will present my analysis of Hinode SOT dopplergrams of a quiescent prominence observed on the 2008-09-27. By investigating the spatial and temporal correlations between the line-of-sight velocity fluctuations, it was possible to determine the scaling of the power laws up to high-order in the velocity difference, which display powers that are at some scales consistent with weak MHD turbulence, and at others is consistent with strong MHD turbulence. I will present some interpretation of these results based on the current theoretical understanding of turbulence, but also highlight areas in which they do not match with theory, and hopfully provide satisfactory explanations as to why this is the case. These results present another piece of the puzzle that is understanding the complex nature of quiescent prominences, and also on the role how turbulence plays in the complex magnetic field found in the solar atmosphere.
Feb 11	Thu	Sarah Penington (Oxford)	Probability seminar
15:00		The front location in Branching Brownian motion with decay of mass
		Hicks Seminar Room J11
	Abstract: We add a competitive interaction between nearby particles in a branching Brownian motion (BBM). Informally, when particles are in competition, the local resources are insufficient to cover the energetic cost of motion, so the particles' masses decay. In standard BBM, we may define the front displacement at time t as the greatest distance of a particle from the origin. For the model with masses, it makes sense to instead define the front displacement as the distance at which the local mass density drops from O(1) to o(1). We can show that in a weak sense this front is ~ c t^{1/3}behind the front for standard BBM. Joint work with Louigi Addario-Berry.
Feb 11	Thu	Simon Tavaré (Cambridge; DAMTP and the Cancer Research Institute)
16:10		Mathematical modeling in cancer research
		Lecture Theatre 3
	Abstract: The mathematical sciences have contributed substantially to our understanding of many aspects of biology and medicine. For example, stochastic process and statistical methods are crucial in population and evolutionary genetics, and computer science and machine learning play a key role in applications of genomics to human health. Conversely, questions in biology and medicine have led to novel mathematics. In this talk I will discuss a relative newcomer to the world of “mathematical biology”, namely cancer evolution. Cancer is a disease of the genome, so my focus will be on mutations in DNA and what they tell us about tumour evolution. I will discuss aspects of tumour heterogeneity, the DNA sequence variation observed between tumours and within them. I will illustrate the theme with two examples: the evolution of colon crypts, and stem cells in colorectal cancer. I hope to make the case that mathematical modeling is essential to understanding how tumours evolve, and is likely to point the way to better treatments for cancer.
Feb 12	Fri	Chris Jones (Leeds)	Applied Mathematics Colloquium
13:00		Joint AM Colloquium + SP2RC Seminar Waves in the Earth's Core
		Hicks, LT 11
	Abstract: The Earth contains a liquid iron core 2,900 km below its surface. The Earth's magnetic field is generated by convective stirring in this electrically conducting core. Slow waves with periods of a several years can occur in the core, due to the interaction of rotational and magnetic forces. These waves can be detected in two different ways. They disturb the geomagnetic field, giving it a time-dependent character, known as the magnetic secular variation, and this variation is being monitored by geomagnetic satellites. The waves can also transport angular momentum, and as they interact with the Earth's mantle, they lead to small but observable changes in the length of the day. The nature of both the axisymmetric and nonaxisymmetric wave modes that can occur in the core will be discussed. Axisymmetric torsional oscillations have been found in dynamo and magnetoconvection simulations, and this has enabled us to identify the excitation mechanism generating these waves, at least in the models. The waves originate primarily from the tangent cylinder, the cylinder coaxial with the rotation axis that encloses the solid inner core. Nonaxisymmetric waves are also seen in simulations, and these can be used to suggest which parts of the secular variation are likely dominated by wave propagation. Waves can also potentially shed light on the question of whether some parts of the core are stably stratified, as has been recently suggested.
Feb 12	Fri	Simon Tavare (Cambridge)	Statistics Seminar
14:00		How often does a random mapping have distinct component sizes?
		Hicks Seminar Room J11
	Abstract: One of the classical results about a random permutation of $[n] = \{1,2, \ldots,n\}$ is that the probability it has distinct cycle lengths is asymptotically $\exp(-\gamma) \approx 0.561$; here $\gamma$ is Euler’s constant. In this talk I will discuss the analogous problem for a broad class of random decomposable combinatorial structures that includes random mappings. I will illustrate how discrete process approximations can be used to answer the question in the title, and many related problems, in a very simple way. As a by-product I will describe some interesting methods for simulating the component count process of these structures.
Feb 15	Mon	Katie Atkins (London School of Hygiene & Tropical Medicine)	Mathematical Biology Seminar
14:00
		Hicks LT B
Feb 17	Wed	Caucher Birkar (University of Cambridge)	Pure Maths Colloquium
14:00		Birational geometry of algebraic varieties
		Hicks Seminar Room J11
	Abstract: In this talk I will try to explain how one tries to classify algebraic varieties, in a birational sense, using certain special varieties as building blocks. By special varieties I mean Fano's, Calabi-Yau's, and varieties of general type. These varieties are also of great interest in other parts of mathematics such as arithmetic and differential geometry.
Feb 18	Thu	Chris Wuthrich (Nottingham)	Number Theory seminar
13:00		A moduli description for the modular curve X_nonsplit
		Hicks Seminar Room J11
	Abstract: Modular curves like X_0(N) have a nice moduli interpretation; they classify elliptic curves together with extra structure in the N-torsion part. For instance, X_0(N) classifies cyclic subgroup of order N. Among the important modular curves, important to Serre's question for a uniform bound on the surjectivity of the Galois representation of an elliptic curve over Q for example, among these curves there is one X_{nonsplit}(N) that did not yet admit a simple moduli interpretation. In joint work with M. Rebolledo, we found that this curve parametrises "necklaces" on the cyclic subgroups of order N. It leads us to a simplifed proof of Chen's isogeny linking the various modular curves.
Feb 18	Thu	Joakim Beck (UCL)	Statistics Seminar
14:00
		Hicks Seminar Room J11
Feb 19	Fri	Tony Ryan (The University of Sheffield)	Equality and diversity discussions at lunch
12:00		Equality and Diversity: Why do we care?
		Hicks LTB
Feb 22	Mon	James Waldron (Newcastle)
14:00		Symmetries of differentiable stacks
		Hicks Seminar Room J11
	Abstract: Differentiable stacks are generalisations of smooth manifolds; they include orbifolds, quotient stacks, and the classifying stacks of Lie groups. I will talk about a 'stacky' generalisation of the fact that the space of vector fields on a smooth manifold carries a natural Lie algebra structure. Building on work of Hepworth, I will explain how vector fields on a differentiable stack form a Lie 2-algebra, and describe some examples. This is joint work with Cristian Ortiz. If there is time, I will also talk about a stacky generalisation of the relationship between vector fields and diffeomorphims. I will describe the automorphism 2-group of a differentiable stack, and explain how this 2-group can be seen as the `integration' of the Lie 2-algebra above.
Feb 23	Tue		Category Theory
13:00		TBA
		LT11
Feb 24	Wed	Helen Kennedy (Sheffield)	RSS Seminar
13:00		Data Visualisation
		LT9
	Abstract: This talk (jointly organised by the Local Group RSS and the Sheffield Methods Institute) will present findings from the Seeing Data research project, which explored the factors that affect their engagement with data visualisations. A range of social, human factors were found to have an impact on engagement, such as subject matter, source/media location, beliefs and opinions, time, emotions and confidence. These findings have implications for how we think about and measure the effectiveness of visualisation. The importrant role that emotions played suggest that different approaches to statistical education might be needed to develop people's confidence in relating to data.
Feb 25	Thu	Alex Bartel (Warwick)	Number Theory seminar
13:00		Heuristics for Arakelov class groups
		Hicks Seminar Room J11
	Abstract: Often, if an algebraic object is drawn "randomly", then the probability that it is isomorphic to a given object A is inverse proportional to #Aut(A). This was first observed by Cohen and Lenstra in the context of class groups of imaginary quadratic fields. That so-called Cohen-Lenstra heuristic was later extended to other families of number fields, at which point more mysterious looking probability weights started appearing. It turns out that if instead of class groups, one considers Arakelov class groups, then the original heuristic holds in great generality, provided one can make sense of "inverse proportional to #Aut(A)" in cases where the automorphism group is infinite. In this talk I will present a theory of commensurability of modules over certain rings, and of their endomorphism rings and automorphism groups, and will use it to formulate a heuristic for Arakelov class groups of number fields, which will imply the general form of the Cohen-Lenstra heuristic. However, there will be a surprising twist at the end. This is joint work with Hendrik Lenstra in Leiden.
Feb 25	Thu	Markus Riedle (Kings College London)	Probability seminar
15:00		Stochastic integration with respect to cylindrical Lévy processes
		Hicks Seminar Room J11
	Abstract: Cylindrical Lévy processes are a natural generalisation of cylindrical Wiener processes and Gaussian white noise. However, since a cylindrical Lévy process does not enjoy a cylindrical version of the semi-martingale decomposition, one cannot apply one of the standard approaches to define stochastic integrals with respect to cylindrical Lévy processes. In this talk, we will introduce a completely novel approach to stochastic integration. In this approach the integrator is not decomposed into a martingale and a bounded variation process. As a consequence, the sequence of stochastic integrals for simple integrands can only be considered as a sequence in the space $L^0$ of Hilbert space valued random variables. Convergence is established by tightness arguments utilising an approach called decoupled tangent sequences. This talk is based on a joint work with Adam Jakubowski.
Feb 25	Thu	Simon Willerton (Sheffield)	Topology Seminar
16:00		The magnitude of odd balls
		Hicks Seminar Room J11
Feb 29	Mon	Marie-Amelie Lawn (Imperial College, London)
14:00		The talk by Marie-Amelie Lawn is postponed to a date to be announced.
		Hicks Seminar Room J11
Mar 2	Wed	Caroline Series (University of Warwick)	Pure Maths Colloquium
14:00		McShane’s identity and Mirzakhani’s thesis
		Lecture Theatre 10
	Abstract: In 2014, Maryam Mirzakhani of Stanford University became the first women to be awarded the Fields medal. The starting point of her work was a remarkable relationship called McShane’s identity, about the lengths of simple closed curves on certain hyperbolic surfaces. The proof of this identity, including the Birman-Series theorem about simple curves on surfaces, uses only quite basic ideas in hyperbolic geometry which I will explain. We will then look briefly at Mirzakhani’s ingenious way of exploiting the identity. Time permitting, we will also touch on some other open questions about McShane’s identity. The talk should be accessible to advanced undergraduates.
Mar 2	Wed	Kensuke Yokoi (Cardiff)	Applied Mathematics Colloquium
14:00		Numerical simulations of free surface flows based on CLSVOF method, multi-moment methods and density-scaled balanced CSF model
		Hicks, LT 9
	Abstract: In this presentation, we propose a practical numerical framework for free surface flows. The numerical framework consists of the CLSVOF (coupled level set and volumeof-fluid) method, the THINC/WLIC (tangent of hyperbola for interface capturing/weighted line interface calculation) scheme, multi-moment methods (CIP-CSL and VSIAM3) and the density-scaled balanced CSF (continuum surface force) model. The framework is validated through several benchmark problems and comparisons with an experiment of droplet splashing. The numerical results have shown that the numerical framework is highly reliable and can well capture free surface flows with complex interface geometries like droplet splashing.
Mar 3	Thu	Bram Mesland (University of Hannover)	Number Theory seminar
13:00		Cohomology of arithmetic groups via Noncommutative Geometry
		Hicks Seminar Room J11
	Abstract: Cohomology of arithmetic groups plays a prominent role in modern number theory. The standard way to study the cohomology of an arithmetic group G goes through studying its action on the associated global symmetric space X. In this talk, we instead consider the action of G on the "boundary" of X. As this action is topologically not good, we employ the approach of Noncommutative Geometry in the style of Connes. In joint work with Haluk Sengun (Sheffield), we show that the cohomology of G, as a Hecke module, can be captured in the K-groups of a certain noncommutative C*-algebra which encodes the action of G on the boundary of X. The talk will start with a 10 minutes introduction by Haluk Sengun.
Mar 3	Thu	Andrew Golightly (Newcastle)	Statistics Seminar
14:00
		Hicks Seminar Room J11
Mar 3	Thu	Sir Michael Atiyah (University of Edinburgh)
17:15		The Topology of Matter
		Lecture Theatre 2
	Abstract: Following in the footsteps of Maxwell, Einstein and Dirac, I will describe geometric models of fundamental particles like electrons, protons, neutrons and neutrinos. I will not assume any significant knowledge of physics and only basic knowledge of elementary geometry. This will be stoppress news, speculative but on firm ground.
Mar 4	Fri	Andrew Soward (Newcastle University)
13:00		The Equatorial Ekman Layer
		Hicks, LT 11
	Abstract: This talk concerns a very old classic problem in rotating (incompressible) viscous fluids of the linear steady flow between two spheres caused by rotating them rapidly with slightly different rates about a common axis. The problem goes back to Proudman but was made famous by Stewartson through his resolution of the many free shear layers in the vicinity of the tangent cylinder (generators parallel to the rotation axis) to the inner sphere. I shall discuss the one he did not solve for, i.e., the limiting form of the Ekman layer on the inner sphere at the equator, where the tangent cylinder touches.
Mar 4	Fri	Andrew Soward (Newcastle)	Applied Mathematics Colloquium
13:00		Joint AM Colloquium + SP2RC. The Equatorial Ekman Layer
		Hicks, LT 11
	Abstract: This talk concerns a very old classic problem in rotating (incompressible) viscous fluids of the linear steady flow between two spheres caused by rotating them rapidly with slightly different rates about a common axis. The problem goes back to Proudman but was made famous by Stewartson through his resolution of the many free shear layers in the vicinity of the tangent cylinder (generators parallel to the rotation axis) to the inner sphere. I shall discuss the one he did not solve for, i.e., the limiting form of the Ekman layer on the inner sphere at the equator, where the tangent cylinder touches.
Mar 8	Tue	Yvette Kosmann-Schwarzbach (Ecole polytechnique, Palaiseau)
16:00		Multiplicativity conditions for tensor fields and forms on Lie groupoids (The visit of Professor Kosmann-Schwarzbach is supported by the LMS by a Scheme 2 grant.)
		Hicks Seminar Room J11
	Abstract: We shall recall how the multiplicativity property of the Poisson bivectors of Poisson-Lie group theory was re-formulated in terms of morphisms of Lie groupoids by K. Mackenzie in 1992, and we shall survey the many generalizations that ensued, the multiplicativity properties of multivectors, forms and Dirac structures on Lie groupoids, as well as their infinitesimal counterparts on Lie algebroids.
Mar 9	Wed	Yvette Kosmann-Schwarzbach (Ecole Polytechnique, Palaiseau)	Pure Maths Colloquium
14:00		The Jacobi identity from Jacobi to Loday and beyond
		Hicks Seminar Room J11
	Abstract: We shall examine whether the story of the Jacobi identity starts with Jacobi, circa 1840, and whether it should rather be called by the name of the British mathematician, William F. Donkin, concluding however that it was Jacobi's. Forty years later, Sophus Lie defined algebras with a skew-symmetric bilinear composition law satisfying the Jacobi identity, which he referred to as "the analytical foundation of my theory of transformations," algebras that were eventually called "Lie algebras" by Hermann Weyl in 1933. The concept of ``Leibniz algebras'', also called "Loday algebras" because of Loday's influential 1993 paper, appeared when the bracket was no longer assumed to be skew-symmetric and the Jacobi identity was suitably written "in Leibniz form". I shall try to give an idea of the many recent variants and generalizations of the Jacobi identity, both in mathematics and in mathematical physics, such as graded Jacobi identities, Jacobi identity for non-commutative double brackets, hom-Jacobi identity, and the Jacobi identity in the theory of triple tangent bundles, of Lie algebroids and of Courant algebroids, or the related properties of classical $r$-matrices and $\mathcal O$-operators.
Mar 9	Wed	Mat Hunt (hyperkahler.co.uk)	Applied Mathematics Colloquium
14:00		3D surface and interfacial waves in MHD
		Hicks, LT 9
	Abstract: We present results on weakly nonlinear surface waves in 2+1 dimensions. Several cases are examined with and without a magnetic field above the plasma. We also present a derivation of the dispersion relation for two non interacting plasmas with different depths to get an interesting dispersion relation with lots of subcases.
Mar 9	Wed	Mat Hunt (hyperkahler.co.uk)	SP2RC seminar
14:00		(joint AM+SP2RC)
		Hicks, LT 9
Mar 10	Thu	Thomas Cass (Imperial College London)	Probability seminar
15:00		Gaussian rough path analysis, a Stratonovich-to-Skorohod conversion formula
		Hicks Seminar Room J11
	Abstract: Rough path theory has made important recent strides in the understanding of nonlinear differential systems driven by non-semimartingale stochastic processes. We recall key aspects of this theory as applied to continuous Gaussian process, and show how the theory can be integrated with existing analytic tools, such as Malliavin's calculus, for the study of functionals on abstract Wiener space. We discuss the so-called CLL tail estimates and, as an extended application, derive a novel Stratonovich-to-Skorohod integral conversion formula for integrands given as path-level solutions to (rough) differential equations driven by Gaussian rough paths. This is based on joint work with Nengli Lim of Imperial College London and the National University of Singapore.
Mar 11	Fri	Alastair Williamson (Sheffield)	SP2RC seminar
13:00		Comparison of Resonant Damping Rates for Slow Surface Waves
		LT 11
	Abstract: Resonant damping of magneto-hydrodynamic (MHD) waves has been mostly investigated in detail with respect to the interaction in the Alfvén continuum, disregarding the slow continuum due mainly to the low levels of thermal pressure in the solar corona. Here, we address this issue and investigate the damping for propagating slow surface waves in both the Alfvén the slow continua, filling a gap in the studies of resonant absorption of MHD waves. Using the well-known, and previously investigated, jump conditions we find the damping rate of slow surface waves through the process of resonant absorption. An expression for the damping of the fast MHD wave in the slow continuum is found and, again, compared against the damping in the Alfvén continuum We find that for low plasma-$\beta$ regions, i.e. those that are typically considered important for solar upper chromospheric or coronal applications, the damping in the Alfvén continuum continues to dominate the damping in the slow continuum under the assumption of a thin tube.
Mar 11	Fri	Ariel Pacetti (Leverhulme Trust Professor) (Buenos Aires/Warwick)	Number Theory seminar
14:00		Lifting Galois representations into GL$_2(\mathbb{Z}/p^n \mathbb{Z})$
		Hicks Seminar Room J11
	Abstract: In this talk we will recall Ramakrishna's ideas on lifting 2-dimentional Galois representations and will explain how one can apply the techniques to lift more general representations. Along the problem we will mention some applications and if time allows what can be done in the ramified situation.
Mar 14	Mon	Cornelia Vizman (West University of Timisoara)
14:00		Dual pairs of Poisson maps (joint work with Francois Gay-Balmaz)
		Hicks Seminar Room J11
	Abstract: After giving some examples of dual pairs of momentum maps (symplectic groupoids included), I will review the symplectic leaf correspondence in dual pairs. Then I will pass to dual pairs of momentum maps associated to mutually completely orthogonal symplectic actions of two Lie groups. In this case, symplectic reduction for one group gives coadjoint orbits for the other group. In the end I will present dual pairs related to fluid dynamics, associated to mutually completely orthogonal actions of two diffeomorphism groups. I will use them to extract information about some coadjoint orbits of diffeomorphism groups.
Mar 14	Mon	Nikolai Bode (Bristol)	Mathematical Biology Seminar
14:00
		Hicks LT B
Mar 15	Tue	Ben Fuller (Sheffield)	Category Theory
13:00		Coherence for Monoidal Categories
		LT11
	Abstract: There are several closely related theorems known as ‘the coherence theorem for monoidal categories’. Although they are distinct theorems, they serve a similar purpose: to allow you to avoid worrying about the coherence data (i.e. the associators and unitors) in a monoidal category. I will give two such results, explain why they are referred to as coherence theorems, and outline their proofs.
Mar 16	Wed	Haluk Sengun (Sheffield)	Number Theory Learning Seminar
11:00		Modular curves and Shimura curves as coarse moduli spaces
		Hicks Seminar Room J11
	Abstract: We will discuss Modular curves and Shimura curves as coarse moduli spaces.
Mar 16	Wed	Balazs Szendroi (Oxford)	Algebra / Algebraic Geometry seminar
12:00		Euler characteristics of Hilbert schemes of points of simple surface singularities
		Hicks Seminar Room J11
Mar 16	Wed	Cornelia Drutu Badea (University of Oxford)	Pure Maths Colloquium
14:00		Fixed Point Properties on Banach Spaces, expanders and random graphs
		Hicks Seminar Room J11
	Abstract: One way of understanding infinite groups is by investigating their actions on special spaces, such as Hilbert and Banach spaces, non-positively curved spaces etc. Kazhdan property (T) is formulated in terms of actions on Hilbert spaces, and turns out to be relevant in many different areas. Several strengthened versions of property (T) in the setting of Banach spaces have been formulated in recent years, each of them interesting for different reasons: relevance for the conjectures of Baum-Connes and Novikov, separation between rank one and higher rank, examples of expanders with stronger properties, presumed connection to the conformal dimension of the boundary, stronger rigidity results etc. In this talk I shall overview various generalisations of property (T) to Banach spaces, especially in connection with random walks, expanders and random graphs and groups. This is based on joint work with J. Mackay and P. Nowak.
Mar 16	Wed	Andy Hoyle (Stirling)	Applied Mathematics Colloquium
14:00		The short- and long-term effects of parasite outbreaks to Salmon populations
		Hicks, LT 9
	Abstract: The UK Salmon industry is worth over £1bn per annum, but as with all ecological systems, it is under constant threat from disease outbreaks. One major threat is a macro-parasite, G. salaris. Initially, I will use an ODE-based model to determine the impact of such a parasite outbreak to a host population in the short-term. Then, by allowing the host to evolve a resistance mechanism, I will start to look at the longer-term effects, such as the time until we are likely to see host populations recover without intervention. Finally, by taking an adaptive dynamics style of approach, I can demonstrate under what conditions will a high level resistance evolve, as those seen in salmon population in other Baltic countries.
Mar 17	Thu	Paul Walton (York)	Equality and diversity discussions at lunch
12:00		Equality and Diversity -- What can we do?
		Hicks LT5
Mar 17	Thu	Jim Stankewicz (University of Bristol)	Number Theory seminar
13:00		Abelian surfaces and their endomorphisms
		Hicks Seminar Room J11
	Abstract: The Gauss class number problem predicts in part that there are only 13 possible endomorphism rings for elliptic curves with complex multiplication which can be defined over the rational numbers. In this talk we explore what a higher dimensional version of the Gauss class number problem might say and use the arithmetic of Shimura curves to give the first results on which quaternion algebras can not be endomorphism rings of Abelian surfaces.
Mar 17	Thu	Jim Griffin (Kent)	Statistics Seminar
14:00		Adaptive MCMC schemes for variable selection problems Co-authors: Krys Latuszynski and Mark Steel
		Hicks, Lecture theatre C
	Abstract: Data set with many variables (often, in the hundreds, thousands, or more) are routinely collected in many disciplines. This has lead to interest in variable selection in regression models with a large number of variables. A standard Bayesian approach defines a prior on the model space and uses Markov chain Monte Carlo methods to sample the posterior. Unfortunately, the size of the space (2^p if there are p potential variables) and the use of simple proposals in Metropolis-Hastings steps has lead to samplers that mix poorly over models. In this talk, I will describe two adaptive Metropolis-Hastings scheme which adapts an independence proposals to the posterior distribution. This leads to substantial improvements in the mixing over standard algorithms in large data sets. The methods will be illustrated on simulated and real data with with hundreds or thousands of possible variables.
Mar 18	Fri	David Southwood (Imperial)	Applied Mathematics Colloquium
13:00		Joint AM Colloquium+SP2RC Seminar: The MHD kink mode and angular momentum transfer
		Hicks, LT 11
	Abstract: Storage and/or transmission of angular momentum in twisted magnetic fields is of fundamental interest in astrophysical problems. The transmission of angular momentum by waves from a rotating conducting object embedded in a stationary plasma is investigated. Our model is simple but enough to suggest a radical conclusion that in many circumstances where the magnetic field in a dissipation-free plasma is being twisted by a torque from a conductor threaded by the same field, kinking of the magnetic column that threads the rotating conductor is inherent. The kinking is produced by a wave with spiral phase characteristics that is standing in the rotating frame. On the outer edges of the distorted column currents flow along the characteristics connecting the rotating source to the wave front established when the rotation started. An immediate motivation was to explain the 10.7 hr magnetic pulsations that are seen to originate in the polar regions of the magnetosphere of Saturn. However, the idea potentially explains the longstanding puzzle as to why pulsars pulse as well as having applications in the solar atmosphere.
Mar 18	Fri	David Southwood (Imperial College)	SP2RC seminar
13:00		The MHD kink mode and angular momentum transfer
		LT 11
	Abstract: Storage and/or transmission of angular momentum in twisted magnetic fields is of fundamental interest in astrophysical problems. The transmission of angular momentum by waves from a rotating conducting object embedded in a stationary plasma is investigated. Our model is simple but enough to suggest a radical conclusion that in many circumstances where the magnetic field in a dissipation-free plasma is being twisted by a torque from a conductor threaded by the same field, kinking of the magnetic column that threads the rotating conductor is inherent. The kinking is produced by a wave with spiral phase characteristics that is standing in the rotating frame. On the outer edges of the distorted column currents flow along the characteristics connecting the rotating source to the wave front established when the rotation started. An immediate motivation was to explain the 10.7 hr magnetic pulsations that are seen to originate in the polar regions of the magnetosphere of Saturn. However, the idea potentially explains the longstanding puzzle as to why pulsars pulse as well as having applications in the solar atmosphere.
Apr 7	Thu	Andy Sutherland / Jairo Lugo-Ocando (Formerly Health & Social Care Information Centre / Leeds)	RSS Seminar
16:00		Statistics in the Media
		LT9
	Abstract: Have I got Statistics for You! Andy Sutherland Government depends on statistics to take forward its work, and to make arguments and debate issues in public. The public depend on Government Statistics to inform themselves and to hold Government to account. In this presentation, Andy reflects on the various methods and mechanisms that can be used for obtaining and presenting figures for use in political debate, how these are used and, sometimes, abused, and how to find the evidence that may underlie contentious or conflicting claims. The Use of Crime Statistics in the News Media in the UK. Jairo Lugo-Ocando Statistics are prominently featured in most news mainstream media on a daily basis, yet most citizens, and even many reporters, do not have the knowledge required to read them critically. The result is that the public is often ill-informed, and democratic participation in the process of policy making is subject to flawed public reasoning. In particular cases of crime reporting, the coverage of statistics seemed to promote the fear of crime, therefore creating a state of moral panic that pushes the public and elected leaders into decisions that are unsound at best. The issue of managing and using crime statistics was brought to the public's attention by the UK Statistics Commission in 2006, which made a national call to improve the use of statistics by the media and politicians. Very few works examine the gathering and dissemination of crime statistics by journalists in the wider media; although some have examined the way journalists report cime statistics in more broad terms, there is still an important gap in our knowledge of this particular issue. This presentation aims to discuss where to go from here and what the research agenda should be in the near future.
Apr 11	Mon	Phillip Murray (Dundee)	Mathematical Biology Seminar
14:00
		Hicks LT B
Apr 13	Wed	Nigel Hitchin (University of Oxford)	Pure Maths Colloquium
14:00		Spinors, Lagrangians and Higgs bundles
		Hicks Seminar Room J11
	Abstract: The talk concerns a construction, due to the physicist Gaiotto, of complex Lagrangian submanifolds in the moduli space of Higgs bundles over a Riemann surface. These are BAA-branes in the physicists’ terminology. Looking at particular examples reveals different aspects of the geometry of Higgs bundle moduli spaces, with links to the classical geometry of the Kummer surface.
Apr 14	Thu	Andrew Wade (Durham)	Probability seminar
15:00		Convex hulls of planar random walks
		Hicks Seminar Room J11
	Abstract: On each of n unsteady steps, a drunken gardener drops a seed. Once the flowers have bloomed, what is the minimum length of fencing required to enclose the garden? What is its area? I will describe recent work with Chang Xu (Strathclyde) on the convex hull of planar random walk, concerned in particular with the large-n asymptotics of its perimeter length and area. We assume finite second moments for the steps of the walk. First-order results for the perimeter length include a remarkable expectation formula due to Spitzer and Widom, and a law of large numbers due to Snyder and Steele, who also proved a variance upper bound. We complement these results by variance asymptotics and distributional limit theorems. Of the four combinations of the two quantities (perimeter and area) in the two regimes (zero drift or non-zero drift for the steps of the walk), one limit is Gaussian; three are not.
Apr 14	Thu	Eugenie Hunsicker (Loughborough)	Topology Seminar
16:00		From Pure Maths to Data Science: How topology, geometry and analysis can help solve data challenges.
		Hicks Seminar Room J11
Apr 15	Fri	James Mather (Sheffield)	SP2RC seminar
13:00		Stability of Magneto-hydrodynamic (MHD) surface waves at a tangential discontinuity in relation to Negative Energy waves.
		LT 11
	Abstract: Background flows are ubiquitous in many physical plasma's. These flows can lead to Doppler shifting of MHD waves. Without a flow, in linear MHD, a surface wave can have a forward and backward propagating solution, traveling with equal phase speed but in opposite directions. With the addition of a strong enough shear flow; this backward wave can reverse its direction of propagation. The addition of dissipation to a system leads to the loss of energy. This loss of energy can lead to damping of a wave. It has been shown, however, that this loss of energy can lead to the amplification of a surface wave over time while a shear flow is present. These types of waves are generally called negative energy waves (NEW). In this presentation we look at the stability of a tangential discontinuity in a system with a shear flow, magnetic field and stratified by a gravitational field in conjunction with NEW’s. We show a governing equation derived for a gravitationally stratified Isothermal Plasma with an arbitrary magnetic field and flow and with dissipative processes. We first consider a problem with no dissipation (ideal MHD), an exponentially decreasing magnetic field and uniform flow and see that indeed a strong enough shear flow can cause backward propagating surface waves to reverse direction causing the surface waves to have negative energy according to the Cairns Criterion. We then look at the same problem but with a slightly viscous plasma. We see that damping occurs whilst the wave is still backwards propagating but when the direction of propagation is reversed the waves are indeed amplified over time. Next a governing equation for a uniform field is derived and solutions are shown. Again it is observed that amplification occurs when the direction of propagation is reversed.
Apr 18	Mon	Madeleine Jotz Lean (Sheffield)
14:00		Split Lie 2-algebroids and matched pairs of 2-representations
		Hicks Seminar Room J11
	Abstract: A matched pair of Lie algebroid representations is equivalent to two seemingly different objects; the bicrossproduct Lie algebroid and the double Lie algebroid of the matched pair. By looking at matched pairs of 2-representations and their bicrossproduct Lie 2-algebroids, the talk will explain how the double of a matched pair can be seen as the geometrisation of its bicrossproduct.
Apr 19	Tue	Dimitar Kodjabachev (Sheffield)	Topological modular forms
16:00		Bousfield localization and the chromatic Hasse square
		Hicks Seminar Room J11
Apr 20	Wed	Frances Kirwan (University of Oxford)	Pure Maths Colloquium
14:00		Non-reductive geometric invariant theory and applications in algebraic geometry
		Hicks Seminar Room J11
	Abstract: Mumford's geometric invariant theory (GIT) developed in the 1960s provided a method for constructing quotient varieties for linear actions of reductive groups on affine and projective varieties, and has many applications (for example in the construction of moduli spaces in algebraic geometry). The aim of this talk is to discuss an extension of Mumford's GIT to actions of linear algebraic groups which are not necessarily reductive, and some of its applications.
Apr 20	Wed	Nikos Kavallaris (Chester)	Applied Mathematics Colloquium
14:00		On a non-local parabolic problem arising in game theory
		Hicks, LT 9
	Abstract: In the current talk we first present the construction of a degenerate non-local equation which arises in the replicator dynamics system coming from the evolutionary game theory. Once the local existence is established we study the long-time behaviour of the preceding equation. Depending on the total mass of the initial data we either prove global-time existence or finite-time blow-up. For total mass equal to 1 then also the convergence towards the steady-states (Nash equilibria) is proven.
Apr 21	Thu	Neil Dummigan (Sheffield)	Number Theory seminar
13:00		Hecke eigenvalue congruences and experiments with degree-8 L-functions
		Hicks Seminar Room J11
	Abstract: I will describe how the moduli of various congruences between Hecke eigenvalues of automorphic forms ought to show up in ratios of critical values of GSp2xGL2 L-functions. To test this experimentally requires the full force of Farmer and Ryan's technique for approximating L-values given few coefficients in the Dirichlet series.
Apr 21	Thu	Ruth King (Edinburgh)	Statistics Seminar
14:00
		Hicks Seminar Room J11
Apr 22	Fri	Fionnlagh Dover (KU Leuven (Belgium))	SP2RC seminar
13:00		Modelling and Synthetic Observations of Waves in Solar Coronal Loops
		LT 11
	Abstract: Kink magnetohydrodynamic (MHD) waves are frequently observed in various magnetic structures of the solar atmosphere. They are currently thought to contribute significantly to coronal heating and could be used as a tool to diagnose the solar plasma. This work is a continuation of Yuan and Van Doorsselaere (2015). In that paper they synthesise the Fe IX λ171.073A emission of a coronal loop supporting a standing kink MHD mode. The kink MHD wave solution of a plasma cylinder is mapped into a semi-torus structure to simulate a curved coronal loop. They convert the calculated plasma parameters into observables by using the Forward Modelling code for optically thin plasmas (FoMo). The synthetic models were compared to coronal loop oscillations observed by the Solar Dynamic Observatories/Atmospheric Imaging Assembly. In Yuan and Van Doorsselaere (2015), the radial density profile applied is a step function (i.e coronal loop surround by a less dense ambient plasma). In my master thesis we have added a transitions region between coronal loop and the ambient plasma to better reflect the physics of the kink oscillations by following the work of Soler et al. (2013). The inclusion of this transitional region allows for resonant absorption to occur because the global kink mode frequency is fixed by the properties of the coronal loop and the Alfvén wave frequency varies depending on the local density. The goal of my work is to show what observational features will occur due to the inclusion of resonant absorption and compare with the results obtained in Yuan and Van Doorsselaere (2015).
Apr 25	Mon	Mathieu Stienon (Penn State)
14:00		Algebraic exponential maps
		Hicks Seminar Room J11
	Abstract: Exponential maps arise naturally in the contexts of Lie theory and connections on smooth manifolds. We will explain how exponential maps can be understood algebraically, how these maps can be extended to graded manifolds and how this problem leads naturally to Dolgushev-Fedosov resolutions.
Apr 25	Mon	Ernest Turro (Cambridge)	Mathematical Biology Seminar
14:00
		Hicks LT B
Apr 26	Tue	Lennart Meier (University of Bonn)	Topological modular forms
16:00		TMF with level structures
		Hicks Seminar Room J11
Apr 27	Wed	Nina Snaith (University of Bristol)	Pure Maths Colloquium
14:00		Unearthing random matrix theory in the statistics L-functions: the story of Beauty and the Beast
		Hicks Seminar Room J11
	Abstract: There has been very convincing numerical evidence since the 1970s that the positions of zeros of the Riemann zeta function and other L-functions show the same statistical distribution (in the appropriate limit) as eigenvalues of random matrices. Proving this connection, even in restricted cases, is difficult, but if one accepts the connection then random matrix theory can provide unique insight into long-standing questions in number theory. I will give a history of the attempt to prove the connection, as well as propose that the way forward may be to forgo the enticing beauty of the determinantal formulae available in random matrix theory in favour of something a little less elegant (work with Brian Conrey and Amy Mason).
Apr 27	Wed	Andrew Gilbert (Exeter)	Applied Mathematics Colloquium
14:00		Fluids/MHD
		Hicks, LT 9
Apr 28	Thu	Ben Hambly (Oxford)	Probability seminar
15:00		A simple probabilistic model for interfaces in a martensitic phase transition
		LT 4
	Abstract: A martensitic phase-transformation for a material is a first-order diffusionless transition involving a change of shape of the underlying crystal lattice. In the transition there is a symmetry breaking leading to the formation of different variants with interfaces between them and the original phase. We will consider a simple fragmentation model for the patterns that arise from this phase transition. We can encode the model using a general branching random walk (GBRW) and develop some new results for the GBRW to determine the growth rates for the proportion of interfaces which are of a certain size after a certain time. We calculate explicit descriptions of the interface asymptotics and determine a power law exponent.
Apr 29	Fri	Eleanor Vickers (Sheffield)	SP2RC seminar
13:00		MHD Surface Waves at a discontinuity
		LT 11
	Abstract: This talk gives an overview of methods and results into the investigation of magneto-acoustic surface waves along a discontinuity in pressure and density. We look at several examples of geometries of magnetic fields with respect to the interface. The discussion is confined to 2-dimensional waves along a straight interface.
May 3	Tue	Dylan Allegretti (Yale and Sheffield)
16:00		The duality conjectures for quantum cluster varieties
		Hicks Seminar Room J11
	Abstract: A result of Fock and Goncharov states that the algebra of regular functions on a cluster variety associated to a surface has a canonical vector space basis parametrized by points of a dual moduli space. This algebra of functions can be canonically quantized, and Fock and Goncharov conjectured that their canonical basis could be deformed to a canonical set of elements in the quantized algebra. In this talk, I will discuss my recent work proving Fock and Goncharov's conjectures for quantum cluster varieties associated to surfaces. The results are partly based on joint work with Hyun Kyu Kim.
May 5	Thu	Pete Dodd (Sheffield)	Statistics Seminar
14:00
		Hicks Seminar Room J11
May 5	Thu	Brendan Owens (Glasgow)	Topology Seminar
16:00		Embeddings of rational homology 4-balls
		Hicks Seminar Room J11
	Abstract: Certain 3-dimensional lens spaces are known to smoothly bound 4-manifolds with the rational homology of a ball. These can sometimes be useful in cut-and-paste constructions of interesting (exotic) smooth 4-manifolds. To this end it is interesting to identify 4-manifolds which contain these rational balls. Khodorovskiy used Kirby calculus to exhibit embeddings of rational balls in certain linear plumbed 4-manifolds, and recently Park-Park-Shin used methods from the minimal model program in 3-dimensional algebraic geometry to generalise Khodorovskiy's result. The goal of this talk is to give an accessible introduction to the objects mentioned above and also to describe a much easier topological proof of Park-Park-Shin's theorem.
May 5	Thu	Alun Owen (Worcester)	RSS Seminar
16:00		Statistics in Sport - Football Prediction Modelling
		LT3
	Abstract: The use of statistical models for predicting the probability of outcomes in football has now become an essential tool for bookmakers to “price” markets, as well as for those engaged with betting and trading on both sides of the many different football betting markets that now exist. Whilst there is now a well-established research literature in the area of football prediction models, it is evident that those using these models for betting or trading actually use modified versions of these models or hybrids to overcome some of their shortcomings. Of course these modifications or hybrid approaches typically go unpublished due to the commercial value of such work! This talk will first summarise some of the developments in predictive models in football over the last 20-30 years, and will identify some of the inadequacies of these models as well as some possible ways of solving these problems. Finally it will look at some of the more recent published work in predictive models in football and consider how things might develop over the next 20-30 years.
May 6	Fri	Andrzej Fludra (Rutherford Appleton Laboratory)	SP2RC seminar
13:00		Solar Orbiter – A new perspective on the Sun
		LT 11
	Abstract: Solar Orbiter is an ESA/NASA mission due for launch in October 2018. It will employ a suite of solar remote sensing and in-situ heliospheric instruments to address the central question of heliophysics: how does the Sun create and control the heliosphere? Solar Orbiter is designed to identify the origins and causes of the solar wind, the solar energetic particles, transient interplanetary disturbances, and the Sun's magnetic field. This talk will outline the science goals of the mission, focusing in particular on questions that can be solved using an EUV imaging spectrometer SPICE, capable of studying the source regions of outflows and ejection processes, composition of plasmas and dynamic processes in the Sun’s atmosphere.
May 9	Mon	Glenn Marion (BIology )	Mathematical Biology Seminar
14:00
		Hicks LT B
May 11	Wed	Samir Siksek (Univesity of Warwick)	Pure Maths Colloquium
14:00		Sums of seven cubes
		Hicks Seminar Room J11
	Abstract: In 1851, Carl Jacobi made the experimental observation that all integers are sums of seven non-negative cubes, with precisely 17 exceptions, the largest of which is 454. Building on previous work by Maillet, Landau, Dickson, Linnik, Watson, Bombieri, Ramaré, Elkies and many others, we complete the proof of Jacobi's observation.
May 11	Wed	Mike Jolly (Indiana)	Applied Mathematics Colloquium
14:00		Turbulence of passive tracers
		Hicks, LT 9
	Abstract: We study the influence that fluid turbulence has on passive tracer turbulence. In particular, we consider the effect the inverse cascade in 2D can have on the tracer cascade. In this case, we assume two power laws for the tracer which are consistent with the power laws of the fluid. We show that the tracer cascade range can extend up to the dissipation wave number of the fluid under certain reasonable constraints on the Grashof number of the fluid, and the gap between the injection of the tracer and the energy. For moderate Prandtl numbers the diffusive wave number is comparable to the dissipation wave number, so this provides an optimal tracer cascade range. For 3D flows we can extend the tracer cascade range up to a power of 2/3 of the diffusion wave number, which is analogous to a result for the fluid cascade in previous work.
May 12	Thu	Inaki Esnaola (Sheffield)	Probability seminar
15:00		Information in Electricity Grids
		Hicks Seminar Room J11
	Abstract: The smart grid paradigm is founded on the integration of existing power grids with advanced sensing and communication infrastructures. While the benefits provided by this setting are crucial for the future development of power grids, it also increases the dependency on data acquisition and system monitoring procedures. Central to the control and optimization of power systems is the state estimation problem in electricity grids. In this talk, we first analyze the state estimation problem with imperfect knowledge of the statistical structure of the underlying random process modelling the state variables. Within this setting, we study the theoretical limits of state estimation when partial prior knowledge is available using information theoretic measures and random matrix theory. The second problem addressed in this talk is the characterisation of the secrecy limits of the information generated by the sensing infrastructure in the grid. We provide a closed form expression for the secrecy region as a function of the network characteristics using the replica method. In the last part of the talk, we design decentralized practical attack strategies in a game theoretic setting. The validity of the presented procedures in real settings is studied through simulations in IEEE test systems.
May 12	Thu	Nick Gurski (Sheffield)	Topology Seminar
16:00		Picard 2-categories and models for the truncated sphere spectrum
		Hicks Seminar Room J11
	Abstract: A Picard n-category is a symmetric monoidal n-category in which all cells, including objects, are invertible. The Stable Homotopy Hypothesis states that Picard n-categories should be a model for the homotopy theory of stable n-types. This is known for n=0,1, and in this talk I will discuss some of the challenges moving to the n=2 case.
May 16	Mon	Charlotte Kirchhoff-Lukat (DAMTP, Cambridge)
14:00		Dorfman brackets in the context of double vector bundles
		Hicks Seminar Room J11
	Abstract: Dorfman brackets constitute a natural non-antisymmetric generalisation of Lie algebroids which still satisfy a type of Jacobi identity. Certain examples play an important role in string theory, where they encode infinitesimal gauge transformations or generalised diffeomorphisms. We (CKL in collaboration with M. Jotz-Lean) aim to understand the construction principles of Dorfman brackets on vector bundles of the form $TM+E^*$ ($E \to M$ a general vector bundle). In this talk I will show that such brackets can be viewed as restrictions of the Courant-Dorfman bracket on the standard VB-Courant algebroid $TE+T^*E$, and discuss how internal symmetries of Dorfman brackets can be described in this context.
May 18	Wed	Steve Tobias (Leeds)	Applied Mathematics Colloquium
15:00		Direct Statistical Simulation of wall-bounded, geophysical and astrophysical flows
		Hicks, LT 9
	Abstract: Fluid flows are often turbulent owing to the extreme values of the Reynolds numbers. A description of these flows via direct numerical simulation (DNS) would therefore have to be able to resolve a huge range of spatial and temporal scales, which, for certain problems, is clearly beyond the capability of current algorithms and computational resources (and indeed those of the immediate future). However these flows often display remarkable organisation. The jets on Jupiter, the differential rotation of the Sun and the solar activity cycle are all examples of this "order from chaos". Laboratory flows are likewise characterised by an interaction between systematic flows and turbulent motions. Owing to the presence of rotation and stratification flows are often (if not always) inhomogeneous and anisotropic.Here I shall describes a new programme, which we term Direct Statistical Simulation (DSS) that attempts to calculate directly the low-order statistics of such flows (such as mean flows and two-point correlation functions). DSS respects the inhomogeneity and anisotropy of the fluid systems, and is predicated on an expansion in cumulants. I shall further discuss generalisations of the quasi-linear approximation that lead to new closure schemes for these flows. As examples I shall use models for the formation of jets on giant planets and the problem of rotating couette flow.
May 19	Thu	Richard Miles (University of East Anglia / University of Uppsala)	Number Theory seminar
13:00		A dynamical zeta function for group actions
		Hicks Seminar Room J11
	Abstract: In their influential 1965 article, Artin and Mazur introduced a dynamical zeta function that can be used to encode the periodic point data of a discrete time dynamical system. This is now an intensely studied function and diverse generalisations and analogues have been developed. In this talk, I will discuss such a generalisation for dynamical systems arising from group actions. The case for this generalised function is made more compelling by its relationship with the zeta function of the acting group which is of independent interest. I will also consider some examples and natural questions in the setting of actions by compact abelian group automorphisms. For example, in this context, when is the dynamical zeta function of a group action rational?
May 19	Thu	Dler Kadir and Abdulaziz Alenazi (Sheffield)	Statistics Seminar
14:00		Dler: Markov chain Monte Carlo estimation for autoregressive time series Abdelaziz: A fully Bayesian differential-shrinkage approach to incorporating functional genomic information into case-control fine mapping studies
		Hicks, Lecture Theatre C
	Abstract: Dler: The purpose of this talk is to discuss Markov chain Monte Carlo estimation (MCMC) for stationary autoregressive time series. In order to do this, we need to derive the stationary conditions to put priors for estimating parameters of autoregressive models. Therefore, first, we study stationary conditions because the stationary affects what priors we will set up in a Bayesian setting. Next, we will apply MCMC in order to estimate parameters based on mentioned priors. Our interest is focused on the autoregressive model of order p (AR(p)) and the development and utility of Bayesian inference. One of the major obstacles in setting up a Bayesian estimation procedure for autoregressive models is the assumption of stationarity. In our view it is the reason why Bayesian estimation for such models is relatively limited. In this talk the stationary conditions of AR(2) to AR(3) are revisited. We show that for the most general model AR(p) one can achieve sufficient stationary conditions, consisting of a set of linear inequalities. This can then be exploited to set up a Metropolis within Gibbs simulation scheme. We discuss in some detail the problem in the case of AR(3) and we propose a second MCMC scheme for the AR(3) model. Throughout, we use simulated data to illustrate the proposed methodology. Abdelaziz: Bayesian approaches are particularly useful in fine mapping case-control studies as they naturally allow the inclusion of prior information relating to functional significance. We use the normal-gamma (NG) prior proposed by Griffin and Brown and modify it to allow the inclusion of function information in the form of published functional significance scores. These scores assimilate functional information from many online sources and combine them into a single score. Rather than use the correct logistic likelihood for the response which is computationally more demanding, we use the asymptotic Gaussian distribution for our maximum likelihood estimate of the model coefficients (log odds ratios). This enables us to speed up our MCMC analysis by using the Gaussian linear model framework. The NG prior assumes a hierarchical form for the coefficients which is similar to the normal-exponential-gamma prior used in Hyperlasso but allows more flexibility in the shrinkage imposed by the prior. We calibrate the NG hyperparameters using published top hits from large breast cancer genome wide association studies. We allow the functional significance scores to alter the prior probability density function of the log odds ratio on a SNP by SNP basis and show how this can be used to improve the detection of causal variants. We show by using simulated case-control data that our modified NG prior can give higher true positive rates at relevant low false positive rates compared to logistic regression, piMASS, HyperLASSO and the standard NG prior.
May 25	Wed	Adam Pound (Southampton)	Applied Mathematics Colloquium
14:00		Gravitational self-force and the future of binary inspiral modelling
		Hicks, LT 9
	Abstract: The recent observation of the black hole binary GW150914 has inaugurated the era of gravitational wave astronomy. Current, ground-based detectors are expected to primarily observe more binaries of the same sort as GW150914, composed of comparable-mass compact objects. However, planned space-based detectors will be able to observe other classes of binaries, with intermediate and extreme mass ratios, which will serve as unheralded probes of strong-field geometry and dynamics. Presently, the only viable method of modeling those binaries is provided by gravitational self-force theory, which uses tools from singular perturbation theory to construct an asymptotic approximation in the extreme-mass-ratio limit. Remarkably, by interfacing with other methods, self-force theory can also be used to improve models of comparable-mass binaries. In this talk, I discuss the foundations of self-force theory, its successes in assisting comparable-mass models, and recent progress in overcoming the largest remaining obstacle to accurate extreme-mass-ratio models: extending self-force computations to second perturbative order.
Jun 8	Wed	Alexander Kuznetsov (Steklov Institute )	Algebra / Algebraic Geometry seminar
16:00		Gushel-Mukai varieties
		Hicks Seminar Room J11
	Abstract: Gushel-Mukai varieties are dimensionally transverse intersections of a cone over Grassmannian Gr(2,5) with a quadric. They include all mildly singular Fano varieties with Picard number 1, coindex 3, and degree 10. I will discuss the geometry of this class of varieties (including their birational properties and the structure of their derived categories) and their relation to Eisenbud-Popescu-Walter sextics. This material is covered by joint works with Olivier Debarre and Alex Perry.
Jun 15	Wed	Robert Gaunt (Oxford)	Probability seminar
14:00		Rates of convergence for multivariate normal approximations by Stein's method
		LT 4
	Abstract: Stein's method is a powerful technique for obtaining distributional approximations in probability theory. We begin by reviewing Stein’s method for normal approximation. We then consider how this approach can be adapted to limits other than the normal. In particular, we see how Stein’s method for normal approximation can be extended relatively easily to the approximation of statistics that are asymptotically distributed as functions of multivariate normal random variables. We obtain some general bounds and a surprising result regarding the rate of convergence. We end with an application to the rate of convergence of Pearson's chi-square statistic. Part of this talk is based on joint work with Alastair Pickett and Gesine Reinert.
Jul 5	Tue	Jacob Lurie (Harvard University)
16:00		Elliptic Cohomology
		Lecture Theatre 5
Jul 12	Tue	Kirill Zaynullin (University of Ottawa)	Algebra / Algebraic Geometry seminar
15:00		From motives of versal flag varieties to modular representations of Hecke-type algebras
		Hicks Seminar Room J11
	Abstract: Let G be a split semisimple linear algebraic group over a field k, let E be a G-torsor over k. Let h be an algebraic oriented cohomology theory in the sense of Levine-Morel (e.g.~Chow ring or an algebraic cobordism). Consider a twisted form E/B of the variety of Borel subgroups G/B. Following the motivic Galois group approach and the Kostant-Kumar results on equivariant cohomology of flag varieties we establish an equivalence between the h-motivic subcategory generated by E/B and the category of projective modules of certain Hecke-type algebra H which depends on the root system of G, its isogeny class, on E, and on the formal group law of the theory h. In particular, taking h to be the Chow groups with finite coefficients F_p and E to be a generic torsor we obtain that all irreducible modules of the affine nil-Hecke algebra H of G with coefficients in F_p are isomorphic and correspond to the generalized Rost-Voevodsky motive for (G,p).
Jul 21	Thu	Krzysztof Klosin (CUNY)	Number Theory seminar
14:00		Deformations of Saito-Kurokawa type
		Hicks Seminar Room J11
	Abstract: I will report on recent work concerning modularity of residually reducible non-semi-simple 4-dimensional Galois representations. Such representations arise from congruences between Saito-Kurokawa lifts and stable forms on GSp(4). We will discuss how our results can potentially be used to verify some cases of the Paramodularity Conjecture of Brumer and Kramer. This is joint work with Tobias Berger.
Sep 13	Tue	Atsuhira Nagano (King's College London)	Number Theory seminar
11:00		The canonical model of a Shimura variety and periods of K3 surfaces
		Hicks Seminar Room J11
	Abstract: Class fields of imaginary quadratic fields are generated by the special values of elliptic modular forms (Kronecker’s Jugendtraum). In the 20th century, G. Shimura gave an extension of Kronecker’s Jugendtraum. His theory is called the theory of Shimura varieties. Today, the theory of Shimura varieties is an important theme in number theory and theoretically well-studied. However, to obtain explicit models of Shimura varieties is still a non-trivial problem. The main theme of this talk is to obtain an explicit model of a Shimura variety using the moduli theory of K3 surfaces. First, we will see basic properties of Shimura varieties. Afterwards, the speaker will present the canonical model of a Shimura variety via explicit periods of K3 surfaces.
Sep 13	Tue	Hironori Shiga (University of Chiba)	Number Theory seminar
13:30		The arithmetic Fuchsian groups, Fuchsian differential equations and period maps with application to number theory
		Hicks Seminar Room J11
	Abstract: The arithmetic triangle groups are listed up by K. Takeuchi in 1977. They act on the complex upper half plane as (most cases) co-compact discrete groups. By this reason, the corresponding modular functions should have an important meaning in number theory. We can use the works of G. Shimura on the theory of complex multiplication as the basement of our study. But the such a research is not completed at all still now. We speak about this story, together with one typical example of quadrangle case.
Sep 21	Wed	Antal Jarai (Bath)	Probability seminar
14:15		Sum of inverse powers of Poisson distances.
		Hicks LT10
	Abstract: Consider a planar Poisson process of constant intensity, and let S be the sum of the inverse 4-th powers of the distances of the points from the origin, which is a positive stable random variable of index 1/2. We give an approximation scheme, with explicit error bounds, for the conditional density of the point nearest to the origin given S = s. The precision of the approximation is uniform in the conditioning.
Sep 21	Wed	Jan Swart (UTIA, Academy of Sciences of the Czech Republic)	Probability seminar
15:45		Self-organised criticality on the stock market.
		Hicks LT10
	Abstract: In this talk, I will discuss a number of interacting particles on the real line that have two features in common. First, they are rank-based, in the sense that the only spatial structure that is relevant for the dynamics is the relative order of the particles. Second, they all seem to exhibit a form of behaviour known as self-organized criticality. Special attention will be given to a model for traders placing orders on a stock market, due to Stigler (1964) and Luckock (2003). Although this is a toy model that is known to be rather unrealistic, it gives important insight into some of the mechanisms that are at work on a real market. Moreover, I will show how with just some minor modifications, the model can be made much more realistic. This is joint work with M. Formentin, J. Plackova, and V. Perzina.
Sep 26	Mon	Jamie Wood (York)	Mathematical Biology Seminar
14:00		Modelling bacteria: how can mathematics contribute to combatting AMR?
		Alfred Denny Conference Room
Sep 27	Tue		Topological K-theory
14:00		Organizational Meeting
		Hicks Seminar Room J11
Oct 3	Mon	Paul Mitchener (Sheffield)	Topological K-theory
13:00		An overview of K-theory
		Hicks Seminar Room J11
	Abstract: In this talk, we shall give an overview of topological and operator K-theory, together with some of its famous applications.
Oct 4	Tue	Christos Aravanis (Sheffield)	Category Theory
14:00		Introduction to fusion categories
		LT10
	Abstract: Fusion categories are monoidal categories with properties similar to representation category of a finite group. In this talk, we will try to unwrap the definition and discuss some examples.
Oct 4	Tue	John Greenlees (Sheffield)	Topology Seminar
16:00		Rational equivariant cohomology theories and the spectrum of the sphere.
		Hicks Seminar Room J11
	Abstract: Rational G-equivariant cohomology theories can be classified in the sense that there is an algebraic model for them. The model can be viewed as a category of sheaves over the space of subgroups of G. This has the character of a category of sheaves of modules over an algebraic variety we might call the spectrum of the sphere. The slides come from the talk I gave at the Saas conference in August, but the world-view behind them has undergone two very constructive upheavals since then.
Oct 5	Wed	Alexandre Borovik (Manchester)	Pure Maths Colloquium
14:00		Black Box Groups
		Hicks Seminar Room J11
	Abstract: Some natural problems in computational algebra and cryptography require analysis of finite algebraic structures (for example, groups or fields) up to homomorphisms computable by randomised algorithms working in probabilistic polynomial time. This opens a fascinating new chapter of algebra, where we need to construct, by randomised algorithms, some structures (for example, fields) within structures of different nature (for example, groups). I will explain, as a na example, an algorithm that solves a key problem in probabilistic computational group theory. The problem was formulated in 1999 by Babai and Beals but remained intractable since then. The question a simple: you are given a few n by n matrices over a finite field of characteristic p > 0. You know that they generate a subgroup X isomorphic to SL_2(p^k). Find, in this group X, an element of order p. The catch is that X can have an astronomical number of elements, while unipotent elements are exceptionally rare. It is a search for a needle not even in the proverbial haystack, ibut in the Universe. Our algorithm has one unusual aspect. On one hand, it is an efficient practical algorithm that can be run on any laptop; on the other hand, it imitates the history of geometry of the physical world in its development from Euclid to Lobachevsky, Minkowski, Lorentz, and Planck. (joint work with Sukru Yalcinakaya)
Oct 7	Fri	Kimball Martin (Oklahoma)	Number Theory seminar
14:00		Eisenstein congruences for algebraic modular forms
		Hicks Seminar Room J11
	Abstract: Many years ago, Mazur proved congruences between weight 2 elliptic cusp forms and Eisenstein series of prime level, which have applications to nonvanishing Fourier coefficients and L-values. I will first explain a different approach to such congruences using quaternion algebras, which easily yields generalizations in level and to Hilbert modular forms. Then I will discuss joint work with Satoshi Wakatsuki generalizing this idea to Gross's algebraic modular forms, focusing on the cases of GSp(4) and, time permitting, G_2.
Oct 7	Fri	Alex Watson (Manchester)	Probability seminar
15:00		Spines in growth-fragmentations
		LT3
	Abstract: In models of fragmentation with growth, one has a number of independent cells, each of which grows continuously in time until a fragmentation event occurs, at which point the cell splits into two or more child cells of a smaller mass. Each of the children is independent and behaves in the same way as its parent. The rate of fragmentation may be infinite, and in this talk I will focus on the homogeneous case, where the rate of fragmentation does not depend on the mass of the cell. I will discuss some recent results on spine methods for Bertoin's 'compensated' fragmentation processes, with applications to the growth-fragmentation equation and derivative martingales. Based on joint work with Jean Bertoin and Quan Shi.
Oct 10	Mon	Daniel Graves (Sheffield)	Topological K-theory
13:00		An introduction to vector bundles.
		Hicks Seminar Room J11
	Abstract: In this talk, we shall discuss the foundations of the theory vector bundles.
Oct 10	Mon	Haluk Sengun (Sheffield)	Number Theory Learning Seminar
14:00		Modular forms and arithmetic manifolds
		F30
	Abstract: This term's seminar will focus on the celebrated Eichler-Shimura Isomorphism which relates spaces of modular forms and the cohomology of arithmetic manifolds as Hecke modules. In this talk I will discuss the case of classical modular forms and the cohomology of modular curves, and follow that by an overview of the general case of GL(2) over number fields.
Oct 11	Tue	Haluk Sengun (Sheffield)	Number Theory seminar
13:00		On Asymptotic Fermat's Last Theorem over Number Fields
		F28
	Abstract: Assuming two deep but standard reciprocity conjectures from the Langlands Programme, we prove that the asymptotic Fermat's Last Theorem holds for imaginary quadratic fields Q(\sqrt{-d}) with -d=2, 3 mod 4. For a general number field K, again assuming standard conjectures, we give a criterion based on the solutions to a certain S-unit equation, which if satisfied implies the asymptotic Fermat's Last Theorem. This is joint work with Samir Siksek.
Oct 11	Tue	Simon Willerton (Sheffield)	Category Theory
14:00		A brief introduction to topological quantum field theory (Fusion categories II)
		LT10
	Abstract: I will give an overview of some of the ideas of 3-d TQFTs, mentioning examples and the rich structure including knot invariants and 3-manifold invariants.
Oct 11	Tue	Sarah Whitehouse (Sheffield)	Topology Seminar
16:00		Derived $A_{\infty}$ algebras and their homotopies
		Hicks Seminar Room J11
	Abstract: The notion of a derived A-infinity algebra, due by Sagave, is a generalisation of the classical A-infinity algebra, relevant to the case where one works over a commutative ring rather than a field. I will describe a hierarchy of notions of homotopy between the morphisms of such algebras, in such a way that r-homotopy equivalences underlie E_r-quasi-isomorphisms, defined via an associated spectral sequence. Along the way, I'll give two new interpretations of derived A-infinity algebras. This is joint work with Joana Cirici, Daniela Egas Santander and Muriel Livernet
Oct 12	Wed	James Maynard (Oxford)	Pure Maths Colloquium
14:00		Primes with Missing Digits
		Hicks Seminar Room J11
	Abstract: We will talk about recent work showing there are infinitely many primes with no 7 in their decimal expansion. (And similarly with 7 replaced by any other digit.) This shows the existence of primes in a 'thin' set of numbers (sets which contain at most X^{1-c} elements less than X) which is typically vey difficult. The proof relies on a fun mixture of tools including Fourier analysis, Markov chains, Diophantine approximation, combinatorial geometry as well as tools from analytic number theory.
Oct 13	Thu	Tom Bridgeland (Sheffield)	Algebra / Algebraic Geometry seminar
16:00		Introduction to mirror symmetry
		Hicks Seminar Room J11
	Abstract: We decided that it would be nice if everyone in the algebraic geometry group gave a talk or two to give a flavour of their research interests. I volunteered to go first and immediately realised that I would need to give (at least) a lecture of background first. So this will be fairly basic: I will remind you about Calabi-Yau manifolds, the Kahler cone and periods, and give a rough statement of mirror symmetry as formulated by Candelas et al: coefficients of series expansions of periods give enumerative invariants of the mirror.
Oct 17	Mon	Edward Pearce (Sheffield)	Topological K-theory
13:00		Vector bundles on compact spaces. Part I.
		Hicks Seminar Room J11
Oct 17	Mon	Jason Matthiopoulos (Glasgow)	Mathematical Biology Seminar
14:00		Quantitative Ecology: Linking statistical models of habitat preference with mathematical models of population dynamics
		Arts Tower LT8
Oct 18	Tue	Jordan Williamson (Sheffield)	Category Theory
14:00		Constructing a 2d-TQFT from a semisimple algebra (Fusion Categories III)
		LT10
	Abstract: Given a semisimple algebra, one can construct a 2d-TQFT by interpreting the dual of a triangulation of a surface as a string diagram. We will explain this construction, and then show how this construction is related to the equivalence between 2d-TQFTs and commutative Frobenius algebras.
Oct 18	Tue	Dimitar Kodjabachev (Sheffield)	Topology Seminar
16:00		Gorenstein duality for topological modular forms with level structure.
		Hicks Seminar Room J11
Oct 19	Wed	Alexander Gorodnik (Bristol)	Pure Maths Colloquium
14:00		Distribution of rational points
		Hicks Seminar Room J11
	Abstract: We will be interested in the problem how rational points are distributed and, in particular, in analysing discrepancy of the distribution. We describe approaches for obtaining upper and lower bounds on discrepancy. It turns out that this problem leads to an interesting interplay between arithmetic geometry, ergodic theory, and the theory of automorphic representations. This is a joint work A. Ghosh and A. Nevo.
Oct 19	Wed		Cosmology, Relativity and Gravitation
16:00		Research updates
		LT9, Hicks
Oct 20	Thu	Tom Bridgeland (Sheffield)	Algebra / Algebraic Geometry seminar
16:00		Wall-crossing and Riemann-Hilbert problems
		Hicks Seminar Room J11
	Abstract: I will start by introducing BPS structures and their variations. The point of this is to axiomatise the behaviour of Donaldson-Thomas invariants under changes in stability parameters, but it is not necessary to understand anything about that to understand the definitions. I will then introduce a natural Riemann-Hilbert problem associated to such structures, which involves holomorphic maps on the complex plane with prescribed discontinuities along a collection of rays. I will also explain how to solve this problem in the simplest example using the gamma function.
Oct 24	Mon	Malte Heuer (Sheffield)	Topological K-theory
13:00		Vector bundles on compact spaces. Part II.
		Hicks Seminar Room J11
Oct 24	Mon	Attila Csikasz-Nagy (KCL)	Mathematical Biology Seminar
14:00		Systems level understanding of cell polarity regulation
		Alfred Denny Conference Room
Oct 24	Mon	David Spencer (Sheffield)	Number Theory Learning Seminar
14:00		Introduction to group cohomology. Part I.
		F-24
	Abstract: In this series of talks, we will cover the basics of the theory of cohomology of groups covering: group rings, group cohomology via cochains, group cohomology via projective resolutions, group homology, induced modules (Shapiro's Lemma), comparing cohomology groups (restriction, inflation, corestriction), cup product.
Oct 25	Tue	Andrew Jones	Number Theory seminar
13:00		Mod p base change for $GL_2$
		F28
	Abstract: Given a extension K/F, with K a quartic CM field and F imaginary quadratic, it is known that one can lift an automorphic Hecke eigenform for $GL_2(F)$ to one for $GL_2(K)$ by means of the base change transfer. Moving to mod $p$ (for $p > 2$), we no longer have this certainty, although it is conjectured that a similar result should hold. In this talk, I will discuss some recent work with Haluk Şengün and Aurel Page investigating this conjecture, and will provide examples of mod p Hecke eigenforms over imaginary quadratic fields which appear to lift to a quartic CM field, and a brief overview of the methods used to obtain this data.
Oct 25	Tue	Ed Prior (Sheffield)	Category Theory
14:00		Invariants of piecewise-linear 3-manifolds 1: spherical categories
		LT10
Oct 25	Tue	Luca Pol (Sheffield)	Topology Seminar
16:00		Connective K-theory from the global perspective
		Hicks Seminar Room J11
	Abstract: In equivariant homotopy theory there are some theories that are defined in a uniform way for all groups in a specific class, rather than just for a particular group. The idea of global stable homotopy theory is to view this collection of compatible equivariant theories as one ``global'' object. One way to formalize this idea is to consider the well-known category of orthogonal spectra and to use a finer notion of equivalence: the global equivalence. In this talk, I will give an overview on global stable homotopy theory via orthogonal spectra and I will present a global equivariant version of connective topological K-theory. Time permitting, I will explain how to generalize this construction to obtain a global equivariant version of connective K-theory of C*-algebras.
Oct 26	Wed	Robert Kerr (Warwick)	Applied Mathematics Colloquium
14:00		Scaling of Navier-Stokes trefoil reconnection
		Hicks, LT 10
	Abstract: The reconnection of a trefoil vortex knot is examined numerically to determine how its helicity and two vorticity norms behave. During an initial phase, the helicity is remarkably preserved, as reported in recent experiments (Scheeler et al. 2014a). Equally unexpected is self-similar growth in the volume-integrated vorticity squared or enstrophy Z, growth where (√ν)Z(tx) is independent of the viscosity at a configuration dependent time txtx which will be interpreted as the end of first reconnection. By rescaling tx−t for times t4tx. Furthermore, by tϵ≈2tx, a viscosity independent dissipation ϵ=νZappears. Taken together, these results could be a new template whereby smooth solutions without singularities or roughness can generate the ν→0 dissipation anomaly (finite dissipation in a finite time) that is observed in all turbulent flows.
	Slides
Oct 26	Wed	David Jordan (Sheffield)	Pure Maths Colloquium
15:00		Periodic quantum cluster algebras
		Hicks Seminar Room J11
	Abstract: Cluster algebras are commutative algebras constructed from quivers by a recursive process called mutation. They were introduced by Fomin and Zelevinsky around 2000 and there are now established connections with many areas of mathematics. Poisson structures were brought into the picture by Gekhtman, Shapiro and Vainshtein in 2003 and the closely related quantum cluster algebras followed in a 2005 paper by Berenstein and Zelevinsky. Quantum cluster algebras are fascinating examples of noncommutative rings and it is from the point of view of noncommutative ring theory that I will discuss them. There have been several papers where known noncommutative algebras, or classes of such algebras, were shown to have quantum cluster algebra structures. An alternative approach is to look for interesting new noncommutative algebras by determining quantum cluster algebras, and the associated Poisson structures on the corresponding commutative cluster algebras, arising from particular quivers. I will start with a simple example (two vertices and one arrow) to illustrate the ideas and then look at the quantum cluster algebras for a family of quivers appearing in the classification of periodic quiver mutation by Fordy and Marsh. The aims will include to present the quantum cluster algebra by generators and relations and to decide whether the algebra is noetherian. The original content of the talk is joint work with Christopher Fish.
Oct 26	Wed		Cosmology, Relativity and Gravitation
16:00		Models of Gravity conference update (Elizabeth) & research update (Sam)
		LT9, Hicks
Oct 26	Wed	Professor Stephen Senn (Competence Center for Methodology and Statistics, CRP-Sante)	Statistics Seminar
17:15		Numbers needed to mislead, meta-analysis and muddled thinking
		Lecture Theatre 4, The Diamond
	Abstract: The ardent espousal by the evidence based medicine movement of numbers needed to treat (NNT) as a way of making difficult statistical concepts simple and concrete, has has the unintended consequence of sowing confusion. Many users, including many in the evidence based movement themselves, have interpreted these statistics as indicating what proportion of patients benefit from treatment. However, they cannot deliver this information. I shall explain this, with the example of a recent Cochrane Collaboration meta-analysis of paracetamol against placebo in trials of tension headache for which the plain language summary claimed: The outcome of being pain free or having only mild pain at two hours was reported by 59 in 100 people taking paracetamol 1000 mg, and in 49 out of 100 people taking placebo (high quality evidence), meaning that only 10 in 100 people benefited because of paracetamol 1000 mg. With the aid of a simple model also illustrated (just for fun) by a simulation, I shall show that the plain language conclusion is plain wrong. The observed facts do not necessarily mean that only 10 in 100 people benefited. The combination of arbitrary dichotomies and NNTs has a dangerous ability to deceive and may be leading us to expect much more of personalised medicine than it can deliver. All welcome. Admission to the lecture is free, but registration is required.
Oct 27	Thu	Alison Parton (Sheffield, SoMaS)	Statistics Seminar
14:00		A hybrid MCMC sampler for inferring animal movements and behaviours from GPS observations
		F20
	Abstract: Although animal locations gained via GPS, etc. are typically observed on a discrete time scale, movement models formulated in continuous time are preferable; avoiding the struggles experienced in discrete time when faced with irregular observations or the prospect of comparing analyses on different time scales. A class of models able to emulate a range of movement ideas are defined by representing movement as a combination of stochastic processes describing both speed and bearing. This framework can then be extended to allow multiple behavioural modes through a continuous time Markov process. Bayesian inference for such models is described through the use of a hybrid MCMC approach. Such inference relies on an augmentation of the animal’s locations in discrete time, with a more detailed movement path gained via simulation techniques. Simulated and real data on an individual reindeer (Rangifer tarandus) will illustrate the presented methods.
Oct 27	Thu	Joe Karmazyn (University of Sheffield)	Algebra / Algebraic Geometry seminar
16:00		Rational curves and noncommutative algebra
		Hicks Seminar Room J11
	Abstract: The geometry of contracting rational curves in three folds can be studied via noncommutative algebra, and I will recap how you can pass from the geometry to the algebra and back again via moduli space constructions. As an example of the advantages of the noncommutative algebra viewpoint I plan to discuss a noncommutative interpretation of the Gopakumar-Vafa invariants attached to the curve realised by Toda.
Oct 28	Fri	Denise Lievesley (Oxford)	RSS Seminar
12:00		Reflections on Quality
		Hicks LT6
	Abstract: Denise will draw on her experience as an official statistician, in a national and international context, as well as her recent role representing users of official statistics to talk about the ways in which the definition of quality of data has changed over time – from a focus on precision to a broader set of indicators of quality including relevance, fitness for purpose, and response burden. She will discuss some of the attempts to involve users in the assessment of quality. The increased use of administrative data (and other data collected for different purposes) raises new challenges in relation to the definition, measurement and communication of quality.
Oct 28	Fri
14:00		SP2RC Discussion and Book Club
		F35
Oct 31	Mon	Rory Potter (Sheffield)	Topological K-theory
13:00		K-theory: basic definitions and properties. Part I.
		Hicks Seminar Room J11
Oct 31	Mon	Ieke Moerdijk (Sheffield)
14:00		Crash course on Line bundles, Connections, and Hamiltonian Actions
		Hicks Seminar Room J11
	Abstract: Line bundles and cocycles: we define complex line bundles over manifolds and show that these can be described in terms of 1-cocycles of nowhere zero complex functions.
Nov 1	Tue	Rudolf Chow (Sheffield)	Number Theory Learning Seminar
13:00		Introduction to group cohomology. Part II.
		F28
	Abstract: In this series of talks, we will cover the basics of the theory of cohomology of groups covering: group rings, group cohomology via cochains, group cohomology via projective resolutions, group homology, induced modules (Shapiro's Lemma), comparing cohomology groups (restriction, inflation, corestriction), cup product.
Nov 1	Tue	Caitlin McAuley, Théo Michelot, Jake Shipley (Sheffield)	Postgraduate seminars
13:00
		Hicks Seminar Room J11
Nov 1	Tue	Rhiannon Griffiths (Sheffield)	Category Theory
14:00		Invariants of piecewise linear 3-manifolds 2
		LT10
Nov 1	Tue	Jeremy Oakley (Sheffield)	Uncertainty Quantification study group
15:00		A tutorial on Bayesian calibration and history matching for inverse problems
		Hicks Seminar Room J11
	Abstract: This is the first in a series of reading group meetings on the theme of calibration/inverse problems for complex mathematical models. To start the series off, I will give an introductory-level tutorial on Bayesian calibration and history matching methods.
Nov 1	Tue	Neil Strickland (Sheffield)	Topology Seminar
16:00		The known part of the Bousfield semiring
		Hicks Seminar Room J11
	Abstract: The Bousfield semiring controls many interesting phenomena in stable homotopy theory. The literature contains many fragmentary results about the structure of this semiring. I will report on a project to combine all of these results into a single consolidated statement.
Nov 2	Wed	Roger Plymen (Southampton)	Pure Maths Colloquium
14:00		Skewes numbers
		Hicks Seminar Room J11
	Abstract: Let $\pi(x)$ denote the number of primes up to $x$, let $\mathrm{li}(x)$ denote the logarithmic integral. The prime number theorem says that $$ \pi(x) \sim \mathrm{li}(x) $$ i.e. that the ratio tends to $1$ as $x \to \infty$. If you look at any table of primes, you will find that $\pi(x) < \mathrm{li}(x)$. However, Littlewood proved in 1914 that the difference $\pi(x) - \mathrm{li}(x)$ changes sign infinitely often. This means that there is a least $X$ for which $\pi(X) > \mathrm{li}(X)$. What is $X$? No-one knows. Any upper bound for $X$ is a Skewes number. In the course of the 20th century, successive upper bounds were discovered, culminating in the Skewes number $\exp 727. 9513$. This number has $312$ digits. All the proofs depend on the explicit formula for $\pi(x)$ due to Riemann in his memoir of 1859. This talk will be accessible to staff, graduate students, and undergraduates with a first course in complex analysis.
Nov 2	Wed	Peter Taylor (Conell/Dublin)	Applied Mathematics Colloquium
14:00		New mode-sum prescriptions for quantum stress-energy tensor regularization
		Hicks, LT 10
	Abstract: Quantum gravity remains one of the most important outstanding problems in physics. In the absence of a full theory, one must rely on approximations. One particularly important approximation is semi-classical gravity, which is the treatment of quantum fields interacting with a classical spacetime metric via the semi-classical Einstein equations. Solving the semi-classical Einstein equations is notoriously difficult. The first major obstacle one encounters is that the source term -- which is the expectation value of the stress-energy tensor for some quantum fields -- is divergent. While this may be handled by normal ordering in Minkowski spacetime, the situation is more complicated in curved spacetime where there is no preferred vacuum. A formal prescription to regularize the quantum stress-energy tensor -- known as the point-splitting scheme -- dates back to DeWitt and Christensen's seminal work in the 1970s. However, applying the point-splitting scheme in a way that is amenable to numerical evaluation has remained a challenge; the first work in this direction was the work of Candelas and Howard in the 1980s. Despite some serious drawbacks, the Candelas-Howard approach has remained more or less the standard prescription for several decades. In recent years, advances in numerical relativity and new techniques for mode-sum regularization developed within the self-force community has made a fully self-consistent semi-classical evolution a realistic goal, which has given new impetus to developing practical and efficient mode-sum schemes in the quantum field theory context. I will discuss two recent independent endeavours in this direction: the first by Taylor, Ottewill and Breen and the other by Levi and Ori.
Nov 3	Thu	Ieke Moerdijk (Sheffield)
10:00		Crash course on Line bundles, Connections and Hamiltonian actions, II
		Hicks Seminar Room J11
	Abstract: Cech cohomology: we introduce Cech cohomology with coefficients in a presheaf and prove some of its basic properties (long exact sequence, acyclicity of fine sheaves, double complex lemma). We deduce that line bundles are characterized by degree 2 cohomology classes with coefficients in (the constant presheaf given by) the integers.
Nov 3	Thu	Heiko Strathmann (Gatsby, UCL)	Statistics Seminar
14:00
		Hicks Seminar Room J11
Nov 3	Thu	Amanda Turner (Lancaster University)	Probability seminar
14:00		Scaling limits of Laplacian random growth models
		LT E
	Abstract: The idea of using conformal mappings to represent randomly growing clusters has been around for almost 20 years. Examples include the Hastings-Levitov models for planar random growth, which cover physically occurring processes such as diffusion-limited aggregation (DLA), dielectric breakdown and the Eden model for biological cell growth, and more recently Miller and Sheffield's Quantum Loewner Evolution (QLE). In this talk we will discuss ongoing work on a natural variation of the Hastings-Levitov family. For this model, we are able to prove that both singular and absolutely continuous scaling limits can occur. Specifically, we can show that for certain parameter values, under a sufficiently weak regularisation, the resulting cluster can be shown to converge to a randomly oriented one-dimensional slit, whereas under sufficiently strong regularisations, the scaling limit is a deterministically growing disk.
Nov 3	Thu	Evgeny Shinder (Sheffield)	Algebra / Algebraic Geometry seminar
16:00		Zero divisors in the Grothendieck ring of varieties via K3 surfaces
		F38
	Abstract: Note non-standard room!
Nov 4	Fri	SP2RC Discussion & Book Group (SP2RC)
14:00		SP2RC Discussion & Book Group
		Hicks F35
Nov 7	Mon	Luca (Sheffield)	Topological K-theory
13:00		K-theory: basic definitions and properties. Part II.
		Hicks Seminar Room J11
Nov 7	Mon	Ieke Moerdijk (Sheffield)
14:00		Crash course in Line bundles, Connections and Hamiltonian actions, III
		Hicks Seminar Room J11
	Abstract: Connections: after completing the proof of the double complex lemma which we didn't quite finish in the previous lecture, we will discuss some differential geometry of line bundles: connections, connection 1-forms, and curvature.
Nov 7	Mon	Nigel Burroughs (Warwick)	Mathematical Biology Seminar
14:00		Tension-clock regulation of microtubule polymerisation state generates pseudo-periodic chromosome oscillations
		Alfred Denny Conference Room
	Abstract: I will present our current understanding of the mechanical regulation processes that are responsible for the oscillatory dynamics of chromosomes across the metaphase plate. In an interdisciplinary project we have used mathematical modelling and computational statistics to understand high-resolution 3+1D imaging data tracking chromosome movements during metaphase of the (HeLA) cell division cycle. We used Bayesian MCMC techniques to fit a mechanical model to 1000s of chromosome trajectories providing a means to automatically detect directional switching points. By analysis of the inferred forces at switching events we propose that chromosome oscillations are regulated by aging of the attached microtubules (a clock) and adjustment of those clock rates by the tension in the centromeric spring connecting the two chromatids (effectively a sister-sister communication). Analysis of the oscillations of this system shows that it has 4 types of oscillatory states. I will discuss our preliminary findings on the phase diagram and bifurcations in this system, and discuss how noise is essential to obtain realistic switching choreographies. This is work in collaboration with Andrew McAinsh.
Nov 7	Mon	Sam Edis (Sheffield)	Number Theory Learning Seminar
14:00		Introduction to group cohomology. Part III.
		F-28
	Abstract: In this series of talks, we will cover the basics of the theory of cohomology of groups covering: group rings, group cohomology via cochains, group cohomology via projective resolutions, group homology, induced modules (Shapiro's Lemma), comparing cohomology groups (restriction, inflation, corestriction), cup product.
Nov 10	Thu	Ieke Moerdijk (Sheffield)
10:00		Crash course on Line bundles, Connections and Hamiltonian actions, IV
		Hicks Seminar Room J11
	Abstract: The integrality theorem: We will use (the proof of) the double complex to show that the de Rham cohomology class given by the curvature 2-form corresponds to the integral cocycle cohomology class of lecture 2. This will show that the de Rham cohomology class is integral.
Nov 10	Thu	Paul Buckingham	Number Theory seminar
13:00		On the Equivariant Tamagawa Number Conjecture for relative biquadratic extensions
		F28
	Abstract: The analytic class number formula is a well-known classical result. The accumulated work of many people over the past century and a half has resulted in a conjectural Galois-theoretic generalization of it, the Equivariant Tamagawa Number Conjecture. There are few known cases of the ETNC where the base field is not simply the field of rationals. After outlining the conjecture, we will describe a class of biquadratic extensions, irrespective of the base field, for which it is possible to conclude the ETNC from a well-studied condition.
Nov 10	Thu	Thomas Michelitsch (CNRS, Paris)	Applied Mathematics Colloquium
14:00		Fractional Lattice Dynamics: Nonlocal constitutive behavior generated by power law matrix functions and their fractional continuum limit kernels
		Hicks, LT 10
	Abstract: We introduce positive elastic potentials in the harmonic approximation leading by Hamilton's variational principle to fractional Laplacian matrices having the forms of power law matrix functions of the simple local Bornvon Karman Laplacian. The fractional Laplacian matrices are well defined on periodic and infinite lattices in n=1,2,3,.. dimensions. The present approach generalizes the central symmetric second difference operator (Born von Karman Laplacian) to its fractional central symmetric counterpart (Fractional Laplacian matrix). For non-integer powers of the Born von Karman Laplacian, the fractional Laplacian matrix is nondiagonal with nonzero matrix elements everywhere, corresponding to nonlocal behavior: For large lattices the matrix elements far from the diagonal expose power law asymptotics leading to continuum limit kernels of Riesz fractional derivative type. We present explicit results for the fractional Laplacian matrix in 1D for finite periodic and infinite linear chains and their Riesz fractional derivative continuum limit kernels. The approach recovers for α=2 the well known classical Born von Karman linear chain (1D lattice) with local next neighbor springsleading in the well known continuum limit of classic local standard elasticity, and for other integer powers to gradient elasticity.We also present a generalization of the fractional Laplacian matrix to n-dimensional cubic periodic (nD tori) and infinite lattices. For the infinite nD lattice we deduce a convenient integral representation.We demonstrate that our fractional lattice approach is a powerful tool to generate physically admissible nonlocal lattice material models and their continuum representations.
	Slides
Nov 10	Thu	Dr David Wyncoll (HR Wallingford)	Statistics Seminar
14:00		National-scale multivariate extreme value analysis for coastal flood risk analysis
		Hicks Seminar Room J11
	Abstract: Coastal flooding in the UK is driven by the joint occurrence of large waves, winds and sea levels. In order to quantify the flood risk at a single site it is important to study the dependence between these variables in extreme values. The spatial dependence between coastal locations is also important for quantifying the likelihood of single large-scale coastal flooding events. We present a national-scale multivariate extreme value analysis of offshore drivers of coastal flooding in England and Wales. This appropriately captures dependences between both extreme and non-extreme driving variables at and between multiple coastal locations. The output of this analysis is a large Monte Carlo sample of plausible joint events that may be propagated though a chain of emulated numerical models to estimate the risk of large-scale coastal flooding.
Nov 10	Thu	Sajni Malde ( HR Wallingford)	Statistics Seminar
15:30
		Hicks Seminar Room J11
Nov 11	Fri	Sam Bennett (Sheffield)	SP2RC seminar
13:00
		LT 10
Nov 11	Fri	Mihai Barbulescu (Sheffield)	SP2RC Discussion & Book Group
14:00
		Hicks F35
Nov 14	Mon	Dimitar Kodjabachev (Sheffield)	Topological K-theory
13:00		Bott Periodicity.
		Hicks Seminar Room J11
Nov 14	Mon	Ieke Moerdijk (Sheffield)
14:00		Crash course in Line bundles, Connections, and Hamiltonian actions, V
		Hicks Seminar Room J11
Nov 15	Tue	Angelo Rendina (Sheffield)	Number Theory Learning Seminar
13:00		Introduction to group cohomology. Part IV.
		F28
	Abstract: In this series of talks, we will cover the basics of the theory of cohomology of groups covering: group rings, group cohomology via cochains, group cohomology via projective resolutions, group homology, induced modules (Shapiro's Lemma), comparing cohomology groups (restriction, inflation, corestriction), cup product.
Nov 15	Tue	Rhiannon Griffiths (Sheffield)	Category Theory
14:00		Invariants of piecewise linear 3-manifolds 3
		LT10
Nov 15	Tue	Jeremy Oakley (Sheffield)	Uncertainty Quantification study group
15:00		A tutorial on Bayesian calibration and history matching for inverse problems: Part 2
Nov 15	Tue	Dae Woong Lee (Chonbuk, Korea)	Topology Seminar
16:00		Strong homology, phantom maps, comultiplications and same n-types
		Hicks Seminar Room J11
	Abstract: In this talk, the following topics in algebraic topology will be briefly outlined. (1) Strong (co)homology groups (2) Phantom maps (3) Comultiplications on a wedge of spheres (4) The same n-type structures of CW-complexes
Nov 16	Wed	Tom Ward (Leeds)	Pure Maths Colloquium
14:00		The space of group automorphisms
		Hicks Seminar Room J11
	Abstract: I will discuss some of the issues that are thrown up when we try to describe the space of compact group automorphisms modulo various natural equivalences coming from dynamical systems. Much of this is joint work with Stephan Baier (Jawarharlal Nehru University, India), Richard Miles (who is in Sheffield), Shaun Stevens (UEA), Sawian Jaidee (Khon Kaen, Thailand) and Jason Bell (Waterloo, Canada).
Nov 16	Wed	Vassilios Dallas (Leeds)	Applied Mathematics Colloquium
14:00		Can we predict the large scales of turbulence?
		Hicks, LT 10
	Abstract: Absolute equilibrium (zero flux) statistical mechanics have been used effectively in the ideal case of zero viscosity to predict the cascade (finite flux) of ideal invariants across scales in dissipative turbulence. We show numerically that the statistical properties of helical hydrodynamic (HD) and helical MHD turbulence at scales larger than the forcing scale can be described to a large degree by the truncated Euler and ideal MHD equations, respectively. Therefore, the functional shape of the large scale spectra can be predicted using absolute equilibrium theory. Provided that scales sufficiently larger than the forcing scale but also sufficiently smaller than the box size are examined, then $E(k) \propto k^2$ and $H_u(k)/(kE(k)) \propto k$ in HD turbulence while $E(k) \propto k^2$ and $kH_b/E(k) \propto k^{-1}$ in MHD turbulence. In these turbulent systems equilibrium and out-of-equilibrium statistical mechanics coexist though instantaneous fluctuations of fluxes towards large and small scales.
Nov 16	Wed	Jake Shipley (Sheffield)	Cosmology, Relativity and Gravitation
16:00		Conference (Gravitational Lensing and Black Hole Shadows Workshop) and research visit updates
		LT9, Hicks
Nov 17	Thu	Kirill Mackenzie (Sheffield)
10:00		Crash course on Line bundles, Connections and Hamiltonian actions, VI
		Hicks Seminar Room J11
	Abstract: I will give a one-off lecture on a nonabelian extension of the principal question treated in Ieke's lectures (When is a closed real-valued 2-form the curvature of a connection in a complex line bundle?) This will be designed to be accessible to people who have not come to Ieke's lectures, but who are familiar with the basics of manifolds and Lie groups. Roughly speaking the question is: when is a 2-form on a manifold, which takes values in a `bundle of Lie algebras', the curvature of a connection in a principal bundle? The answer is recognizably similar to the answer in the case of complex line bundles, but the techniques are substantially different. I will cover principal bundles and their connections at the start. (If you happen to be familiar with the classification of extensions of discrete groups, or Lie algebras, by cohomology, the differences are roughly the same as the differences between when the kernel is abelian and when it is not.)
Nov 18	Fri	Mihai Barbulescu (University of Sheffield)	SP2RC seminar
13:00
		LT 10
Nov 18	Fri	Mihai Barbulescu	SP2RC Discussion & Book Group
14:00
		Hicks F35
Nov 21	Mon	Dimitar Kodjabachev (Sheffield)	Topological K-theory
13:00		Bott Periodicity. Part II.
		Hicks Seminar Room J11
Nov 21	Mon	Kirill Mackenzie (Sheffield)
14:00		Crash course in Line bundles, Connections and Hamiltonian actions, VII
		Hicks Seminar Room J11
	Abstract: I'll conclude the account, begun on Thursday, of the non-abelian extension of the Weil Lemma. I will be able to go a bit slower than I did on Thursday.
Nov 21	Mon	Ben Macarthur (Southampton)	Mathematical Biology Seminar
14:00
		Alfred Denny Conference Room
Nov 21	Mon	Di Zhang (Sheffield)	Number Theory Learning Seminar
14:00		Crash course on classical modular forms
		G-29
	Abstract: We will discuss the basic theory of classical holomorphic modular forms.
Nov 22	Tue	Sam Edis (Sheffield)	Postgraduate seminars
11:00		Congruent Numbers
		Hicks Seminar Room J11
	Abstract: Congruent numbers are the areas of right angled triangles with rational side lengths. While they are easy to define, a complete method of determining them is still not known. In this talk we will start from the definition to work up to some of what is currently known and use it as an example of why elliptic curves and L-functions are so important.
Nov 22	Tue	James Newton (King's College)	Number Theory seminar
13:00		Galois representations and the completed homology of locally symmetric spaces
		F28
	Abstract: I will discuss some applications of a variant of Taylor-Wiles patching to the study of the completed homology of locally symmetric spaces for GL_n over a CM field F. I will mostly consider the special case with n = 2, F imaginary quadratic, and p an odd prime which splits in F. In this situation we give some evidence for a conjectural relationship between p-adic Galois representations and 'p-adic Bianchi modular forms'. This is joint work with Toby Gee.
Nov 22	Tue	Christos Aravanis (Sheffield)	Category Theory
14:00		Reshetikhin-Turaev invariants 1
		LT10
	Abstract: In the previous two talks, we discussed how to define invariants of three manifolds via a triangulation of the manifold and using a spherical fusion category. Reshetikhin and Turaev defined invariants of three manifolds by applying surgery on the manifold and using modular tensor categories, quantum groups, and link polynomials. In this talk, we will start backwards, describing an appropriate setup from quantum groups and links. Time permitting, we will discuss their relation with modular tensor categories.
Nov 22	Tue	Frank Neumann (Leicester)	Topology Seminar
16:00		Spectral sequences for Hochschild cohomology and graded centers of differential graded categories
		Hicks Seminar Room J11
	Abstract: The Hochschild cohomology of a differential graded algebra or more generally of a differential graded category admits a natural map to the graded center of its derived category: the characteristic homomorphism. We interpret it as an edge homomorphism in a spectral sequence. This gives a conceptual explanation of the possible failure of the characteristic homomorphism to be injective or surjective. To illustrate this, we will discuss several examples from geometry and topology, like modules over the dual numbers, coherent sheaves over algebraic curves, as well as examples related to free loop spaces and string topology. This is joint work with Markus Szymik (NTNU Trondheim).
Nov 23	Wed	Konstanze Rietsch (King's College )	Pure Maths Colloquium
14:00		Mirror Symmetry for Grassmannians
		Hicks Seminar Room J11
	Abstract: I will report on results obtained jointly with R.Marsh. We construct the superpotential of a Grassmannian X as a regular function W on the complement of the anticanonical divisor on a Langlands dual Grassmannian, X^, and prove that it encodes Gromov-Witten invariants of the original Grassmannian via an associated Gauss-Manin system.
Nov 23	Wed	Chuong Tran (St. Andrews)	Applied Mathematics Colloquium
14:00		The pressure force in Navier--Stokes flows: Depletion of nonlinearity versus regularity
		Hicks, LT 10
	Abstract: The issue of solution regularity of the three-dimensional Navier--Stokes equations is a long-standing problem in mathematical fluid mechanics. It is well known that classical solutions exist locally in time for sufficiently smooth initial velocity fields. The question is whether such solutions remain regular globally. Active research since Leray's seminal work in the 1930s appears to have suggested a negative answer to this question. Indeed, the volume of results on partial regularity in the literature unmistakably casts doubt on the capability of viscous effects in controlling the Navier--Stokes nonlinearity. The pressure force driving Navier--Stokes flows apparently exhibits some depletion of nonlinearity. It is possbile that such depletion is sufficient to allow for a balance between nonlinear and viscous effects, thereby ensuring global regularity. This seminar presents results from recent investigations into this possibility. Regularity criteria in terms of pressure and velocity gradients along streamlines are derived and discussed.
Nov 24	Thu	Richard Cracknell (House of Commons Research)	RSS Seminar
16:30		Politicians and Statistics
		Hicks LT6
	Abstract: Political debate is frequently supported by statistics. What could otherwise be seen as conjecture becomes immutable fact with the inclusion of a few "killer" numbers. Politicians, however, do not always have the skills (or time) to source and assess data for themselves and the advent of a world of "big data" further adds to the universe of statistical possibilities. Whether the issue is joblessness, new businesses opening, migration, school enrolments, admissions to A&E – where do MPs and go for the latest, most accurate evidence? Is the data broken down by constituency or do they have to work with figures relating to council areas or regions? Who’s guaranteeing the data is accurate? Richard Cracknell is head of social statistics in the Research and Information Service of the House of Commons and it's his team MPs go to for answers. Andrew Dilnot, head of the U.K. Statistics Authority, has described the work done by Richard and his colleagues as "the UK constitution's best kept secret". Come and find out why. Richard will talk about how politicians use statistics and how his team in House of Commons equips MPs with the statistics and understanding they need.
Nov 25	Fri	Kirill Mackenzie (Sheffield)
11:00		Crash course on Line bundles, Connections and Hamiltonian actions, VIII
		F20
	Abstract: I will begin the lectures on coadjoint orbits and Hamiltonian actions. I will start with concrete examples, at a leisurely pace. No knowledge of the preceding lectures is needed.
Nov 25	Fri	Dr Abhishek Srivastava (Indian Institute of Technology (Banaras Hindu University))	SP2RC seminar
13:00		On the Estimation of Streamer's Magnetic Field in Outer Corona by Observed Kink Waves
		LT 10
	Abstract: Using MHD seismology by observed kink waves, the magnetic field profile of a coronal streamer has been investigated in outer corona. STEREO-B/EUVI temporal image data on 7 March 2012 shows an evolution of two consecutive EUV waves that interact with the footpoint of a coronal streamer evident in the co-spatial and co-temporal STEREO-B/COR- I observations. We estimate the phase velocities of the evolved kink wave perturbations by tracking it at different heights of the coronal streamer. We also estimate the electron densities inside and outside the streamer using SSI of polarized brightness images in STEREO-B/COR- 1 observations. Taking into account the MHD theory of kink waves in a cylindrical waveguide, their observed properties at various heights, and density contrast of the streamer, we estimate the radial profile of exponentially decaying magnetic field in outer corona upto 3.0 solar radii. The precisely estimated magnetic field profiles with the uncertainty less than 10% match well with the empirical profile and various observational estimations of the outer coronal magnetic field.
Nov 25	Fri	Mihai Barbulescu	SP2RC Discussion & Book Group
14:00
		Hicks F35
Nov 28	Mon	Caitlin McAuley (Sheffield)	Topological K-theory
13:00		Characteristic Classes. Part I.
		Hicks Seminar Room J11
Nov 28	Mon	Stanley Strawbridge (Cambridge)	Mathematical Biology Seminar
14:00
		Alfred Denny Conference Room
Nov 28	Mon	Kirill Mackenzie (Sheffield)
16:00		Crash course in Line bundles, Connections, and Hamiltonian Actions, IX
		LT 10
	Abstract: I will demonstrate the symplectic structure on coadjoint orbits and go on to discuss Hamiltonian actions.
Nov 29	Tue	Ariel Weiss (Sheffield)	Number Theory Learning Seminar
13:00		The Eichler-Shimura Isomorphism. Part I.
		F28
Nov 29	Tue	Christos Aravanis (Sheffield)	Category Theory
14:00		Reshetikhin-Turaev invariants 2
		LT10
	Abstract: In the first talk, we discussed basic notions of links and quantum groups. In this talk, we will define the associated quantum invariants of tangles and links and will introduce the notion of modular tensor category. Then, we will use the latter to construct invariants of three dimensional manifolds, after N. Reshetikhin and V. Turaev.
Nov 29	Tue	Oliver Jones	Uncertainty Quantification study group
15:00		Discussion of Knowles, J. (2005). ParEGO: A hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems, IEEE Transactions on Evolutionary Computation, 10 (1), pp. 50-66.
		Hicks Seminar Room J11
Nov 29	Tue	Joao Faria Martins (Leeds)	Topology Seminar
16:00		Infinitesimal 2-braidings and KZ-2-connections.
		Hicks Seminar Room J11
	Abstract: I will report on joint work with Lucio Cirio on categorifications of the Lie algebra of chord diagrams via infinitesimal 2-braidings in differential crossed modules.
Nov 30	Wed	Alex Wilkie (Manchester)	Pure Maths Colloquium
14:00		Diophantine properties of analytic sets
		Hicks Seminar Room J11
	Abstract: The motivation behind this talk is to make precise the feeling that if an analytic (or otherwise well-behaved) function takes, in a suitable sense, many rational values for rational arguments, then there should be algebraic reasons for this. For example, a result of Bombieri and Pila from 1989 states that if $f:[0, 1] \to [0, 1]$ is a real analytic function, then either $f$ is algebraic (over $\mathbb{Q}(x)$) or else for all $\epsilon > 0$ and all sufficiently large $H$, there are at most $H^{\epsilon}$ pairs of rationals $p, q$ with denominators bounded by $H$ such that $f(p) = q$. It was suspected at the time that a similar result should be true for functions of many variables and much work was done in dimensions two and three by using the classical theory of analytic sets. However, the general case was finally solved (by Pila and myself in 2006) by setting the problem in the much wider and more flexible framework of o-minimal structures (a notion from Mathematical Logic). I shall discuss these developments and, if time permits, their applications to some classical number theoretic problems.
Nov 30	Wed	John Gibbon (Imperial)	Applied Mathematics Colloquium
14:00		Analysis of PDEs involving the Rayleigh-Taylor instability
		Hicks, LT 10
	Abstract: The phenomenon of the Rayleigh-Taylor instability (RTI), involving the mixing of a heavy fluid overlaying a lighter, has a long history, not least because it occurs in laboratory tank and plasma fusion experiments, multi-phase physics and astro-physical phenomena. The approach taken by different schools varies widely. We will briefly review this work but spend most of the talk on what is known as the variable density model (VDM) pioneered by Cook and Dimotakis (2001) and Livescu and Ristorcelli (2007). The PDEs, coupled to the 3D Navier-Stokes equations, have a remarkably elegant nature but pose hard technical challenges. Our analysis uses the data generated by Daniel Livescu (LANL) and available on the Johns Hopkins Turbulence data-base (JHTDB). If time permits I will briefly discuss the occurrence of the RTI at interfaces in multi-phase physics which involves the coupling of the 3D Navier-Stokes equations to the 3D Cahn-Hilliard equations.
Dec 1	Thu	Kirill Mackenzie (Sheffield)
10:00		Crash course on Line bundles, Connections and Hamiltonian actions, X
		Hicks Seminar Room J11
	Abstract: I will give an exposition of the two main results stated on Monday; that the coadjoint orbits of a connected Lie group are the symplectic leaves of the Lie algebra dual with its Poisson structure, and that the Marsden-Weinstein reduced spaces of a Hamiltonian action are the symplectic leaves of the quotient manifold (assumed to exist) with its Poisson structure. The proofs won't be complete in every detail, but should give an idea of what is involved. I aim to be faster than last Friday but slower than Monday.
Dec 1	Thu	Chistian Fonseca Mora	Probability seminar
14:00
		Hicks Seminar Room J11
Dec 1	Thu	Paul Johnson (Sheffield)	Algebra / Algebraic Geometry seminar
16:00		Tropical geometry and Gromov-Witten theory I
		Hicks Seminar Room J11
Dec 2	Fri	No Seminar This Week	SP2RC seminar
13:00
		LT 10
Dec 2	Fri	Mihai Barbulescu	SP2RC Discussion & Book Group
14:00
		Hicks F35
Dec 5	Mon	Eoin Murphy (Sheffield)	Topological K-theory
13:00		Characteristic Classes. Part II.
		Hicks Seminar Room J11
Dec 5	Mon	Kirill Mackenzie (Sheffield)
14:00		TBA
		Hicks Seminar Room J11
Dec 5	Mon	Angela Oliveira Pisco (KCL)	Mathematical Biology Seminar
14:00		Modelling the postnatal dermal maturation process during skin development
		Alfred Denny Conference Room
Dec 5	Mon	Ciaran Schembri (Sheffield)	Number Theory Learning Seminar
14:00		The Eichler-Shimura isomorphism. Part II.
		F-24
Dec 6	Tue	Jolanta Marzec (Durham)	Number Theory seminar
13:00		On L-functions attached to Jacobi forms of higher index
		F28
	Abstract: Jacobi forms have been studied by several people and it has been known that they enjoy many similar properties to those possessed by Siegel modular forms. Therefore it is natural to ask whether the same holds for the associated L-functions (even though it is not known whether they may be identified with L-functions obtained from Galois representations). First of all: do they have meromorphic continuation and satisfy functional equation? can we say anything about their poles? During the talk we will briefly introduce Jacobi forms and explain how one can use a doubling method to associate to them a (standard) L-function. We will present current knowledge on their properties and discuss challenges one have to face if (s)he works with Jacobi forms of higher index and non-trivial level. This is joint work with Thanasis Bouganis.
Dec 6	Tue	Daniel Schaeppi (Regensburg)	Category Theory
14:00		Higher distributive laws
		LT10
Dec 6	Tue	Dean Barber (Sheffield)	Topology Seminar
16:00		A combinatorial model for Euclidean configuration spaces
		Hicks Seminar Room J11
	Abstract: Configuration spaces appear in many areas of mathematics. They are simple to define but produce extremely complicated spaces. In this talk, we will introduce a family of posets, indexed by the natural numbers and finite sets, called the poset of chained linear preorders. It turns out that the geometric realisations of these posets are homotopy equivalent to configuration spaces on real vector spaces, and that the combinatorics involved can reveal some of the homotopical properties of these spaces.
Dec 7	Wed	Ping Xu (Penn State)	Pure Maths Colloquium
14:00		Symplectic realizations of Poisson manifolds
		Hicks Seminar Room J11
	Abstract: Poisson structures were originally invented in the early 19th century to provide a framework for optics and classical mechanics. In this talk, we will discuss the existence of symplectic realizations of Poisson manifolds, a longstanding problem which can be traced back to Sophus Lie. In particular, we will present an explicit existence result for arbitrary holomorphic Poisson manifolds.
Dec 8	Thu	Stefano Castruccio (Newcastle)	Statistics Seminar
14:00		Global Space-Time Emulators for Ensemble of Opportunities: Assessing Scenario Uncertainty for CMIP5
		Hicks Seminar Room J11
	Abstract: Simulating Earth System Models (ESMs) is among the most challenging exercises of contemporary science. ESMs require an extremely high-dimensional input comprising of a value of the forcing scenario for each year, and produce an even higher dimensional output in space, time and variables. Given the considerable computational and logistic challenges of performing even a small set of simulations, an ensemble comprises of a very limited number of runs. In the case of the CMIP5 ensemble, the reference for the latest IPCC assessment report, each modelling group submitted long-term simulations under at most four scenarios, thus providing very limited information for policy making. An emulator in scenario space can be developed to overcome these limitations. However, the modest number of runs, paired with the extremely large dimensionality of the input and output space, poses significant challenges in the development of the statistical methodology. In this talk, I will present a scenario emulator for ESMs that leverages on the temporal structure of the input/output space, on the causality principle and on the gridded geometry of the output. I will present an application to this methodology for temperature and wind data in the case of two ensembles, and I will show how the emulator provides accurate results for a dataset of tens of millions of data points.
Dec 8	Thu	Balint Toth	Probability seminar
14:00		Central Limit Theorem for Random Walks in Doubly Stochastic Random Environment
		LT E
	Abstract: We prove a CLT under diffusive scaling for the displacement of a random walk on $Z^d$ in stationary and ergodic doubly stochastic random environment, under the $H_{-1}$-condition imposed on the drift field. The condition is equivalent to assuming that the stream tensor of the drift field be stationary and square integrable. Based on joint work with Gady Kozma (Weizmann Institute).
Dec 8	Thu	Finn Lindgren (Edinburgh)	Statistics Seminar
15:30		EUSTACE: Latent Gaussian process models for weather and climate reconstruction
		Hicks Seminar Room J11
	Abstract: The EUSTACE project will give publicly available daily estimates of surface air temperature since 1850 across the globe for the first time by combining surface and satellite data using novel statistical techniques. To this end, a spatio-temporal multiscale statistical Gaussian random field model is constructed, using connections between SPDEs and Markov random fields to obtain sparse matrices for the practical computations. The extreme size of the problem necessitates the use of iterative solvers, making use of the multiscale structure of the model to design an effective preconditioner.
Dec 8	Thu	Paul Johnson (Sheffield)	Algebra / Algebraic Geometry seminar
16:00		Tropical geometry and Gromov-Witten theory II
		F38
Dec 9	Fri	Antonio Ferriz Mas (Departamento de Fısica Aplicada, Facultad de Ciencias de Orense, Universidad de Vigo, E-32004 Orense (Spain))	SP2RC seminar
13:00		Is there a planetary influence on solar activity?
		LT 10
	Abstract: An international team based at the ETH-Zurich has reconstructed the cycles of solar magnetic activity over the past 10,000 years using ice cores from Greenland and Antarctica, in which radionuclides produced by cosmic rays are stored. The analysis of the resulting time series suggests that the relatively small torque exerted by the planets may be the cause of the long-term cycles of solar activity. The well-known periodicities of 88, 104, 150, 208 and 506 years observable for the last 10,000 years correspond precisely to the periodic changes in the torque exerted by the planets on a thin layer in the solar interior known as the tachocline. Marking a transition between the radiative and convective zones in the Sun, the tachocline is believed to play a fundamental role in the generation and storage of the magnetic flux responsible for the sunspot cycle. In this talk I will focus on a possible physical mechanism that could cause the coupling between the planetary forcing and the long-term variation of the magnetic activity.
Dec 9	Fri	Mihai Barbulescu	SP2RC Discussion & Book Group
14:00
		Hicks F35
Dec 12	Mon	Haluk Sengun (Sheffield)	Topological K-theory
13:00		The Chern character.
		Hicks Seminar Room J11
	Abstract: We will discuss the Chern character isomorphism between K-theory and cohomology.
Dec 13	Tue	Haluk Sengun (Sheffield)	Number Theory Learning Seminar
13:00		Hecke Operators on group cohomology and the Eichler-Shimura Isomorphism
		F-28
	Abstract: We will introduce Hecke operators on group cohomology and prove that the Eichler-Shimura isomorphism is not just an isomorphism of vector spaces but of Hecke modules. In the second half of the talk, we shall derive a dimension formula for the cohomology of PSL(2,Z).
Dec 13	Tue	Christos Aravanis (Sheffield)	Category Theory
14:00		Modular Tensor Categories and Invariants of 3d-manifolds
		LT10
	Abstract: In this talk, we will define the invariants of Reshetikhin and Turaev for three manifolds which are obtained as a surgery of the three sphere along a link. To do this, we will use the quantum invariants of links which constructed in the previous two talks and will introduce a ribbon fusion category with a non-degeneracy condition, the modular tensor category.
Dec 13	Tue	Jeremy Oakley and Richard Wilkinson	Uncertainty Quantification study group
15:00		Calibration, history matching and ABC.
Dec 13	Tue	Andrew Baker (University of Glasgow)	Topology Seminar
16:00		Hopf invariant one elements and E-infinity ring spectra
		Hicks Seminar Room J11
	Abstract: At the prime 2, there are 4 Hopf invariant one elements (mod 2). These can be used to build some small complexes which also appear as low dimensional skeleta of some important classifying spaces and Thom spectra over them. Passing to free infinite loop spaces we can build some additional Thom spectra E-infinity ring spectra which have interesting properties. These have E-infinity ring maps to some important spectra including kO and tmf. I will describe these spectra and some conjectures about splitting them and survey what is known so far.
Dec 14	Wed	Andrew Baker (Glasgow)	Pure Maths Colloquium
14:00		Derived commutative rings
		Hicks Seminar Room J11
	Abstract: Derived commutative rings are supposed to be commutative ring-like entities with additional homotopy theoretic data. There are several candidates for these including simplicial commutative rings, E-infinity dgas, E-infinity ring spaces or spectra or equivalent topology versions. I will explain the basic ideas involved in introducing homotopical versions of algebraic structures, then discuss the implications for the homology of spaces with such structure.
Dec 15	Thu	Neils Jacob (University of Swansea)	Probability seminar
14:00		Is there some semi-classical limit theory possible related to Levy processes?
		LT3
	Abstract: A Levy process is generated by a pseudo-differential operator the symbol of which is the negative of a continuos negative definite function. You may add to the generator a potential and look at this new operator as a type of Schroedinger operator, for example so called relativistic Schroedinger operators fall into this class. The problem we want to address, better we want to present first ideas to, is the following : Consider the Hamiltonian function associated with the Schroedinger operator and use this as starting point to develop a “classical mechanics”. Can we consider “classical trajectories” with respect to this “mechanics” as limits of scaled solutions of the Schroedinger operator.
Dec 16	Fri	Mihai Barbulescu	SP2RC Discussion & Book Group
14:00
		Hicks F35
Jan 9	Mon	Barbara Bolognese (Sheffield)	Algebra / Algebraic Geometry seminar
11:30		Lecture 1: Triangulated and derived categories
		F20
	Abstract: This lecture series is part of a workshop on "Stability conditions, Donaldson-Thomas invariants and cluster varieties". More information about the workshop can be found at http://www.tom-bridgeland.staff.shef.ac.uk/workshop.html
Jan 9	Mon	Dylan Allegretti (Sheffield)	Algebra / Algebraic Geometry seminar
14:00		Lecture 1: Cluster varieties and quantization
		F20
	Abstract: This lecture series is part of a workshop on "Stability conditions, Donaldson-Thomas invariants and cluster varieties". More information about the workshop can be found at http://www.tom-bridgeland.staff.shef.ac.uk/workshop.html
Jan 9	Mon	Sven Meinhardt (Sheffield)	Algebra / Algebraic Geometry seminar
15:30		Lecture 1: The motivic Hall algebra
		F20
	Abstract: This lecture series is part of a workshop on "Stability conditions, Donaldson-Thomas invariants and cluster varieties". More information about the workshop can be found at http://www.tom-bridgeland.staff.shef.ac.uk/workshop.html
Jan 9	Mon	Tom Bridgeland (Sheffield)	Algebra / Algebraic Geometry seminar
17:00		Lecture 1: Overall aims. Simple tilts in CY3 categories.
		F20
	Abstract: This lecture series is part of a workshop on "Stability conditions, Donaldson-Thomas invariants and cluster varieties". More information about the workshop can be found at http://www.tom-bridgeland.staff.shef.ac.uk/workshop.html
Jan 10	Tue	Dylan Allegretti (Sheffield)	Algebra / Algebraic Geometry seminar
10:00		Lecture 2: Moduli spaces of local systems
		F20
Jan 10	Tue	Sven Meinhardt (Sheffield)	Algebra / Algebraic Geometry seminar
11:30		Lecture 2: Integration map and Poisson automorphisms
		F20
Jan 10	Tue	Tom Bridgeland (Sheffield)	Algebra / Algebraic Geometry seminar
14:00		Lecture 2: Exchange graph. Space of stability conditions. Cluster variety.
		F20
Jan 10	Tue	Barbara Bolognese (Sheffield)	Algebra / Algebraic Geometry seminar
15:30		Lecture 2: Stability conditions on abelian and triangulated categories
		F20
Jan 11	Wed	Sven Meinhardt (Sheffield)	Algebra / Algebraic Geometry seminar
10:00		Lecture 3: Donaldson-Thomas invariants
		F20
Jan 11	Wed	Tom Bridgeland (Sheffield)	Algebra / Algebraic Geometry seminar
11:30		Lecture 3: Examples from triangulated surfaces: triangulations, quadratic differentials.
		F20
Jan 11	Wed	Barbara Bolognese (Sheffield)	Algebra / Algebraic Geometry seminar
14:00		Lecture 3: Examples of stability conditions
		F20
Jan 11	Wed	Dylan Allegretti (Sheffield)	Algebra / Algebraic Geometry seminar
15:30		Lecture 3: Teichmüller and lamination spaces
		F20
Jan 12	Thu	Tom Bridgeland (Sheffield)	Algebra / Algebraic Geometry seminar
10:00		Lecture 4: Wall-crossing formula for DT invariants.
		F20
Jan 12	Thu	Barbara Bolognese (Sheffield)	Algebra / Algebraic Geometry seminar
11:30		Lecture 4: The space of stability conditions
		F20
Jan 12	Thu	Dylan Allegretti (Sheffield)	Algebra / Algebraic Geometry seminar
14:00		Lecture 4: Canonical bases for coordinate rings
		Hicks Seminar Room J11
Jan 12	Thu	Iakovos Androulidakis (Athens)
14:00		Almost regular Poisson manifolds and their holonomy groupoids. Visit of Professor Androulidakis supported by the MSRC,
		LT 11
	Abstract: We introduce a big class of Poisson manifolds, the "almost regular" ones. Roughly, these are the Poisson manifolds whose symplectic foliation is regular in a dense open subset. All regular Poisson manifolds are included in this class, as well as all the log-symplectic manifolds and certain Heisenberg-Poisson manifolds. We are looking for desingularizations of such structures. A natural candidate is the holonomy groupoid of the symplectic foliation, which is always smooth in this category. We show that, moreover, this is a regular Poisson groupoid. In the case of log-symplectic manifolds it coincides with the symplectic groupoid constructed by Gualtieri and Li. And for the Heisenberg-Poisson manifolds it is Connes' tangent groupoid. All this hints that various blow-up constructions in Poisson geometry might be replaced by the systematic construction of the holonomy groupoid of a singular foliation
Jan 12	Thu	Sven Meinhardt (Sheffield)	Algebra / Algebraic Geometry seminar
15:30		Lecture 4: Vanishing cycles
		F20
Jan 13	Fri	Barbara Bolognese (Sheffield)	Algebra / Algebraic Geometry seminar
10:00		Lecture 5: Stability conditions and MMP
		F20
Jan 13	Fri	Dylan Allegretti (Sheffield)	Algebra / Algebraic Geometry seminar
11:30		Lecture 5: Representations of quantized cluster varieties
		F20
Jan 13	Fri	Sven Meinhardt (Sheffield)	Algebra / Algebraic Geometry seminar
14:00		Lecture 5: The cohomological Hall algebra
		F20
Jan 13	Fri	Tom Bridgeland (Sheffield)	Algebra / Algebraic Geometry seminar
15:30		Lecture 5: Riemann-Hilbert problems.
		F20
Jan 16	Mon	John Greenlees (Sheffield)
11:00		What we want from G spectra
		Hicks Seminar Room J11
Jan 17	Tue	Jordan Williamson (Sheffield)
14:00		Orthogonal G-spectra
		Hicks Seminar Room J11
Jan 17	Tue	Sara Kalisnik (Brown)	Topology Seminar
16:00		A short introduction to applied topology
		Hicks Seminar Room J11
	Abstract: In the last two decades applied topologists have developed numerous methods for ‘measuring’ and building combinatorial representations of the shape of the data. The most famous example of the former is persistent homology and of the latter, mapper. I will briefly talk about both of these methods and show several successful applications. Time permitting I will talk about my work on making persistent homology easier to combine with standard machine learning tools.
Jan 19	Thu	Jordan Williamson (Sheffield)
15:00		Orthogonal G-spectra II
		Hicks Seminar Room J11
Jan 20	Fri	Dr Jiajia Liu (University of Science and Technology of China)	SP2RC seminar
13:00		Energy Rules of Solar Jets from Observational Perspectives
		LT 11
	Abstract: Solar jets are bulks of plasma materials ejected along elongated trajectories from the solar surface into the atmosphere of the Sun, often leaving the inner corona and determining the physical conditions far outwards in the interplanetary space. These impulsive and energetic ejecta are one of the most common dynamic phenomena occurring within the solar atmosphere. They are often accompanied by (nano-)flares, and some times by Coronal Mass Ejections (CMEs) and radio bursts, which could lead to significant changes of the space weather and terrestrial magnetic fields. After the nearly one-century efforts studying solar jets, we now have mature models for solar jets explaining the process of how magnetic reconnection triggers jets. However, due to the limits of the observational technology, many issues such as the detailed dynamics of, the energy transport during and the interaction with waves of solar jets are not well addressed before. In this talk, I will introduce part of my work during the past few years on the topic of "Energy Rules of Solar Jets from Observational Perspectives". Via high-resolution observations from the SDO and STEREO, I try to address the following questions of solar jets: (1) how the free magnetic energy is distributed between the thermal and kinetic energy during magnetic reconnection, (2) how the kinetic energy of solar jets is gained during and after the magnetic reconnection, and (3) how further release of the free magnetic reconnection proceeds after solar jets.
Jan 24	Tue	Luca Pol (Sheffield)
14:00		Complex cobordism and K theory with reality
Jan 24	Tue	Jonathan Sykes	Uncertainty Quantification study group
15:00		Discussion of "Bayesian History Matching of Complex Infectious Disease Models Using Emulation: A Tutorial and a Case Study on HIV in Uganda", by Andrianikis et al.
		Hicks Seminar Room J11
Jan 26	Thu	Luca Pol (Sheffield)
15:00		Change of groups
Jan 27	Fri	Prof. B. Hindman (University of Colorado, Boulder)	SP2RC seminar
13:00		Solar convection in the rotationally constrained regime
		LT 11
	Abstract: Despite knowing that convection and rotation are indispensable components of the solar dynamo, we know vexingly little about how the influence of rotation manifests across the broad range of convective scales present in the Sun. We do know that the structure of deep meridional circulation, which may bear on the timing of the solar cycle, is sensitive to the degree of rotational constraint felt by its underlying convective motions. Similarly, the solar differential rotation, a vital source of large-scale shear in some dynamo models, results from convective motions that transport not just heat, but angular momentum. Rotation imbues convection with a sense of helicity, supplying a source of turbulent EMF to the dynamo, and it is only in regimes of strong rotational constraint that fully nonlinear models of stellar convection have evinced cyclic dynamo behavior. Current helioseismic measurements of the convective flows suggest that rotational influence is strong within the deep convection zone, but are inconsistent in how strong. Therefore, it is prudent to ask ourselves how rotation shapes the spectral distribution of convective power. I will present numerical results from a series of nonrotating and rotating convection simulations conducted in full spherical geometry. This presentation will focus on how convective spectra differ between the rotating and non-rotating models and how that behavior changes as simulations are pushed toward more turbulent and/or more rotationally-constrained regimes. I will conclude with a discussion of the implications that strong rotational constraint in the deep convection zone should have on the surface convective and how decades of surface observations may need re-interpretation.
Jan 31	Tue	Dimitar Kodjabachev (Sheffield)
14:00		Mackey functors
Feb 2	Thu	Dimitar Kodjabachev (Sheffield)
15:00		Fixed point functors
Feb 3	Fri	Dr. Rekha Jain (University of Sheffield)	SP2RC seminar
13:00
		LT 11
Feb 6	Mon	Moty Katzman (Sheffield)
02:00		Cohen-Macaulay modules
		Hicks Seminar Room J11
Feb 6	Mon	Torbjorn Lundh (Chalmers)	Mathematical Biology Seminar
14:00		Four surgery problems "solved" by a "mathematical" approach
		Hicks LT9
Feb 7	Tue	Jeremy Oakley (Sheffield)	Uncertainty Quantification study group
15:00		Discussion of Wu, H., & Browne, M. W. (2015). Quantifying adventitious error in a covariance structure as a random effect. Psychometrika.
		Hicks Seminar Room J11
Feb 7	Tue	Jeff Giansiracusa (Swansea)	Topology Seminar
16:00
		Hicks Seminar Room J11
Feb 8	Wed	John Coates (University of Cambridge)	Pure Maths Colloquium
14:00		The conjecture of Birch and Swinnerton-Dyer
		Hicks Seminar Room J11
	Abstract: The conjecture of Birch and Swinnerton-Dyer is one of the principal open problems in number theory today. In my lecture, I shall give a brief account of the history of the conjecture, its precise formulation, and the partial results obtained so far in support of it.
Feb 8	Wed	George Papadakis (Imperial)	Applied Mathematics Colloquium
14:00		Nonlinear optimal control of bypass transition in a boundary layer flow
		Hicks, LT 10
	Abstract: We apply and assess a nonlinear optimal control strategy to suppress bypass transition in a zero-pressure-gradient boundary layer. To this end, a Lagrange variational formulation is employed that results in a set of adjoint equations. The optimal wall actuation (blowing and suction from a control slot) is found by solving iteratively the nonlinear Navier-Stokes and the adjoint equations in a forward/backward loop using DNS. The optimization is performed in a finite time horizon. Large values of optimization horizon result in instability of the adjoint equations. The control slot is located exactly in the region of transition. The results show that the control is able to significantly reduce the objective function, which is defined as the spatial and temporal integral of the quadratic deviation from the Blasius profile plus a term that quantifies the control cost. The physical mechanism with which the actuation interacts with the flow field is investigated and analysed in relation to the objective function employed. The spanwise averaged velocity is distorted by the control action, resulting in a significant reduction of the skin friction coefficient. We performed simulations with and without zero-net mass flow constraint of the actuation velocity. Results are also compared with uniform blowing using the same time-average velocity obtained from the non-linear optimal algorithm.
Feb 10	Fri	Dr Andrew Leonard (University of Sheffield)	SP2RC seminar
13:00
		F41
Feb 13	Mon	Moty Katzman (Sheffield)
02:00		Maximal Cohen Macaulay modules over hypersurfaces: matrix factorizations and periodic resolutions
		Hicks Seminar Room J11
Feb 14	Tue	Nick Kuhn (Virginia)	Topology Seminar
16:00		The circle product of O-bimodules with O-algebras, with applications.
		Hicks Seminar Room J11
	Abstract: If O is an operad (in a friendly category, e.g. the category of S-modules of stable homotopy theory), M is an O-bimodule, A is an O-algebra, then the circle product over O of M with A is again an O-algebra. A useful derived version is the bar construction B(M,O,A). We survey many interesting constructions on O-algebras that have this form. These include an augmentation ideal filtration of an augmented O-algebra A, the topological Andre-Quillen homology of A, the topological Hochschild homology of A, and the tensor product of A with a space. Right O-modules come with canonical increasing filtrations, and this leads to filtrations of all of the above. In particular, I can show that a filtration on TAQ(A) defined recently by Behrens and Rezk agrees with one I defined about a decade ago, as was suspected. This is joint work with Luis Pereira.
Feb 15	Wed	Nicola Gambino (University of Leeds)	Pure Maths Colloquium
14:00		Commutative 2-algebra, operads, and analytic functors
		Hicks Seminar Room J11
	Abstract: Standard commutative algebra is based on commutative monoids, Abelian groups and commutative rings. In recent years, there has been some progress in developing an area that may be referred to as commutative 2-algebra, in which the familiar notions used in commutative algebra are replaced by their categorified counterparts (for example, commutative monoids are replaced by symmetric monoidal categories). The aim of this talk is to explain the analogy between standard commutative algebra and commutative 2-algebra, and to outline how this analogy suggests analogues of basic aspects of algebraic geometry. In particular, I will describe how some joint work with Andre’ Joyal on operads and analytic functors fits in this context.
Feb 15	Wed	Felix Ng (Department of Geography, Sheffiled)	Applied Mathematics Colloquium
15:00		Grain-scale processes in the Earth's polar ice sheets
		Hicks, LT 10
	Abstract: The spreading of the Antarctic and Greenland Ice Sheets is a slow viscous flow with nonlinear rheology. Besides temperature, grain sizes and crystal orientation within the polycrystalline ice are important factors behind the rheology. After giving this glaciological background, I will describe two mathematical models recently built to understand grain-size evolution. The first model is formulated to capture the observed grain-size profiles in ice cores. The second model tackles the fundamental process of normal grain growth (NGG), a coarsening process that occurs in metals as well as ice.
Feb 20	Mon	Nebojsa Pavic (Sheffield)
02:00		Singularity category and MCM sheaves
		Hicks Seminar Room J11
Feb 20	Mon	Gary Mirams (Nottingham)	Mathematical Biology Seminar
14:00
		Alfred Denny Conference Room
Feb 21	Tue	Paul Gardner (Sheffield)	Uncertainty Quantification study group
15:00		The use of Bayesian calibration in the prediction of damage in structures
		Hicks Seminar Room J11
	Abstract: This talk will include an overview of the field of structural health monitoring and damage identification, where the use of Bayesian calibrated models fit in and the aims of using this technique. It will conclude with challenges and future aims of using Bayesian calibrated subsystem models to make full system predictions of damage.
Feb 21	Tue	Angelica Osorno (Reed College)	Topology Seminar
16:00		On equivariant infinite loop space machines
		Hicks Seminar Room J11
	Abstract: An equivariant infinite loop space machine is a functor that constructs genuine equivariant spectra out of simpler categorical or space level data. In the late 80's Lewis-May-Steinberger and Shimakawa developed generalizations of the operadic approach and the Gamma-space approach respectively. In this talk I will describe work in progress that aims to understand these machines conceptually, relate them to each other, and develop new machines that are more suitable for certain kinds of input. This work is joint with Anna Marie Bohmann, Bert Guillou, Peter May and Mona Merling.
Feb 23	Thu		Number Theory Learning Seminar
13:00		Organizational First Seminar
		Hicks Seminar Room J11
	Abstract: Organizational meeting: all interested parties are invited.
Feb 24	Fri	Alex Shukhobodskiy (University of Sheffield)	SP2RC seminar
13:00		Kink oscillations of expanding coronal loops
		F41
	Abstract: Kink waves and oscillations in a thin expanding magnetic tube in the presence of flow are studied. The tube consists of a core region and a thin transitional region at the tube boundary. In this region the plasma density monotonically decreases from its value in the core region to the value outside the tube. Both the plasma density and velocity of background flow vary along the tube and in time. Using the multiscale expansions the system of two equations describing the kink oscillations is derived. When there is no transitional layer the oscillations are described by the first of these two equations. This equation is used to study the effect of plasma density variation with time on kink oscillations of expanding tube with a sharp boundary. It is assumed that the characteristic time of the density variation is much larger than the characteristic time of kink oscillations. Then the WKB method is used to derive the expression for the aidiabatic invariant, which is the quantity that is coserved when the plasma density varies. The general theoretical results are applied to the kink oscillations of coronal magnetic loops. The expanding loops with the half-circle shape is considered and it is assumed that the plasma temperature inside a loop decays exponentially. The dependencies of the fundamental mode frequency, the ratio of frequencies of the first overtone and fundamental mode, and the oscillation amplitude on time are calculated numerically.
Feb 27	Mon	Evgeny Shinder (Sheffield)
02:00		Knorrer periodicity
		Hicks Seminar Room J11
Feb 27	Mon	David Grimes (Oxford)	Mathematical Biology Seminar
14:00
		Alfred Denny Conference Room
Feb 28	Tue	Sam Morgan (Sheffield)
11:00		Double Lie groupoids and their double Lie algebroids, I
		Hicks Seminar Room J11
	Abstract: The series of talks will consist of a precise formulation of the double Lie algebroid of a double Lie groupoid. We will also discuss some of the examples arising in Poisson geometry. In the first talk we will consider the construction of the double Lie algebroid of an LA-groupoid. This will be a stepping stone in the general construction for a double Lie groupoid. Knowledge of the standard formation of the Lie algebroid of a Lie groupoid will not be assumed, and the notions of a Lie groupoid and a Lie algebroid will be recalled.
Feb 28	Tue	Haluk Sengun (Sheffield)	Number Theory Learning Seminar
13:00		Automorphic Forms and Representation Theory: An Overview
		Hicks Seminar Room J11
	Abstract: We shall sketch the path that goes from modular forms to automorphic representations.
Feb 28	Tue		Operator K-theory and Noncommutative Geometry Seminar
14:00		Organizational First Meeting
		Hicks Seminar Room J11
Feb 28	Tue	Gareth Williams (Open)	Topology Seminar
16:00		Weighted projective spaces, equivariant K-theory and piecewise algebra
		Hicks Seminar Room J11
	Abstract: Weighted projective spaces are interesting through many lenses: for example, as natural generalisations of ordinary projective spaces, as toric varieties and as orbifolds. From the point of view of algebraic topology, it is natural to study their algebraic topological invariants – notably, their (equivariant) cohomology rings. Recent work has provided satisfying qualitative descriptions for these rings, in terms of piecewise algebra, for various cohomology theories. This talk will introduce weighted projective spaces as toric varieties and survey results on their (equivariant) cohomology rings, with particular focus on equivariant K-theory. It will conclude with recent results of Megumi Harada, Tara Holm, Nige Ray and the speaker, and indicate the flavour of current work of Tara Holm and the speaker.
Mar 1	Wed	Anne Taormina (University of Durham)	Pure Maths Colloquium
15:00		The riches of Mathieu Moonshine
		Hicks Seminar Room J11
	Abstract: In 2009, three Japanese theoretical particle physicists observed that the elliptic genus of a K3 surface, when expressed in terms of mock modular forms, exposes numbers that can be linked to the dimensions of finite dimensional representations of the sporadic group Mathieu 24. Since then, this intriguing connection has been studied from several points of view, other examples of the same type of phenomenon for other finite groups and mock modular forms have been discovered, and the research topic of `New Moonshines’ has slowly caught the attention of researchers across fields. In this talk, I will describe the 2009 observation, now referred to as `Mathieu Moonshine’, and explain the challenges faced by the theoretical physics community in understanding the origin and role of the huge Mathieu 24 finite symmetry in the context of strings compactified on K3 surfaces. In particular, I will discuss how this phenomenon is related to the geometry of K3 surfaces and introduce the concept of symmetry surfing.
Mar 2	Thu	Andrew Corbett (Bristol)	Number Theory seminar
13:00		Period integrals and special values of L-functions
		Hicks Seminar Room J11
	Abstract: In many ways L-functions have been seen to contain interesting arithmetic information; evaluating at special points can make this connection very explicit. In this talk we shall ask what information is contained in central values of certain automorphic L-functions, in the spirit of the Gan--Gross--Prasad conjectures, and report on recent progress. We also describe some surprising applications in analytic number theory regarding the `size' of a modular form.
Mar 2	Thu	Mark Walters (Queen Mary)	Probability seminar
14:00
Mar 7	Tue	Sam Morgan (Sheffield)
11:00		Double Lie groupoids and their double Lie algebroids, II
		Hicks Seminar Room J11
	Abstract: In the second talk, we will briefly discuss some examples of Lie algebroids arising from Lie groupoids; this should tie in with the description of the Lie functor, given in the first seminar. We shall then continue the construction of a double Lie algebroid of an LA-groupoid.
Mar 7	Tue	Haluk Sengun (Sheffield)	Number Theory Learning Seminar
13:00		Background. Part I.
		Hicks Seminar Room J11
Mar 7	Tue	Neil Hansford (Sheffield)	Operator K-theory and Noncommutative Geometry Seminar
14:00		An introduction to C*-algebras. Part I.
		Hicks Seminar Room J11
Mar 7	Tue	Jeremy Colman (Sheffield)	Uncertainty Quantification study group
15:00		Discussion of "Modelling extremes using approximate Bayesian Computation", by R. Erhardt and S. A. Sisson
		Hicks Seminar Room J11
Mar 7	Tue	Will Mycroft	Topology Seminar
16:00		Plethories of Cohomology Operations
		Hicks Seminar Room J11
	Abstract: Cohomology operations are a very useful property of a cohomology theory. The collection of cohomology operations has a very rich structure. Historically the dual notion, of homology cooperations, have been the main target of attention and a nice algebraic structure called a Hopf ring has been used to understand these. Unfortunately, the Hopf ring contains no structure that is dual to the notion of composition. Boardman, Wilson and Johnson attempt to rectify this situation by defining an enriched Hopf ring, although this structure is rather less pleasant. A 2009 theorem of Stacey and Whitehouse shows that the collection of cohomology operations has the structure of an algebraic object called a plethory and this expresses all the structure, including composition. In this talk I shall define the above concepts and illustrate some examples of plethories for known cohomology theories.
Mar 14	Tue	Jordan Williamson (Sheffield)	Number Theory Learning Seminar
13:00		Background. Part II.
		Hicks Seminar Room J11
	Abstract: Operators on Hilbert spaces.
Mar 14	Tue	Jordan Williamson (Sheffield)	Operator K-theory and Noncommutative Geometry Seminar
14:00		An introduction to C*-algebras. Part II.
		Hicks Seminar Room J11
Mar 14	Tue	Dimitar Kodjabachev (Sheffield)	Topology Seminar
16:00
		Hicks Seminar Room J11
Mar 14	Tue	Dimitar Kodjabachev (Sheffield)	Topology Seminar
16:00		Gorenstein duality for topological modular forms with level structure
		Hicks Seminar Room J11
	Abstract: Gorenstein duality is a homotopy theoretic framework that allows one to view a number of dualities in algebra, geometry and topology as examples of a single phenomenon. I will briefly introduce the framework and concentrate on illustrating it with examples coming from derived algebraic geometry, especially topological modular forms with level structure.
Mar 15	Wed	Andrei Jaikin (Autonomous University of Madrid)	Pure Maths Colloquium
14:00		On $l^2$-Betti numbers and their analogues in positive characteristic
		Hicks Seminar Room J11
	Abstract: Let $G$ be a group, $K$ a field and $A$ a $n$ by $m$ matrix over the group ring $K[G]$. Let $G=G_1>G_2>G_3\cdots$ be a chain of normal subgroups of $G$ of finite index with trivial intersection. The multiplication on the right side by $A$ induces linear maps $$\begin{array}{cccc} \phi_i: & K[G/G_i]^n & \to& K[G/G_i]^m\\ &&&\\ &(v_1,\ldots,v_n) &\mapsto& (v_1,\ldots,v_n)A.\end{array}$$ We are interested in properties of the sequence $\{\frac{\dim_K \ker \phi_i}{|G:G_i|}\}$. In particular, we would like to answer the following questions. Is there the limit $ \lim_{i\to \infty}\frac{\dim_K \ker \phi_i}{|G:G_i|}$? If the limit exists, how does it depend on the chain $\{G_i\}$? What is the range of possible values for $ \lim_{i\to \infty}\frac{\dim_K \ker \phi_i}{|G:G_i|}$ for a given group $G$? It turns out that the answers on these questions are known for many groups $G$ if $K$ is a number field, less known if $K$ is an arbitrary field of characteristic 0 and almost unknown if $K$ is a field of positive characteristic. In my talk I will give several motivations to consider these questions, describe the known results and present recent advances in the case where $K$ has characteristic 0.
Mar 16	Thu	Martin Dickson (King's College)	Number Theory seminar
13:00		Central $L$-values of twists of Siegel cusp forms of degree two
		Hicks Seminar Room J11
	Abstract: The $L$-functions attached to Siegel cusp forms of degree two are conjectured, and in some cases known, to satisfy algebraicity properties at central values. This algebraicity is particularly interesting for those cusp forms which are expected to correspond to rational abelian surfaces. I will discuss these conjectures, the periods for these $L$-values, and finally the formulation of exact formula for the central values of twists of the degree four $L$-function. This includes some joint work with A. Saha, A. Pitale, and R. Schmidt.
Mar 16	Thu	Lasse Rempe-Gillen (Liverpool)
16:00
		LT7
Mar 16	Thu	Lesley Longstone (Independent Police Complaints Commission)	RSS Seminar
16:30		Independent Police Complaints Commission: using statistics to improve public confidence
		Hicks Room K14
	Abstract: As part of the IPCC’s role in securing and maintaining public confidence in the complaints system, the IPCC uses learning from its work to influence changes in policing, ensure accountability and spreads best practice and high standards of service. We are responsible for producing national statistics on deaths in or following police contact and official statistics on public complaints made about the police. We also procure a nationally representative survey in England and Wales to measure public confidence in the police complaints system. The presentation provides an overview of the methodologies for these main statistical outputs and the challenges faced, including external interpretations and quality issues. It also considers uses of the data and making evidenced based decisions that allow us to drive continuous improvement.
Mar 20	Mon	Evgeny Shinder (Sheffield)
02:00		BGG correspondence
		Hicks Seminar Room J11
Mar 20	Mon	Louise Riotte-Lambert (Glasgow)	Mathematical Biology Seminar
14:00		Consequences of memory-based movement at the individual and population levels
		Alfred Denny Conference Room
Mar 21	Tue	Sam Morgan (Sheffield)
11:00		Double Lie groupoids and their double Lie algebroids, III
		Hicks Seminar Room J11
	Abstract: In the third talk we will complete the construction of a double Lie algebroid of an LA-groupoid, and look at a specific example of an LA-groupoid arising naturally from a Poisson Lie group. We will finish by discussing the general notion of a double Lie algebroid of a double Lie groupoid.
Mar 21	Tue	Prathan Jarupoonphol (Sheffield)	Number Theory Learning Seminar
13:00		Background. Part III.
		Hicks Seminar Room J11
	Abstract: The Lie algebra of $SL(2,\mathbb{R})$, the universal enveloping algebra and its centre, action on smooth functions on $SL(2,\mathbb{R})$.
Mar 21	Tue	Paul Mitchener (Sheffield)	Operator K-theory and Noncommutative Geometry Seminar
14:00		K-theory of C*-algebras. Part I.
		Hicks Seminar Room J11
Mar 22	Wed	Martin Lotz (University of Manchester)	Pure Maths Colloquium
14:00		Geometric Probability and Phase Transitions: Applications of the Steiner and Weyl Tube Formula
		Hicks Seminar Room J11
	Abstract: The tube formulas of Steiner and Weyl express the measure of tubular neighbourhoods of geometric objects (convex sets and Riemannian manifolds, respectively) as polynomials with certain curvature invariants as coefficients. We introduce these formulas and discuss recent applications to fields such as geometric probability, concentration of measure, numerical analysis, and convex optimization. Based on work with D. Amelunxen, M.B. McCoy, J.A. Tropp, F. Cucker, P. Buergisser
Mar 22	Wed	Abraham Harte (Dublin City University)	Applied Mathematics Colloquium
14:00		Metric-independence of electromagnetic fields
		Hicks, LT 10
Mar 23	Thu	Jeroen Sijsling (Ulm)	Number Theory seminar
13:00		Reconstructing plane quartics from their invariants
		Hicks Seminar Room J11
	Abstract: Up to isomorphism, elliptic curves over $\mathbb{C}$ are classified by their j-invariant; their coarse moduli space is an affine line with the j-invariant as coordinate. Conversely, it is not difficult to construct an elliptic curve with a specified j-invariant. In higher genus the situation is quite a bit more complicated. The moduli space of smooth genus 2 curves, as determined by Igusa, is already no longer a quasi-affine space, although it is still birational. In this genus Clebsch and Mestre have developed methods to reconstruct curves from their invariants, which also apply to hyperelliptic curves of higher genus. These methods are however very specific to the hyperelliptic case and do not at all generalize. This talk describes joint work with Reynald Lercier and Christophe Ritzenthaler that describes how reconstruction is possible in the next simplest case: that of non-hyperelliptic curves in genus 3, or in other words smooth plane quartics in $\mathbb{P}^2$.
Mar 23	Thu	Jordan Williamson (Sheffield)	Category Theory
14:00		The category of representations of a finite group
		LT10
Mar 23	Thu	Weijun Xu (Warwick)	Probability seminar
14:00
Mar 23	Thu	Lasse Rempe-Gillen (Liverpool )
16:05		Metronomes and fireflies: Stability in the Arnold family
		LT7
	Abstract: *Phase-locking* (or phase synchronisation) is a phenomenon, first discovered by Huygens in the 17th century, in which two interacting oscillators synchronise their frequencies. It occurs in a plethora of physical and biological systems, from simple interacting pendula (search for “metronomes synchronise” on youtube …) to the synchronised behaviour of fireflies. In the 1960s, Vladimir Arnold proposed a one-dimensional discrete-time model of a periodically forced oscillator as the simplest context in which to study phase-locking phenomena. In this talk, I will describe a long-standing problem concerning the density of stable parameters within this family (arising from phase-locking phenomena), which we were able to resolve in recent work with van Strien (Duke Math. J., 2015). The talk will begin with a gentle introduction to one-dimensional discrete dynamics, including computer experiments of both the Arnold family and the well-known logistic family from population dynamics. These experiments naturally lead to the formulation of the density problem. The talk will hence be accessible to a general mathematical audience, including postgraduate students. Time permitting, I will also discuss how these developments are connected to, and were made possible by, recent progress in the study of the dynamics of transcendental entire functions.
Mar 24	Fri	Eleanor Vickers (Sheffield)	SP2RC seminar
13:00		MHD surface waves in an inclined magnetic field
		F41
Mar 27	Mon	John Greenlees (Sheffield)
02:00		Graded singularity category
		Hicks Seminar Room J11
Mar 28	Tue	David Spencer (Sheffield)	Number Theory Learning Seminar
13:00		Real story. Part I.
		Hicks Seminar Room J11
	Abstract: Automorphic forms on $SL(2,\mathbb{R})$, automorphic form associated to a classical cusp form.
Mar 28	Tue	Paul Mitchener (Sheffield)	Operator K-theory and Noncommutative Geometry Seminar
14:00		K-theory of C*-algebras. Part II.
		Hicks Seminar Room J11
Mar 29	Wed	Ulrike Tillmann (University of Oxford)	Pure Maths Colloquium
14:00		Riemann's moduli spaces and operads
		Hicks Seminar Room J11
	Abstract: Riemann's moduli spaces are at the heart of much modern mathematics. In this lecture we will explore their properties as an operad. Operads were introduced in the 1970 in homotopy theory to study loop spaces. Infinite loop spaces are of particular interest as they give rise to generalised cohomology theories. In the 1990's operads had a renaissance with much interest stimulated from mathematical physics. In particular, Segal's axiomatic approach to conformal field theory defines an operad of Riemann surfaces. We will show that this is an example of a new generation of operads detecting infinite loop spaces. The talk will introduce the main concepts and is addressed to a general mathematical audience.
Mar 30	Thu	Sven Meinhardt (Sheffield)	Category Theory
14:00		The Drinfeld Double and the Drinfeld Centre
		Hicks Seminar Room J11
Mar 31	Fri	Norbert Gyenge (Sheffield)	SP2RC seminar
13:00		On Active Longitudes and their Relation to Loci of Coronal Mass Ejections
		F41
	Abstract: The spatial inhomogeneity of the distribution of coronal mass ejection (CME) loci in the solar atmosphere could provide a new tool to estimate the longitudinal position of the most probable CME-capable active regions in the Sun. The anomaly in the longitudinal distribution of active regions themselves is often referred to as active longitude (AL). In order to reveal the connection between the AL and CME loci, here, we investigate the morphological properties of active regions. The first morphological property studied is the separateness parameter, which is suitable to characterise the probability of the locus of an energetic event, such as solar flare or CME. The second morphological property we focus on is the tilt angle of sunspot groups. Analysis of tilt angle of sunspot groups allows us to estimate the helicity of active regions. An increased helicity leads to a more complex built-up of the magnetic structure and also can be the cause of CME eruption. We found that the most complex active regions appear statisticlly significantly near to the AL and that the AL itself is associated with the most tilted active regions. Therefore, the number of CME loci is higher around the enhanced longitudinal activity. Further, the origin of the fast CMEs is also found to be associated with the AL belt. We concluded that the source of the most probably CME-capable active regions is at the AL. Applying our method may allow us to predict the potential flare and CME sources several Carrington Rotation (CR) in advance, and, our further findings could provide new information for solar dynamo modelling.
Apr 4	Tue	Richard Wilkinson (Sheffield)	Uncertainty Quantification study group
15:00		Discussion of Wong, R. K. W., Storlie, C. B. and Lee, T. C. M. (2017), A frequentist approach to computer model calibration. J. R. Stat. Soc. B, 79: 635–648.
		Hicks LT9
Apr 24	Mon	Sven Meinhardt (Sheffield)
02:00		Matrix factorizations and Homological Mirror Symmetry
		Hicks Seminar Room J11
Apr 24	Mon	Mirela Domijan (Liverpool)	Mathematical Biology Seminar
14:00
		Alfred Denny Conference Room
Apr 25	Tue	Di Zhang (Sheffield)	Number Theory Learning Seminar
13:00		Real story. Part II.
		Hicks Seminar Room J11
	Abstract: Representations of $SL(2,\mathbb{R})$.
Apr 25	Tue	Sarah Browne (Sheffield)	Operator K-theory and Noncommutative Geometry Seminar
14:00		Bott periodicity.
		Hicks Seminar Room J11
	Abstract: We present a proof of the Bott Periodicity theorem.
Apr 25	Tue	Ana Lecuona	Topology Seminar
16:00		Complexity and Casson-Gordon invariants
		Hicks Seminar Room J11
	Abstract: Homology groups provide bounds on the minimal number of handles needed in any handle decomposition of a manifold. We will use Casson-Gordon invariants to get better bounds in the case of 4-dimensional rational homology balls whose boundary is a given rational homology 3-sphere. This analysis can be used to understand the complexity of the discs associated to ribbon knots in S^3. This is a joint work with P. Aceto and M. Golla.
Apr 26	Wed	Vidit Nanda (Oxford)	Pure Maths Colloquium
14:00		Local cohomology and canonical stratifications
		Hicks Seminar Room J11
	Abstract: Every finite regular CW complex is, ipso facto, a cohomologically stratified space when filtered by skeleta. In this talk, I will outline a method to discover the canonical (i.e., coarsest possible) stratification of such a complex that is compatible with its underlying cell structure. The construction proceeds by first localizing and then resolving a complex of cosheaves which capture local cohomology at every cell. The result is a sequence of categories whose limit recovers the desired strata via its (isomorphism classes of) objects. As a bonus, the entire process is algorithmic and amenable to efficient computations.
Apr 26	Wed	Cedric Beaume (Leeds)	Applied Mathematics Colloquium
14:00		From convectons to complexity in doubly diffusive convection
		Hicks, LT 10
	Abstract: Doubly diffusive convection arises frequently in natural phenomena and industrial processes. It occurs in systems where heat and another quantity diffuse at different rates. Well-known examples are provided by thermohaline convection and the salt finger instability. In this talk, we consider three-dimensional thermohaline convection where a binary mixture is confined between vertical walls maintained at different temperatures and salinities. In this configuration, we found stationary spatially localised solutions consisting of spots of convection embedded in a background conduction state. These convectons are formed through a subcritical bifurcation from the conductive state (motionless fluid) and display a variety of patterns while simulations above onset reveal chaotic dynamics.
Apr 27	Thu	Rachel Newton (Reading)	Number Theory seminar
13:00		Transcendental Brauer-Manin obstructions on Kummer surfaces
		Hicks Seminar Room J11
	Abstract: In 1970, Manin observed that the Brauer group Br(X) of a variety X over a number field K can obstruct the Hasse principle on X. In other words, the lack of a K-point on X despite the existence of points over every completion of K is sometimes explained by non-trivial elements in Br(X). The 'algebraic' part of Br(X) is the part which becomes trivial upon base change to an algebraic closure of K. It is generally easier to handle than the remaining 'transcendental' part and has been widely studied. Until recently, very little was known about the transcendental part of the Brauer group. Results of Skorobogatov and Zarhin allow one to compute the transcendental Brauer group of a product of elliptic curves. Ieronymou and Skorobogatov used these results to compute the odd order torsion in the transcendental Brauer group of diagonal quartic surfaces. The first step in their approach is to relate a diagonal quartic surface to a product of elliptic curves with complex multiplication by the Gaussian integers. I will show how to extend their methods to compute transcendental Brauer groups of products of other elliptic curves with complex multiplication. Using these results, I will give examples of Kummer surfaces where there is no Brauer-Manin obstruction coming from the algebraic part of the Brauer group but a transcendental Brauer class causes a failure of weak approximation.
Apr 27	Thu	Sven Meinhardt (Sheffield)	Category Theory
14:00		The Drinfeld Double and the Drinfeld Centre (II)
		Hicks Seminar Room J11
Apr 27	Thu	Nick Bingham	Probability seminar
14:00
Apr 27	Thu	Nebojsa Pavic (Sheffield)	Algebra / Algebraic Geometry seminar
16:00		Relative zero cycles on the universal polarized K3 surface
		Hicks Seminar Room J11
	Abstract: The generalized Franchetta Conjecture on K3 surfaces, claimed by O'Grady, says that any codimension 2 cycle of the universal K3 surface $\mathcal{X}_g\to \mathcal{F}_g$ restricted to any (closed) fibre lies in the group generated by the Beauville-Voisin class. In this talk, Chow groups will be introduced and some main results will be mentioned, especially some properties of Chow groups of K3 surfaces. Finally, the generalized Franchetta Conjecture will be stated and a proof for the cases $g=3,\ldots ,10,12,18,20$ will be presented using Mukai's characterization of the moduli space of K3 surfaces with these genera.
Apr 27	Thu	Jonty Rougier (Bristol)
16:00		Assessing the risk from large volcanic eruptions
		LT7
	Abstract: Volcanoes threaten many millions of people worldwide, disproportionately in developing countries. Fortunately, large explosive volcanic eruptions are rare, but this also makes it harder to assess the rate of eruptions for the purposes of risk assessment. This difficulty is compounded by an unreliable historical record, in which the probability of an eruption being recorded in a modern database is affected by the size of the eruption, and also the time and location. In joint work with volcanologists Steve Sparks and Kathy Cashman, I have been quantifying the frequency/magnitude relationship for large explosive eruptions, up to and beyond the 'super-eruptions' which, were they to happen today, would threaten our whole civilisation.
May 2	Tue	Rudolf Chow (Sheffield)	Number Theory Learning Seminar
13:00		Real sotry. Part III.
		Hicks Seminar Room J11
	Abstract: Spectral decomposition of $L^2(\Gamma \backslash SL(2,\mathbb{R}))$, the Duality Theorem.
May 2	Tue	John Greenlees (Sheffield)	Topology Seminar
16:00		Thick and localizing subcategories of rational G-spectra
		Hicks Seminar Room J11
	Abstract: The Balmer spectrum of the category of rational G-spectra as a poset is the closed subgroups of G under cotoral inclusion. In December, I posted a preprint on the arXiv that proved this for tori: the talk will describe a much simpler proof of a theorem for all compact Lie groups. The method applies in other contexts with only a few special inputs from equivariant topology: the Localization Theorem, The calculation of the Burnside ring and a method of calculation for maps between free G-spectra.
May 4	Thu	Sam Edis (Sheffield)	Number Theory seminar
13:00		Congruent numbers in totally real number fields
		Hicks Seminar Room J11
	Abstract: In this talk we will extend the definition of congruent numbers to totally real number fields. Adapting methods of Tunnell we will show that some real quadratic fields possess finite time tests to determine if a number is congruent.
May 4	Thu	Ziyu Zhang (Hannover)	Algebra / Algebraic Geometry seminar
16:00		Degenerations of Hilbert schemes of points on K3 surfaces
		Hicks Seminar Room J11
	Abstract: It is a widely open problem to understand the degenerations of higher dimensional hyperkähler manifolds. The simplest case would be to study the degenerations of Hilbert schemes of points on K3 surfaces. Given a simple degeneration family of K3 surfaces, there are two constructions of degenerations of their Hilbert schemes in the literature, due to Nagai and Gulbrandsen-Halle-Hulek respectively, which result in different central fibers. I will compare the two constructions with an emphasis on the geometry of the latter. Based on joint work in progress with M.G.Gulbrandsen, L.H.Halle and K.Hulek.
May 5	Fri	Dr Nabil Freij (University of the Balearic Islands)	SP2RC seminar
13:00		Coronal loop seismology using NOGIS
		F41
	Abstract: Coronal loops have been observed to host a myriad of magnetohydrodynamics (MHD) waves over the past two decades. Frequently, kink oscillations have been shown to be damped and this damping has allowed the calculation of several key plasma properties such as density and magnetic field strength. I will showcase the first detection of both kink and longitudinal MHD waves with a ground-based coronal imager called NOGIS. Using a recently derived theoretical framework for kink wave damping by mode conversion, it is possible to calculate background properties of the loop system with improved accuracy. This information is important to solve current outstanding problems in coronal seismology.
May 8	Mon	Joseph Karmazyn (Sheffield)
02:00		McKay correspondence / G-actions / AR-quivers, or something similar
		Hicks Seminar Room J11
May 8	Mon	Steve Webb (Liverpool John Moores)	Mathematical Biology Seminar
14:00		Development and Mathematical Modelling of Liver Bioreactors for In Vitro to In Vivo Extrapolation of Systemic Chemical Toxicity
		Alfred Denny Conference Room
May 9	Tue	Dimitar Kodjabachev (Sheffield)	Number Theory Learning Seminar
13:00		Adelic story. Part I.
		Hicks Seminar Room J11
	Abstract: Adeles, ideles. $GL(2)$ over the adeles, strong approximation.
May 10	Wed	Barbara Bolognese (Sheffield)	Pure Maths Colloquium
14:00		On the connectivity of dual graphs of projective curves
		Hicks Seminar Room J11
	Abstract: In 1962, Hartshorne proved that the dual graphs of an arithmetically Cohen-Macaulay scheme is connected. After establishing a correspondence between the languages of algebraic geometry, commutative algebra and combinatorics, we are going to refine Hartshorne's result and measure the connectedness of the dual graphs of certain projective schemes in terms of an algebro-geometric invariant of the projective schemes themselves, namely their Castelnuovo-Mumford regularity. Time permitting, we are also going to address briefly the inverse problem of Hartshorne's result, by showing that any connected graph is the dual graph of a projective curve with nice geometric properties. This is joint work with Bruno Benedetti and Matteo Varbaro.
May 10	Wed	Schuyler Nicholson (U Mass Boston)	Applied Mathematics Colloquium
14:00		Information, patterns, and learning the rules of an explosion
		Hicks, LT 10
	Abstract: At the right pressures and temperatures, gaseous mixtures of hydrogen and oxygen explode. Experimental advances continue to extract chemical processes at ever shorter timescales. The goal of these experiments is to transform this data into chemical mechanisms which describe the sequences of transient chemical species formed during an explosion. Constructing this chemical mechanism will enhance the eciency, reliability, and safety of hydrogen technologies from combustion engines to fuel cells. However, this need to learn the basic rules of combustion is hampered by constraints on the experimentally accessible information. In this talk, I will introduce our recent work applying theoretical tools from information theory and statistical mechanics, which respects these constraints and allows for the systematic discovery of chemical mechanisms.
May 11	Thu	Herbert Gangl (Durham)	Number Theory seminar
13:00		Zagier's polylogarithm conjecture revisited
		Hicks Seminar Room J11
	Abstract: In the early nineties, Goncharov proved the weight 3 case of Zagier's Conjecture stating that the special value $\zeta_F(3)$ of a number field $F$ is essentially expressed as a determinant of trilogarithm values taken in that field. He also envisioned a vast--partly conjectural--programme of how to approach the conjecture for higher weight. We can remove one important obstacle in weight~4 by solving one of Goncharov's conjectures. It further allows us to deduce a functional equation for $Li_4$ in four variables as one expects to enter in a more explicit definition of a certain algebraic K-group of $F$ (viz. $K_7(F)$).
May 11	Thu	Xiaolei Zhao (Northeastern)	Algebra / Algebraic Geometry seminar
14:30		0-cycles on moduli spaces of sheaves on K3 surfaces and second Chern classes
		Hicks Seminar Room J11
	Abstract: The Chow groups of algebraic cycles on algebraic varieties have many mysterious properties. For K3 surfaces, on the one hand, the Chow group of 0-cycles is known to be huge. On the other hand, the 0-cycles arising from intersections of divisors and the second Chern class of the tangent bundle all lie in a one dimensional subgroup. In my talk, I will recall some recent attempt to generalize this property to hyper-Kähler varieties, and explain a conjectural connection between the K3 surface case and the hyper-Kähler case. In particular, this proves a conjecture of O’Grady. If time permits, I will also explain how to extend this connection to Fano varieties of lines on a cubic fourfold containing a plane. This talk is based on a joint work with Junliang Shen and Qizheng Yin.
May 11	Thu	Alistair Craw (Bath)	Algebra / Algebraic Geometry seminar
16:00		Birational geometry and Bridgeland stability for compact support
		Hicks Seminar Room J11
	Abstract: I'll discuss joint work with Arend Bayer and Ziyu Zhang in which we define a nef divisor class on moduli spaces of Bridgeland-stable objects in the derived category of coherent sheaves with compact support, generalising earlier work of Bayer and Macri for smooth projective varieties. This work forms part of a programme to study the birational geometry of moduli spaces of Bridgeland-stable objects for a nice class of varieties that are not projective.
May 12	Fri	Chris Nelson (University of Sheffield)	SP2RC seminar
13:00		Bursts, Bombs, and Jets In The Lower Solar Atmosphere
		F41
	Abstract: Small-scale explosive phenomena in the lower solar atmosphere were first discovered exactly one century ago by Ferdinand Ellerman. These ‘Ellerman bombs’ (EBs) went relatively unexplored for around 80 years, however, the research output from the Flare Genesis Experiment and the development of instruments such as the CRisp Imaging SpectroPolarimeter (CRISP) has driven an exponential increase in interest in these events over the past two decades. It is now thought that these features pinpoint the locations of energetic photospheric magnetic reconnection, which heats pockets of photospheric gas to temperatures as high as 80,000 K. In this talk, we introduce the EB phenomena (including outlining their observational signatures), discuss exciting links between these events and other transient explosive features (such as IRIS bursts), and explore the validity of magnetic reconnection as the driving force behind these events. Finally, signatures of IRIS bursts co-spatial to EB-like events in the quiet-Sun will be presented providing the first evidence that magnetic reconnection energetic enough to heat photospheric plasma to temperatures close to 80,000 K can occur throughout the lower solar atmosphere.
May 15	Mon	Khaled Alhazmy (Sheffield)
02:00		On the finite F-representation type (FFRT) of hypersurfaces
		Hicks Seminar Room J11
May 16	Tue	Sarah Browne (Sheffield)	Topology Seminar
00:00		An orthogonal quasi-spectrum for graded E-theory
		Hicks Seminar Room J11
	Abstract: Graded E-theory is a bivariant functor from the category where objects are graded C*-algebras and arrows are graded *-homomorphisms to the category where objects are abelian groups and arrows are group homomorphisms. It is bivariant in the sense that it is a cohomology theory in its first variable and a homology theory in its second variable. In this talk I'll give a description of a quasi-topological space and explain why this notion is necessary in our case. We will define the notion of an orthogonal quasi-spectrum as an orthogonal spectrum for quasi-topological spaces, and further give the quasi-topological spaces to form the spectrum for graded E-theory. If time allows I will give the smash product structure.
May 16	Tue	Ariel Weiss (Sheffield)	Number Theory Learning Seminar
13:00		Adelic story. Part II.
		Hicks Seminar Room J11
	Abstract: Automorphic forms on $GL(2)$ over the adeles, the automorphic representation associated to a classical cuspidal modular form.
May 16	Tue	David O'Sullivan (Sheffield Hallam )	Operator K-theory and Noncommutative Geometry Seminar
14:00		K-homology
		Hicks Seminar Room J11
May 16	Tue	Sarah Browne (Sheffield)	Topology Seminar
16:00		Quasi-topological assembly for K theory
		Hicks Seminar Room J11
May 17	Wed	Jaroslaw Buczynski (IMPAN Warsaw)	Pure Maths Colloquium
15:00		Constructions of k-regular maps using finite local schemes
		Hicks Seminar Room J11
	Abstract: A continuous map $\mathbb{R}^m \rightarrow \mathbb{R}^N$ or $\mathbb{C}^m \rightarrow \mathbb{C}^N$ is called $k$-regular if the images of any $k$ distinct points are linearly independent. Given integers m and k a problem going back to Chebyshev and Borsuk is to determine the minimal value of $N$ for which such maps exist. The methods of algebraic topology provide lower bounds for $N$, however there are very few results on the existence of such maps for particular values m. During the talk, using the methods of algebraic geometry, we will construct $k$-regular maps. We will relate the upper bounds on the minimal value of $N$ with the dimension of the a Hilbert scheme. The computation of the dimension of this space is explicit for $k< 10$, and we provide explicit examples for $k$ at most $5$. We will also provide upper bounds for arbitrary m and k. The problem has its interpretation in terms of interpolation theory: for a topological space X and a vector space $V$, a map $X \rightarrow V$ is k-regular if and only if the dual space $V^*$ embedded in space of continuous maps from $X$ to the base field $\mathbb{R}$ or $\mathbb{C}$ is $k$-interpolating, i.e. for any $k$ distinct points $x_1,...,x_k$ of $X$ and any values $f_i$, there is a function in $V^*$, which takes values $f_i$ at $x_i$. Similarly, we can interpolate vector valued continuous functions, and analogous methods provide interesting results.
May 17	Wed	Matthew Peddie (Manchester)
16:00		A super approach to Drinfeld doubles
		LT5
	Abstract: Drinfeld's double construction for a Lie bialgebra produces a unique Lie bialgebra suitable for quantisation. With the introduction of Lie bialgebroids as linearisations of Poisson-Lie groupoids, followed the same question as to whether a double can be constructed. This proved to be not so straightforward, and indeed, can be considered to be only partially answered. We will review these double constructions for Lie bialgebras and Lie bialgebroids using the language of supermathematics, and will discuss some of the problems encountered for the bialgebroid case. We will then define the Drinfeld double of a homotopy Lie bialgebra, or an $L_\infty$-bialgebra, and find a necessary condition for the existence.
May 18	Thu	Sean Ledger (Bristol)	Probability seminar
14:00
		Hicks LT E
May 22	Mon	Barbara Bolognese (Sheffield)
02:00		Categorical resolutions of singularities
		Hicks Seminar Room J11
May 23	Tue	Haluk Sengun (Sheffield)	Number Theory Learning Seminar
13:00		Adelic story. Part III.
		Hicks Seminar Room J11
	Abstract: Tensor product theorem, odds and ends.
May 23	Tue	Sven Meinhardt (Sheffield)	Operator K-theory and Noncommutative Geometry Seminar
14:00		Group actions, group C*-algebra, crossed product algebras.
		Hicks Seminar Room J11
May 23	Tue	Magdalena Kedziorek (Lausanne)	Topology Seminar
16:00		Rational commutative ring G-spectra
		Hicks Seminar Room J11
	Abstract: Recently, there has been some new understanding of various possible commutative ring G-spectra. In this talk I will recall these possibilities and discuss the most naive (or trivial) commutative ring G-spectra. Then I will sketch the main ingredients coming into the proof that if G is finite and we work rationally these objects correspond to (the usual) commutative differential algebras in the algebraic model for rational G-spectra. This is joint work with David Barnes and John Greenlees.
May 24	Wed	Kasia Rejzner (University of York)	Pure Maths Colloquium
14:00		Mathematical quantum field theory: from analysis to homological algebra
		Hicks Seminar Room J11
	Abstract: In this talk I will give an overview of mathematical structures used in modern quantum filed theory. I will focus on notions from functional analysis, like nets of operator algebras, and show how these combine with homological algebra methods to provide a rigorous description of perturbative gauge theories on curved spacetimes and of effective quantum gravity. The framework I present is called perturbative algebraic quantum field theory (pAQFT) and it is an emerging new way of approaching mathematical foundations of QFT.
May 24	Wed	Alvar Daza (Universidad Rey Juan Carlos)	Applied Mathematics Colloquium
14:00		Fractal basins and unpredictability in dynamical systems
		Hicks, LT 10
	Abstract: Basins of attraction take its name from hydrology, and in dynamical systems they refer to the set of initial conditions that lead to a particular final state. When different final states are possible, the predictability of the system depends on the structure of these basins. In this talk, we will revise the main kinds of fractal basin boundaries appearing in dissipative and Hamiltonian systems. Finally, we will introduce the concept of basin entropy in order to answer an apparently naïve question: how can we say that one basin is more unpredictable than another?
May 25	Thu	Anthony Licata (Canberra)	Algebra / Algebraic Geometry seminar
16:00		Hilbert schemes, Heisenberg algebras, and braid group actions
		Hicks Seminar Room J11
	Abstract: Let X be the minimal resolution of an ADE simple singularity. The derived category of the Hilbert scheme of points on X is acted on by a number of interesting algebraic objects. For example, there is a`categorical Heisenberg action' on \oplus_n D(Hilb_n(X)), which categorifies the Nakajima-Grojnowski action on cohomology; in addition, there is also a braid group action on each D(Hilb_n(X)). The goal of the talk will be to explain how the categorical Heisenberg action gives rise to the categorical braid group action. Time permitting, we'll discuss the connection to Khovanov homology, and state some conjectures.
Jun 1	Thu	TBA	Algebra / Algebraic Geometry seminar
16:00
		Hicks Seminar Room J11
Jun 6	Tue	Titanic Ten	Topology Seminar
16:00		Gong Show
		Hicks Seminar Room J11
	Abstract: Tea then ten ten-minute talks.
Jun 7	Wed	Haluk Sengun (Sheffield)	Operator K-theory and Noncommutative Geometry Seminar
14:00		The Baum-Connes conjecture.
		Hicks Seminar Room J11
	Abstract: We make a gentle introduction to the Baum-Connes conjecture.
Jun 8	Thu	David Spencer (Sheffield)	Number Theory Learning Seminar
14:00		Introduction to elliptic curves Part 2
		Hicks Seminar Room J11
Jun 8	Thu	Ciaran Meachan (Glasgow)	Algebra / Algebraic Geometry seminar
16:00		Universal functors and derived autoequivalences
		Hicks Seminar Room J11
	Abstract: The group of autoequivalences of the derived category of coherent sheaves on a variety is an interesting and subtle geometric geometric object. Any autoequivalences beyond the 'standard' ones -- automorphisms of the variety itself, twists by line bundles, and homological shift -- should be thought of as 'hidden symmetries' of the variety. I will discuss new examples of such symmetries when the underlying variety is the Hilbert scheme of points on an Abelian surface. This is based on joint work with Andreas Krug.
Jun 9	Fri	Nikos Diamantis (Nottingham)	Number Theory seminar
11:00		Cohomology associated to general weight modular forms
		Hicks Seminar Room J11
	Abstract: The cohomological interpretation of classical modular forms, of integral weight, has proved very fruitful for arithmetic applications. Bruggeman, Lewis and Zagier provided an analogous interpretation for Maass cusp forms. We will discuss joint work with Bruggeman and Choie that incorporates general real weight holomorphic modular forms into a similar cohomological framework as that of the Maass cusp forms.
Jun 9	Fri	Marianna Korsos (Sheffield)	SP2RC seminar
13:00		On the evolution of pre-flare patterns in 3-dimensional real and simulated Active Regions
		LT 10
	Abstract: In this presentation, we address newly discovered pre-flare behavioural patterns in typical sunspot groups by focusing on their evolution as a function of height above the solar surface in a 3-dimensional solar AR. Here, we further probe and apply the concept of the pre-flare behavioural patterns using a magneto-hydrodynamic (MHD) simulation generating solar-like flares. We introduce and discuss the relevant properties and the capability of pre-flare tracking of ARs to improve Space Weather forecasting by focusing on the evolution from the photosphere towards the chromosphere, Transition Region and low corona. The basis of a proxy measure of our approach is the so-called weighted horizontal gradient of magnetic field (W_GM) defined between spots of opposite polarities closer to the polarity inversion line(s) of an AR. The value and the temporal variation of W_GM is found to possess novel and potentially important diagnostic information about (i) the intensity of expected flares and (ii) the accuracy of onset time prediction. Next, we will demonstrate how, by tracking the temporal evolution of W_GM, distance between opposite polarity spots and the associated net flux at various heights in the lower solar atmosphere evolves as function of height. We show that this latter temporal behaviour across the chromosphere-low corona has fundamentally new forecast capabilities. We found, that at a certain height the converging of opposite polarities begins much earlier than at the photosphere or at other heights. Therefore we present a tool to identify the optimum height in the solar atmosphere for flare forecasting that may considerably increase the capability of the time prediction .
Jun 13	Tue	Ariel Weiss (Sheffield)	Number Theory Learning Seminar
14:00		Elliptic curves over finite fields
		Hicks Seminar Room J11
Jun 15	Thu	Di Zhang (Sheffield)	Number Theory Learning Seminar
14:00		Elliptic curves over local fields
		Hicks Seminar Room J11
Jun 15	Thu	Dr Catie Lichten (RAND corporation)
15:00		Ever wondered what happens in a Think Tank and how these organisations influence Government policy? (https://www.eventbrite.co.uk/o/science-in-policy-7880796098)
		LT C
Jun 15	Thu	Agnieszka Bodzenta (Edinburgh)	Algebra / Algebraic Geometry seminar
16:00		Tilting relative generators for birational morphisms
		Hicks Seminar Room J11
	Abstract: For a birational morphism of smooth varieties f: X \to Y with the dimension of fibers bounded by one, the derived category of X admits a relative tilting object over Y. It is a direct sum of copies of the canonical line bundle restricted to relative canonical divisors of partial contractions g:X \to Z. It endows the derived category of X with a t-structure related to the map f. I will show that Y is the fine moduli space of simple quotients of O_X in the heart of this t-structure. I will also prove that the t-structures for f and any partial contraction g are related by two tilts in torsion pairs. This is a joint work with A. Bondal.
Jun 20	Tue	Angelo Rendina (Sheffield)	Number Theory Learning Seminar
14:00		Elliptic curves over global fields: the weak Mordell-Weil theorem
		Hicks Seminar Room J11
Jun 22	Thu	Benjamin Schmidt (Austin, Texas)	Algebra / Algebraic Geometry seminar
16:00		The genus of space curves
		Hicks Seminar Room J11
	Abstract: A 19th century problem in algebraic geometry is to understand the relation between the genus and the degree of a curve in complex projective space. This is easy in the case of the projective plane, but becomes quite involved already in the case of three dimensional projective space. In this talk I will give an introduction to the topic, introduce stability conditions in the derived category, and explain how the two can be related. This is based on joint work in progress with Emanuele Macri.
Jun 23	Fri	Dr Jane Pratt (University of Exeter)	SP2RC seminar
13:00		Magnetic islands under the influence of heating and current
		LT 11
	Abstract: Magnetic reconnection is a fundamental process in plasmas, complementary to the dynamo. In astrophysical contexts, magnetic reconnection can be observed on large scales. In a fusion plasma, the goal is not only to observe, but to manipulate the reconnection process and the magnetic islands that result. I will present a broad review of magnetic reconnection. In the context of my own research, I present a numerical study of the dynamics of magnetic islands that are formed by magnetic reconnection. I explore how heating and current influence a magnetic island's growth, and discuss implications for suppression and prevention of a tearing mode in a tokamak fusion reactor.
Jun 26	Mon	Rudolf Chow (Sheffield)	Number Theory Learning Seminar
12:00		Elliptic curves over global fields: the descent procedure and the Mordell-Weil theorem over Q
		Hicks Seminar Room J11
Jun 28	Wed	Luca Pol (Sheffield)	Number Theory Learning Seminar
14:00		Elliptic curves over global fields: key invariants of elliptic curves
		Hicks Seminar Room J11
Jun 29	Thu	Ciaran Schembri (Sheffield)	Number Theory Learning Seminar
14:00		Group and Galois cohomology
		Hicks Seminar Room J11
Jun 29	Thu	Daniel Labardini-Fragoso (UNAM, Mexico)	Algebra / Algebraic Geometry seminar
16:00		Species with potential from surfaces with orbifold points
		Hicks Seminar Room J11
	Abstract: Felikson-Shapiro-Tumarkin have shown that surfaces with marked points and orbifold points of order 2 give rise to cluster algebras. They have done so by associating skew-symmetrizable matrices to the triangulations of such surfaces, and by showing that flips of triangulations are compatible with matrix mutations. In this talk I will sketch a construction of 'species with potential' that Jan Geuenich and myself have given for these triangulations in the hope of being able to produce a representation-theoretic approach to the corresponding skew-symmetrizable cluster algebras similar to the approach given by Derksen-Weyman-Zelevinsky for skew-symmetric cluster algebras via quiver representations.
Jul 3	Mon	Ariel Weiss (Sheffield)	Number Theory Learning Seminar
14:00		The Birch and Swinnerton-Dyer conjecture
		Hicks Seminar Room J11
Jul 4	Tue	Neil Dummigan (Sheffield)	Number Theory Learning Seminar
14:00		The Bloch-Kato conjecture Part 1
		Hicks Seminar Room J11
Jul 5	Wed	Honglei Lang (MPIM Bonn)
15:00		Double principal bundles
		Hicks Seminar Room J11
	Abstract: We define double principal bundles (DPBs), for which the frame bundle of a double vector bundle, double Lie groups and double homogeneous spaces are basic examples. It is shown that a double vector bundle can be realized as the associated bundle of its frame bundle. Also dual structures, gauge transformations and connections in DPBs are investigated. The visit of Honglei Lang is supported by the MSRC.
Jul 6	Thu	Neil Dummigan (Sheffield)	Number Theory Learning Seminar
14:00		The Bloch-Kato conjecture Part 2
		Hicks Seminar Room J11
Jul 7	Fri	Dr Aaron Reid (Queen's University, Belfast)	SP2RC seminar
13:00		Spectropolarimetric inversions of dynamic brightenings in the lower solar atmosphere
		K14
	Abstract: Ellerman Bombs are small-scale impulsive photospheric brightenings, most notably appearing in the wings of the Balmer lines of hydrogen. Recent polarimetric studies hint that these events are caused via magnetic flux cancellation in the solar photosphere. With the high spatial resolution spectropolarimetry now available from ground-based observatories, it is now possible to magnetically probe these small reconnection events to determine the conditions and evolution of the surrounding atmosphere. A statistical approach is taken to identify Ellerman Bombs which are to be inverted, with the events showing strong photospheric magnetic flux cancellation of the order 10^14 - 10^15 Mx/s. This results in localised temperature enhancements of the order of 1,000K. Spectropolarimetric observations of the chromosphere were also acquired, which show a brightened event with a similar atmosphere to inverted Ellerman Bombs, only occurring in the chromosphere and not the photosphere. We postulate that the formation mechanism of this event is identical to an Ellerman Bomb, with the cancellation occurring across the overlying chromospheric canopy.
Jul 11	Tue	Neil Dummigan (Sheffield)	Number Theory Learning Seminar
14:00		The Bloch-Kato conjecture Part 3
		Hicks Seminar Room J11
Jul 13	Thu	Neil Dummigan (Sheffield)	Number Theory Learning Seminar
14:00		The Bloch-Kato conjecture Part 4
		Hicks Seminar Room J11
Aug 3	Thu	Kris Klosin (CUNY)	Number Theory seminar
14:00		Congruence primes for hermitian Ikeda lifts
		Hicks Seminar Room J11
	Abstract: Hermitian Ikeda lift is a procedure which associates an automorphic form on the unitary group U(n,n) to an elliptic modular form. I will discuss some arithmetic properties of Fourier coefficients of the Ikeda lift as well as a construction of congruences between these lifts and stable forms. This is joint work with Jim Brown.
Sep 19	Tue	Elizabeth Winstanley (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Quantum field theory on anti-de Sitter space-time
		Hicks Seminar Room J11
Sep 21	Thu	Sam Dolan (Sheffield)	Cosmology, Relativity and Gravitation
14:00		Geometrical optics and spin-helicity effects.
		Hicks Seminar Room J11
	Abstract: The Belem group have recently shown a "spin-helicity effect" in the absorption of circularly-polarized electromagnetic & gravitational waves by a Kerr black hole, in which the counter-rotating helicity is more absorbed than the co-rotating helicity. The difference in the absorption cross sections scales with the inverse wavelength, so the helicity-dependence disappears in the zero-wavelength limit. The aim of this talk is to extend geometricaloptics beyond leading order to understand this effect.
Sep 21	Thu	Christopher Fewster (University of York)	Cosmology, Relativity and Gravitation
15:00		Preferred states in quantum field theories, ancient and modern
		Hicks Seminar Room J11
	Abstract: The vacuum state of Minkowski space quantum field theory is distinguished as a state of maximal symmetry. General curved spacetimes have no nontrivial symmetry and therefore lack an obvious candidate vacuum state. Nonetheless, one might wonder whether there is still a way of selecting a preferred state and there have been many attempts in that direction. I will discuss various aspects of this issue, describing a general model-independent no-go theorem that excludes the existence of a local and covariant choice of preferred state. I will also discuss recently-introduced class of "SJ states" and its extensions.
Sep 27	Wed	Matthew Allcock/Mihai Barbulescu (Sheffield)	Applied Mathematics Colloquium
14:00		Magneto-acoustic waves in asymmetric solar waveguides: magneto-seismology and the Kelvin-Helmholtz instability
		Hicks, LT 9
	Abstract: Matthew Allcock's abstract - Our Sun is a restless plasma with a strong and evolving magnetic field, making magnetohydrodynamics (MHD) an essential tool to describe its behaviour. The Sun’s atmosphere, where magnetic forces dominate, is permeated by MHD waves that can be used as an indirect method for diagnosing difficult-to-measure parameters of the solar plasma. This technique is known as solar magneto-seismology. In this talk, we will introduce a novel equilibrium structure consisting of two parallel discontinuities with a uniform magnetic field in the central region. We perturb the system and illustrate the eigenmodes using 3D animations to demonstrate the change in character of symmetric MHD wave modes when the system is asymmetric. We derive two methods that use this asymmetry to estimate the strength of the background magnetic field. This advances the field of solar magneto-seismology in locally asymmetric structures in the solar atmosphere. Mihai Barbulescu's abstract - Solar plasma is highly dynamic and subject to various kinetic and magnetic forces. Many of these forces create bulk flows which need to be included in analytical models, especially when studying time dependent phenomena. Building up from the previous talk, we study the effects that a steady flow has on wave propagation in an asymmetric waveguide, and on its stability. When flow speeds are high enough, they force perturbations of the waveguide to steepen, and the Kelvin-Helmholtz instability (KHI) occurs. We calculate the critical values required by the KHI under different parameter regimes and discuss how these results may change how we view various solar phenomena.
Sep 28	Thu	Steven Julious and Jo Rothwell (Sheffield)	RSS Seminar
16:00		Quantifying Effect Sizes in Clinical Trials
		Hicks LT2
	Abstract: Central to the validity of a RCT is a calculation of the number of participants required (the sample size) which provides reassurance that the trial will be informative. Conventionally, this is usually based upon a difference in the primary outcome (target difference) between groups that is desired to be detectable; the corresponding number of participants needed to be recruited is then calculated. From both a scientific and ethical standpoint, selecting an appropriate target difference is very important. However it has been neglected until relatively recently. A variety of approaches have been proposed and addressed by a large recent review. However there is need for greater guidance to aid researchers and funders. The DELTA2 study was commissioned by two UK academic trial funders (MRC and NIHR) to improve guidance in this area. However the project has engaged stakeholders from all sectors and the recommendations applicable to all clinical trials whether they be academic or industry sponsored. This session will present findings from this project and related work as part of a process of engagement with stakeholders prior to finalizing the guidance on specifying the target difference in a randomized trial sample size calculation.
Oct 2	Mon	Etienne Farcot (Nottingham)	Mathematical Biology Seminar
14:00		Examples of Boolean modelling in plant development
		Alfred Denny Conference Room
Oct 3	Tue	Beth Romano (Cambridge)	Number Theory seminar
13:00		On the arithmetic of simple singularities of type E
		Hicks Seminar Room J11
	Abstract: Given a simply laced Dynkin diagram, one can use Vinberg theory of graded Lie algebras to construct a family of algebraic curves. In the case when the diagram is of type $E_7$ or $E_8$, Jack Thorne and I have used the relationship between these families of curves and their associated Vinberg representations to gain information about integral points on the curves. In my talk, I’ll focus on the role Lie theory plays in the construction of the curves and in our proofs.
Oct 3	Tue	Dave Applebaum (TUOS)
15:00		Introduction to reproducing kernel Hilbert spaces
		Hicks, LT 6
Oct 4	Wed	Chris Nelson (University of Sheffield)	SP2RC Discussion & Book Group
13:00		An introduction to data analysis using SDO
		Hicks LT10
Oct 4	Wed	Anna Felikson (University of Durham)	Pure Maths Colloquium
14:00		Quiver mutations, reflection groups and curves on punctured disc
		Hicks Seminar Room J11
	Abstract: Mutations of quivers were introduced by Fomin and Zelevinsky in 2002 in the context of cluster algebras. For some classes of quivers, mutations can be realised using geometric or combinatorial models. We will discuss a construction of a geometric model for all acyclic quivers. The construction is based on the geometry of reflection groups acting in quadratic spaces. As an application, we show an easy and explicit way to characterise real Schur roots (i.e. dimension vectors of indecomposable rigid representations of Q over the path algebra kQ), which proves a recent conjecture of K.-H. Lee and K. Lee for a large class of acyclic quivers.
Oct 4	Wed	Zijing Ding (Bristol)	Applied Mathematics Colloquium
14:00		Thin liquid film flowing down a vertical fibre
		Hicks, LT 9
	Abstract: We consider the motion of a gravity-driven flow coating a vertical fibre rotating about its axis. This flow exhibits rich dynamics including the formation of droplets, or beads, driven by a Rayleigh-Plateau mechanism modified by the presence of gravity and rotation. We derived an evolution equation for the film thickness using a long-wave approximation. We focus on the effect of rotation on the linear stability, absolute-convective instabilities (CI/AI), nonlinear evolution and the travelling solutions. The results of the linear stability analysis show that the effect of rotating is destabilizing. A spatial-temporal stability analysis is performed to investigate the convective-absolute instability characteristics of the problem. We also perform a numerical simulation on the nonlinear evolution of the film to examine the transition from CI to AI regime. It has been shown that the effect of rotation enhances the absolute instability and promotes the breakup of the film into smaller droplets. The travelling wave solutions of the evolution equation yield information regarding the shape of the interface and propagation speed of the disturbance
Oct 4	Wed	Eoin Murphy	ShEAF: postgraduate pure maths seminar
16:00		t = 1 Limits of Hall Algebras and Quantum Groups
		Hicks Seminar Room J11
	Abstract: In this talk I hope to discuss how two isomorphic algebras degenerate on setting a parameter t=1. One of these is the quantum group Q associated to a simple Lie algebra. The other is a Hall algebra H of a certain category of complexes of quiver representations. The interesting thing is that for either algebra there are in fact different "ways to set t=1" resulting in different degenerate algebras. On the one hand one gets the universal enveloping algebra of a Lie algebra, on the other a Poisson algebra of functions on a Poisson-Lie group. We describe the t=1 theory of H and explain how it is related to that of Q. The story involves work for my PhD thesis and builds on results due to Ringel, Bridgeland, Deng, Chen and others.
Oct 5	Thu	Simon Willerton (Sheffield)	Topology Seminar
16:00		The magnitude of odd balls
		Hicks Seminar Room J11
	Abstract: Tom Leinster introduced the magnitude of finite metric spaces by formal analogy with his notion of Euler characteristic of finite categories. This can be thought of an 'effective number of points' n the metric space. It soon became clear that this notion of magnitude could
Oct 6	Fri	Neil Strickland	Chromatic homotopy theory reading seminar
13:00		An introduction to chromatic homotopy theory
		Hicks Seminar Room J11
Oct 10	Tue	Daniel Loughran (Manchester)	Number Theory seminar
13:00		Determinants as sums of two squares
		Hicks Seminar Room J11
	Abstract: A classical theorem due independently to Landau and Ramanujan gives an asymptotic formula for the number of integers which can be written as a sum of two squares. We prove an analogous result for the determinant of a matrix using the spectral theory of automorphic forms. This is a special case of a more general result on a problem of Serre concerning specialisations of Brauer group elements on semisimple algebraic groups. This is joint work with Sho Tanimoto and Ramin Takloo-Bighash.
Oct 10	Tue	Antonin Coutant (Nottingham)	Cosmology, Relativity and Gravitation
16:00		The draining bathtub experiment
		Hicks Seminar Room J11
Oct 11	Wed	Susan Sierra (University of Edinburgh)	Pure Maths Colloquium
14:00		Noncommutative birational geometry
		Hicks Seminar Room J11
	Abstract: One of the motivating problems in ring theory in the past twenty-five years has been the classification of noncommutative projective surfaces: that is, classifying all noetherian N-graded rings of cubic growth. In particular, one may ask: Fix a division ring D. What are the N-graded rings as above that are contained in the polynomial extension D[t] and have the same (graded) division ring of fractions? This is known as "classifying noncommutative surfaces birational to D''. This question is particularly interesting where D is the division ring which comes from the famous Sklyanin algebra: a graded ring which behaves like the coordinate ring of a noncommutative version of the projective plane. Remarkably, although this situation is highly noncommutative, many of the famous theorems of (commutative) algebraic geometry of surfaces have very strong analogues. We describe how to do birational geometry in this noncommutative context, including noncommutative versions of blowing up a point and contracting a curve. However, these techniques, when applied to noncommutative rings, have applications which are extremely counterintuitive when compared with the commutative context.
Oct 11	Wed	Ed Ryan (Lancaster)	Uncertainty Quantification study group
14:00		Calibrating a global atmospheric chemistry transport model using a Gaussian process emulator and measurements of surface ozone and surface CO
		Hicks LT A
Oct 11	Wed	Jordan Williamson (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		Morita Theory in Stable Homotopy Theory
		Hicks Seminar Room J11
	Abstract: Morita theory was developed in the 1950s as a tool for studying rings by studying their categories of modules. Since then, reincarnations of Morita theory for abelian categories, derived categories and stable model categories have been developed. We will outline the classical version of Morita theory, the extension to the world of stable homotopy theory, and then use this extension to show how this result can be powerful in the search for algebraic models of spectra.
Oct 12	Thu	Dino Sejdinovic (Oxford)	Statistics Seminar
14:00		Approximate Kernel Embeddings and Symmetric Noise Invariance
		LT 9
	Abstract: Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric hypothesis testing and for learning on distributional inputs. I will give an overview of this framework and present some of the applications of the approximate kernel embeddings to Bayesian computation. Further, I will discuss a recent modification of MMD which aims to encode invariance to additive symmetric noise and leads to learning on distributions robust to the distributional covariate shift, e.g. where measurement noise on the training data differs from that on the testing data. https://arxiv.org/abs/1703.07596
Oct 12	Thu	Akos Matszangosz	Topology Seminar
16:00		Real enumerative geometry and equivariant cohomology: Borel-Haefliger type theorems
		Hicks Seminar Room J11
	Abstract: Enumerative geometry studies questions of the type: how many geometric objects satisfy a prescribed set of (generic) conditions? Over the complex field the answer is a single number. However, over R the answer depends on the configuration. A theorem of Borel and Haefliger states that mod 2 the answer is the same. Thom realized, that for a generic a) smooth, b) holomorphic map f, the cohomology class [Si(f)] of the singular points of f of a given type can be expressed as a universal polynomial evaluated at the characteristic classes of the map. The second theorem of Borel and Haefliger states that mod 2, the universal polynomial is the same in the smooth and holomorphic case. In this talk I plan to discuss these questions from the point of view of equivariant topology. The spaces satisfying the condition of the Borel-Haefliger theorem are part of a class of Z2-spaces called conjugation spaces introduced by Hausmann, Holm and Puppe. Analogously we introduce a class of U(1)-spaces which we call circle spaces in an attempt to say something more than parity about these questions. This is joint work with László Fehér.
Oct 13	Fri	Dr Jiajia Liu (University of Sheffield)	SP2RC seminar
13:00		Solar jets
		LT 11
Oct 13	Fri	Daniel Graves	Chromatic homotopy theory reading seminar
14:00		Formal group laws and Lazard's theorem
		Hicks Seminar Room J11
Oct 17	Tue	Lassina Dembele (King's College London)	Number Theory seminar
13:00		On the compatibility between base change and Hecke action
		Hicks Seminar Room J11
	Abstract: Let $F/E$ be a Galois extension of totally real number fields. In this talk, we will discuss the action of $Gal(F/E)$ on Hecke orbits of automorphic forms on $GL_2$. This reveals some compatibility between base change and Hecke action, which has several implications for Langlands functoriality.
Oct 17	Tue	Alexander Vishik (Nottingham)	Algebra / Algebraic Geometry seminar
14:00		Subtle Stiefel-Whitney classes
		Hicks Seminar Room J11
Oct 17	Tue	Andrew Morozov (Leicester)	Mathematical Biology Seminar
15:00		Revisiting the concept of evolutionary fitness in systems with inheritance.
		Hicks LT 10
Oct 18	Wed	Hovhannes Khudaverdian (University of Manchester)	Pure Maths Colloquium
14:00		Thick morphisms and Koszul brackets
		Hicks Seminar Room J11
	Abstract: We show an application of the new notion of a thick morphism of (super)manifolds. For an arbitrary manifold $M$, consider the supermanifolds $\Pi TM$ and $\Pi T^*M$, where $\Pi$ is the parity reversion functor. The space $\Pi TM$ has an odd vector field that can be identified with the canonical de Rham differential $d$; functions on it can be identified with differential forms on $M$. The space $\Pi T^*M$ has an odd Poisson bracket $[ - , - ]$; functions on it can be identified with multivector fields on $M$ and the bracket is the canonical Schouten bracket. An arbitrary even function $P$ which obeys the master-equation $[P,P]=0$ defines an even homotopy Poisson structure on the manifold $M$ and an odd homotopy Poisson structure (the "higher Koszul brackets") on differential forms on $M$. In the case when the function $P$ is quadratic on fibres, then the homotopy Poisson structure on $M$ and the higher Koszul bracket on differential forms are ordinary even and odd Poisson structures. It is a classical fact that there is a linear map of differential forms endowed with the Koszul bracket to multivector fields endowed with the canonical odd Schouten bracket $[ -, - ]$. In the general case, when we have a homotopy Poisson structure on $M$, this linear map does not exist. We show how to construct a non-linear transformation from differential forms endowed with the higher Koszul brackets to multivector fields with the canonical Schouten bracket. This is done as a non-linear pullback with respect to some thick morphism of supermanifolds, a notion recently introduced. (The talk is based on the work with Ted Voronov.)
Oct 18	Wed	Thomas Prince (Imperial)	Algebra / Algebraic Geometry seminar
15:00		From period integrals to toric degenerations of Fano manifolds
		Hicks Seminar Room J11
	Abstract: Given a Fano manifold we will consider two ways of attaching a (usually infinite) collection of polytopes, and a certain combinatorial transformation relating them, to it. The first is via Mirror Symmetry, following a proposal of Coates-Corti-Kasprzyk-Galkin-Golyshev. The second is via symplectic topology, and comes from considering degenerating Lagrangian torus fibrations. We then relate these two collections using the Gross--Siebert program. I will also comment on the situation in higher dimensions, noting particularly that by 'inverting' the second method (degenerating Lagrangian fibrations) we can produce topological constructions of Fano threefolds.
Oct 18	Wed	Angelo Rendina (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		Ramanujan sums, the Casimir effect and the Riemann zeta function
		Hicks Seminar Room J11
	Abstract: In 1913 Ramanujan claimed in a letter to Hardy that $1+2+3+4+...=-1/12$, proving it with elementary methods. We also find examples of such divergent series appearing in some quantum physics phenomena, e.g. the Casimir effect, where a suitable renormalization allows to deal with converge problems; again, we find the same value of $-1/12$. The theory of analytic functions and meromorphic continuation makes sense of this absurd value: in particular, we will see how to extend the generalized harmonic series to the whole complex plane and find its functional equation.
Oct 19	Thu	Mauricio Alvarez (Sheffield)	Statistics Seminar
14:00
Oct 19	Thu	Xue-Mei Li (Imperial)	Probability seminar
14:00		Brownian motions, Brownian Bridges and all that…
		LT3
	Abstract: BMs are well understood, Brownian bridges are conditioned Brownian motions and are well understood as such. On an Euclidean space, each induces a Gaussian measures on the space of paths. They are the Wiener measures. These measures can be used to construct Dirichlet forms and Ornstein-Uhlenbeck processes. Brownian bridges play the role of a delta measure and can be used for heat kernel estimates. In this talk we explore Brownian bridges, semi-classical bridges and even `generalized Brownian bridges’ for general elliptic differential operators.
Oct 20	Fri	Hope Thackray (Sheffield)	SP2RC seminar
13:00		Ring Diagram Analysis
		LT11
	Abstract: In helioseismology, acoustic waves within the Sun are studied in order to derive sub-surface properties. One such helioseismological technique is known as Ring Diagram Analysis, first described in Hill (1988). Spectral data of Doppler shifted flows at the surface of the Sun can be used to deduce flow estimates beneath. Here, I illustrate the analysis using Global Oscillation Network Group (GONG) data.
Oct 20	Fri	Igor Sikora	Chromatic homotopy theory reading seminar
14:00		Complex oriented cohomology theories
		Hicks Seminar Room J11
Oct 24	Tue	Henri Johnston (Exeter)	Number Theory seminar
13:00		The p-adic Stark conjecture at s=1 and applications
		Hicks Seminar Room J11
	Abstract: Let E/F be a finite Galois extension of totally real number fields and let p be a prime. The `p-adic Stark conjecture at s=1' relates the leading terms at s=1 of p-adic Artin L-functions to those of the complex Artin L-functions attached to E/F. When E=F this is equivalent to Leopoldt’s conjecture for E at p and the ‘p-adic class number formula’ of Colmez. In this talk we discuss the p-adic Stark conjecture at s=1 and applications to certain cases of the equivariant Tamagawa number conjecture (ETNC). This is joint work with Andreas Nickel.
Oct 24	Tue	Pierrick Bousseau (Imperial)	Algebra / Algebraic Geometry seminar
14:00		Quantum mirrors of log Calabi-Yau surfaces
		Hicks Seminar Room J11
	Abstract: I will start describing the Gross-Hacking-Keel realization of mirror symmetry for log Calabi-Yau surfaces: the mirror variety is constructed by gluing elementary pieces together according to some gluing functions determined by counting rational curves in the original variety. I will then explain how to construct non-commutative deformations of these mirrors by including contributions of counts of higher genus curves in the original variety.
Oct 25	Wed	Ivan Cheltsov (University of Edinburgh)	Pure Maths Colloquium
14:00		Finite collineation groups and birational geometry
		Hicks Seminar Room J11
	Abstract: Finite groups acting linearly on complex projective spaces have been studies by many people including Blichfeldt, Brauer, Lindsey, Wales, Collins, Thompson and Robinson. In dimension one (projective line) they had been classified in antiquity. Aside from cyclic and dyhedral groups, there are just three such groups, which are the groups of symmetries of Platonic solids. In higher dimensions, the classification is much more complicated. Finite subgroups of the projective transformations of the plane have been classified by Blichfeldt in 1917. He also classified finite subgroups of projective transformations of the three-dimensional space. In my talk I will describe Blichfeldt's classification and explain how to use it to describe equivariant birational geometry of the projective plane and three-dimensional space.
Oct 25	Wed	James Mather (Sheffield)	Applied Mathematics Colloquium
14:00		Flow Instabilities in Partially Ionised Plasmas: Dissipative and Resonant Instabilities
		Hicks, LT 9
	Abstract: The solar atmosphere is a vastly complex and dynamic area, containing many different magnetic structures. The temperature can vary from approximately 4500 K at the temperature minimum to over 10 MK in parts of the solar corona. This temperature stratification affects how ionised the solar plasma is at different layers. Prominences are largely characterised as chromospheric material, at approximately 10000 K, suspended within the coronal plasma and, therefore, may not be fully ionised. They are also very dynamic and may exhibit bulk flows, with observations showing the presence of numerous instabilities. In this talk we firstly briefly introduce the fully ionised magnetic plasma slab moving under. Next, we investigate a plasma slab that has a uniform background bulk flow in the single fluid approximation, where partial ionisation is considered in Cowling’s resistive term in the induction equation, modelling a prominence surrounded by a viscous corona. We study the dissipative instability that can occur at flow speeds that match the internal tube/slow speed. Secondly, we set up a completely two fluid magnetic slab (ions and neutrals) moving under a bulk flow and investigate, in both the compressible and incompressible cases, a quasi-resonant instability that occurs between a new mode, that appears due to neutral molecules, which is always KHI unstable for any shear in flow and the normal magneto-acoustic modes of a slab moving under a uniform bulk flow.
Oct 25	Wed	Giovanni Marchetti (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		Perverse dimensions
		Hicks Seminar Room J11
	Abstract: Exactly 100 years ago, Felix Hausdorff came up with the original idea that some geometrical objects might have non-integer dimension. However, very few steps have been made in homological algebra to pursue this idea. We discuss how the formalism of Bridgeland's stability can be exploited to build homology objects indexed by sets more general than the integers. Finally, we borrow an example from the theory of perverse sheaves to show that dimensions could be even worse behaved: they could be uncomparable.
Oct 26	Thu	Sam Cohen (Oxford)	Probability seminar
14:00		Statistical Uncertainty and nonlinear expectations
		LT 3
	Abstract: In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be explicitly and consistently incorporated in the valuation of decisions, using the theory of nonlinear expectations.
Oct 26	Thu	Scott Balchin (Sheffield)	Topology Seminar
16:00		Lifting cyclic model structures to the category of groupoids
		Hicks Seminar Room J11
	Abstract: Abstract: We consider the problem of lifting certain Quillen model structures on the category of cyclic sets to the category of groupoids, echoing the construction of the Thomason model structure on Cat. We prove that this model structure only captures the theory of homotopy 1-types, and as a consequence, that SO(2)-equivariant homotopy 1-types cannot be encoded in a discrete manner. We will fully describe all of the components required for this model structure, in particular, assuming no familiarity with the model structures on cyclic sets or the Thomason model structure on Cat. This work is joint with Richard Garner.
Oct 27	Fri	Yudong Ye (National Space Science, Beijing)	SP2RC seminar
13:00		A Brief Introduction of Machine Learning and its Application in Space Physics
		LT 11
	Abstract: Machine learning is more and more useful in this data explosion era and could be a powerful tool to reveal hidden connections and pave the way to new discoveries. In this talk, I will give an introduction to machine learning covering from its concepts, brief history, and different categories to its recent applications in space physics. With an example of deciding whether there is a strong geomagnetic storm (namely, the Dst index is less than -100) from ICME’s plasma and magnetic field parameters using support vector machine, I’ll explain step by step on how to apply machine learning method on a specific problem.
Oct 27	Fri	Akos Matszangosz	Chromatic homotopy theory reading seminar
13:00		Complex bordism - Part 1
		Hicks Seminar Room J11
Oct 27	Fri	Mathias Fuchs (Zaha Hadid Architects)	Non-commutative Geometry, Analysis and Groups
14:45		Operator K-theory, Lie groups and lattices
		Hicks Seminar Room J11
	Abstract: We will give a short glimpse into $K$-theory of $C^*$-algebras associated with Lie groups of low real rank, and with their discrete subgroups. We will subsequently report on work which computes the $K$-theory of the reduced group $C^*$-algebra of the Bianchi groups, making use of the Borel-Serre boundary of the associated global symmetric space.
Oct 30	Mon	Mukul Tewary (Toronto)	Mathematical Biology Seminar
14:00		In vitro models of early developmental morphogenesis using human pluripotent stem cells
		Hicks LT 9
Oct 31	Tue	Nicola Franchini (Nottingham)	Cosmology, Relativity and Gravitation
16:00		Black Holes with Light Boson Hair and QPOs
		Hicks Seminar Room J11
	Abstract: A complex bosonic field minimally coupled to gravity, can give rise to black holes solutions that evade the no-hair theorem. These solutions are spinning black holes that can be drastically different from Kerr ones. A phenomenological way to distinguish hairy and Kerr black holes is to measure the quasi-periodic oscillations, which are peaks in the X-ray flux , emitted in the inner region of the accretion disk. Interpreting these peaks with the relativistic precession model, one can predict the emission around hairy black holes. Future generation X-ray telescopes will be able to measure with high precision the quasi-periodic oscillations, hence giving a way to test the no-hair theorem.
Nov 1	Wed	Brita Nucinkis (University of London - Royal Holloway)	Pure Maths Colloquium
14:00		Finiteness conditions for classifying spaces for the family of virtually cyclic subgroups
		Hicks Seminar Room J11
	Abstract: A conjecture of Juan-Pineda and Leary states that any group admitting a cocompact model for the classifying space for the family of virtually cyclic subgroups has to b be virtually cyclic already. This conjecture has been proved for large classes of groups. In this talk I will give an overview of some of these results and constructions, will discuss a weakened condition for these spaces, and will give examples of groups satisfying this condition. This is joint work with N. Petrosyan.
Nov 1	Wed	Malte Heuer (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		Generalised complex geometry
		Hicks Seminar Room J11
	Abstract: Generalised complex structures were introduced by Nigel Hitchin in 2003 and further developed by his student Marco Gualtieri. They give a unification of complex and symplectic geometry. We will see in which way these two seemingly very different structures can be thought of as extremal cases of generalised complex structures. The definition was motivated by phenomena in string theory, especially mirror symmetry where there is a link between symplectic and complex geometry.
Nov 2	Thu	Julian Holstein (Lancaster)	Topology Seminar
16:00		Maurer-Cartan elements and infinity local systems
		Hicks Seminar Room J11
	Abstract: Maurer-Cartan elements for differential graded Lie algebras or associative algebras play an important role in several branches of mathematics, in particular for classifying deformations . There are different sensible notions of equivalence for Maurer-Cartan elements, and while they agree in the nilpotent case, the general theory is not yet well-understood. This talk will compare gauge equivalence and different notions of homotopy equivalence for Maurer-Cartan elements of a dg-algebra. As an application we extend the study of cohesive modules introduced by Block, and find a new algebraic characterisation of infinity local systems on a topological space. This is joint work with Joe Chuang and Andrey Lazarev.
Nov 3	Fri	Fionnlagh Dover (University of Sheffield)	SP2RC seminar
13:00		MHD simulations of Jets with Applications to the Sun
		LT 11
	Abstract: I will be presenting an overview of the open source software MPI-AMRVAC, with a focus on solar physical applications modelled by its inbuilt magnetohydrodynamic module. In particular, I have used this code for simulating MHD jets in gravitationally stratified atmospheres.
Nov 3	Fri	Akos Matszangosz	Chromatic homotopy theory reading seminar
14:00		Complex bordism - Part 2
		Hicks Seminar Room J11
Nov 6	Mon	Dimitar Kodjabachev	HHR
15:00		An introduction to the Arf-Kervaire invariant problem
		Hicks Seminar Room J11
Nov 7	Tue	Soheyla Feyzbakhsh (Edinburgh)	Algebra / Algebraic Geometry seminar
14:00		Reconstructing a K3 surface from a curve via wall-crossing
		Hicks Seminar Room J11
	Abstract: In 1997, Mukai introduced a geometric program to reconstruct a K3 surface from a curve on that surface. The idea is to first consider a Brill-Noether locus of vector bundles on the curve. Then the K3 surface containing the curve can be obtained uniquely as a Fourier-Mukai partner of the Brill-Noether locus. Mukai carried out this program for curves of genus 11. I will explain how wall-crossing with respect to Bridgeland stability conditions implies that the Mukai's strategy works for curves of higher genera.
Nov 7	Tue	Theo Torres (Nottingham)	Cosmology, Relativity and Gravitation
16:00		Non-shallow water waves on a vortex: A model for dispersive fields around rotating black holes
		Hicks Seminar Room J11
	Abstract: Shallow water waves scattering on a draining and rotating potential flow constitute the analogue of a rotating black hole. In such a spacetime, it has been shown theoretically that, at low frequency, waves can extract energy from black holes. Such a process in known as superradiance. Our recent observation of this effect in an experiment at the University of Nottigham (T.T. et al. Nature Phys. 13 (2017) 833-836 arXiv:1612.06180 [gr-qc]) suggests that superradiance persists beyond the shallow water regime. In this talk, I will present the experiment we conducted and I will extend some features of analogue rotating black holes to the dispersive regime. Especially I will focus on light rings and quasi-normal modes.
Nov 9	Thu	Arthur Gretton (UCL)	Statistics Seminar
14:00
Nov 9	Thu	Constanze Roitzheim (Kent)	Topology Seminar
16:00		K-local equivariant rigidity
		Hicks Seminar Room J11
	Abstract: Equivariant stable homotopy concerns the study of objects with symmetry. It has been shown recently by Patchkoria that the G-equivariant stable homotopy category is uniquely determined by its triangulated structure, G-action and induction/transfer/restriction maps. In particular this implies that all reasonable categories of G-spectra realise the same homotopy theory. We consider this result with respect to equivariant K-theory, which merges model category techniques, equivariant structures and calculations from the stable homotopy groups of spheres.
Nov 10	Fri	Luca Pol	Chromatic homotopy theory reading seminar
12:00		The Adams spectral sequence
		Hicks Seminar Room J11
Nov 10	Fri	Matt Allcock (University of Sheffield)	SP2RC seminar
13:00		Solar magneto-seismology with asymmetric waveguides
		LT 11
	Abstract: The Sun’s atmosphere, where magnetic forces dominate, is permeated by MHD waves that can be used as an indirect method for diagnosing difficult-to-measure parameters of solar plasma. This technique is known as solar magneto-seismology (SMS). In this talk, I will give a brief history of SMS development followed by a derivation of two novel techniques for SMS that use the asymmetry of the eigenmodes of asymmetric waveguides to estimate the strength of the background magnetic field, which is traditionally difficult to measure.
Nov 13	Mon	Natalia Petrovskaya (Birmingham)	Mathematical Biology Seminar
14:00		Spatial patterns arising in a model of biological invasion with short-distance and long-distance dispersal.
		Alfred Denny Conference Room
Nov 13	Mon	Dimitar Kodjabachev	HHR
15:00		The Arf-Kervaire invariant problem - HHR proof strategy
		Hicks Seminar Room J11
Nov 14	Tue	Christopher Berry (University of Birmingham)	Cosmology, Relativity and Gravitation
16:00		Binary observations with LIGO and Virgo
		Hicks Seminar Room J11
	Abstract: Gravitational waves provide a new method for exploring the properties of black hole and neutron star binaries. I'll review the discoveries of LIGO and Virgo, and in particular GW170817, the first observation of a binary neutron star coalescence and the first gravitational wave signal to have a confirmed electromagnetic counterpart.
Nov 15	Wed	Magdalini Flari (Sheffield)
14:00		Warps and grids for double and triple vector bundles (Despite the day and time, this is not the Pure Maths Colloquium.)
		F38
	Abstract: Grids are a natural extension of the notion of section to double vector bundles. A grid consists of a pair of linear sections, and constitutes two non-commuting paths from the base manifold to the total space; the warp measures the lack of commutativity. Well-known geometric objects can be expressed as warps: for example, the bracket of two vector fields is a warp, and, given a connection in a vector bundle, the covariant derivative of a section along a vector field is a warp. In triple vector bundles, analysis of the six paths from the base manifold to the total space leads to identities among the warps of the constituent double vector bundles. In this talk we will start with the concept of warp for double and triple vector bundles, build up to a general result for grids in triple vector bundles, and see some applications of this result for grids in the iterated tangent and cotangent bundles. This is joint work with Kirill Mackenzie.
Nov 15	Wed	Rebecca Hoyle (Southampton)	Applied Mathematics Colloquium
14:00		Maternal effects and environmental change
		Hicks, LT 9
	Abstract: Maternal effects are influences of the maternal phenotype on offspring phenotypes by routes other than direct genetic transmission. Potentially they provide an additional means of adaptation to changing environmental conditions over and above that afforded by within-generation phenotypic plasticity. However, maternal effects have also been implicated in the risks of heart disease, diabetes and obesity. I will show how mathematical modelling can provide insight into the interaction of maternal effects and phenotypic plasticity under different patterns of environmental change and suggest when maternal effects might be expected to evolve and why.
Nov 15	Wed	Daniel Graves (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		A Simplicial View of Algebraic Topology
		Hicks Seminar Room J11
	Abstract: Simplicial sets give a nice combinatorial model for topological spaces. In this talk I will introduce the foundations of the theory of simplicial sets and, time permitting, give some idea of how I use them in my own work
Nov 16	Thu	Timothy Waite (Manchester)	Statistics Seminar
14:00
Nov 16	Thu	Sandra Palau (Bath)	Probability seminar
15:30		Extinction properties and asymptotic behaviour of multi-type continuous state branching processes
		LT 7
	Abstract: First, we will discuss how to construct multi-type continuous state branching processes. Under mild conditions, we will see that there exists a lead eigenvalue associated with the first-moment semigroup. The sign of this eigenvalue distinguishes between the cases where there is extinction and exponential growth. Finally, in the supercritical case, we will give the a.s. rate of growth and the convergence of the proportion of each type.
Nov 16	Thu	Markus Hausmann (Copenhagen)	Topology Seminar
16:00		The Balmer spectrum of the equivariant homotopy category of a finite abelian group
		Hicks Seminar Room J11
	Abstract: One of the basic tools to study a tensor-triangulated category is a classification of its thick tensor ideals. In my talk, I will discuss such a classification for the category of compact G-spectra for a finite abelian group G. This is joint work with Tobias Barthel, Niko Naumann, Thomas Nikolaus, Justin Noel and Nat Stapleton, and builds on work of Strickland and Balmer-Sanders.
Nov 17	Fri	Freddie Mather (University of Sheffield)	SP2RC seminar
13:00		Magneto-Acoustic Waves in the Stratified Solar Atmosphere: Single to Multi-Fluid Approach
		LT 11
	Abstract: The solar atmosphere is a highly complex and structured media exhibiting stratification by gravity as well as containing many wave guide structures such as prominences. The temperature is also incredibly varied starting at around 5,000 K at the photosphere, dipping to 4,400 K at the temperature minimum and reaching the giddy heights of 1MK in the corona. Due to this temperature stratification the plasma may not be fully ionised in parts of the solar atmosphere. Much of the solar atmosphere is dynamic with flows following magnetic field lines readily observed. All of these must be taken into consideration when studying MHD waves in the solar atmosphere. In this talk we first consider the magneto-acoustic gravity (MAG) waves in a “vertical” field and study the energy distribution of the eigen-modes in two layer and single layer models of the solar atmosphere. Secondly we consider the effect of a constant bulk flow on the MAG surface waves given in Miles and Roberts (1992). The second part considers partial ionisation in slab structures such as prominences, in which bulk flows and the corresponding instabilities are considered.
Nov 17	Fri	Luca Pol	Chromatic homotopy theory reading seminar
14:00		Quillen's theorem
		Hicks Seminar Room J11
Nov 21	Tue	Davide Masoero (Lisbon)	Algebra / Algebraic Geometry seminar
14:00		The isomonodromic deformation method for Painleve I and meromorphic functions with 5 transcendental singularities
		Hicks Seminar Room J11
	Abstract: I will introduce the isomonodromic deformation method for Painleve I and the corresponding Riemann-Hilbert problem in term of Stokes multipliers. I will then use a theory due to R. Nevanlinna, [Ueber Riemannsche Flaechen mit endlich vielen Windungspunkten, Acta Math 1932] to give an alternative construction of the monodromy manifold, and a proof of the surjectivity of the monodromy map. Finally, I will comment on some applications of the same method to other Painleve equations: in particular, I will show how to compute the numer of real roots of the rational solutions of the fourth Painleve equations.
Nov 21	Tue	Vladimir Toussaint (University of Nottingham)	Cosmology, Relativity and Gravitation
16:00		Massive conformal zero-mode for the untwisted, free scalar field in the (1+1)-dimensional, spatially compactified Friedmann-Robertson-Walker (FRW) cosmological spacetimes.
		Hicks Seminar Room J11
	Abstract: We consider a massive scalar field in the (1 + 1)- dimensional, spatially compactified Friedmann-Robertson-Walker (FRW) cosmological spacetimes. We consider both twisted and untwisted fields. The issue of the massive conformal zero mode arises for the untwisted field whenever the effective mass vanishes at early or late times. More precisely we show that this occurs whenever the zero-momentum mode of the untwisted field reduces to a massive conformal zero-mode in the corresponding asymptotic region(s). To resolve this issue, we develop a new scheme for quantizing the zero momentum mode. This new quantization scheme introduces a family of two real parameters for every zero-momentum mode with an associated two-real-parameter set of in/out vacua. Moreover, we show that the zero momentum ground state's wave functional corresponds to a family of two-real parameter Gaussian wave packets that do not spread out in time. For applications, we examine the finite-time detector’s response to a massive scalar field in the (1 + 1)-dimensional, spatially compactified Milne spacetime. Explicit analytic results are obtained for the comoving and inertially non-comoving trajectories. Numerical results are provided for the comoving trajectory. The numerical results suggest that when the in-vacuum is chosen to be very far from the conventional Minkowski vacuum state, then it contains particles. As result, spontaneous excitation of the comoving detector occurs.
Nov 22	Wed	Jonathan Sherratt (Heriot-Watt)	Applied Mathematics Colloquium
14:00		Using Mathematics to Infer the Historical Origin of Vegetation Patterns in Semi-Deserts
		Hicks, LT 9
	Abstract: Landscape-scale patterns of vegetation occur worldwide at interfaces between semi-arid and arid climates. They are important as potential indicators of climate change and imminent regime shifts, and arise from positive feedback between vegetation and infiltration of rainwater. On gentle slopes the typical pattern form is bands (stripes), oriented parallel to the contours, and their wavelength is probably the most accessible statistic for vegetation patterns. I will discuss the use of mathematical models to investigate different possible mechanisms for the origin of these patterns. I will show that patterns can arise either from degradation of uniform vegetation, or from the colonisation of bare ground. Most significantly, I will show that these two mechanisms can be distinguished by the relationship between pattern wavelength and slope gradient: degradation of uniform vegetation generates patterns whose wavelength increases with slope, while colonisation of bare ground gives the opposite trend. This makes it possible to infer the historical origin of the patterns. Specifically, for sub-Saharan Africa (the "Sahel" region) model predictions and historical rainfall data together imply that vegetation patterns originated by the colonisation of bare ground, either during c.1760-1790 or since c.1850.
Nov 22	Wed	Neil Hansford (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		A Whistle Stop Tour of C*-categories
		Hicks Seminar Room J11
	Abstract: C*-categories are categories in the usual 'objects and arrows' sense, equipped with additional structure comparable with the more analytic C*-algebras. Familiar concepts from either side of the fence include norms, completeness, involutions, the C*-identity, morphism sets, (C*-) functors, and much more. We will have a brief overview of C*-categories, taking in their abstract definition, some specific examples, functors, representations, ideals and quotients, as well as the generalisation of an important construction from the world of C*-algebras.
Nov 23	Thu	Claudia Scheimbauer (Oxford)	Topology Seminar
16:00		Fully extended functorial field theories and dualizability in the higher Morita category
		Hicks Seminar Room J11
	Abstract: Atiyah and Segal's axiomatic approach to topological and conformal quantum field theories provided a beautiful link between the geometry of "spacetimes" (cobordisms) and algebraic structures. Combining this with the physical notion of "locality" led to the introduction of the language of higher categories into the topic. Natural targets for extended topological field theories are higher Morita categories: generalizations of the bicategory of algebras, bimodules, and homomorphisms. After giving an introduction to topological field theories, I will explain how one can use geometric arguments to obtain results on dualizablity in a ``factorization version’’ of the Morita category and using this, examples of low-dimensional field theories “relative” to their observables. An example will be given by polynomial differential operators, i.e. the Weyl algebra, in positive characteristic and its center. This is joint work with Owen Gwilliam.
Nov 23	Thu	Andrew Bell (Sheffield)	RSS Seminar
16:30		Formula for success: multilevel modelling of Formula One driver and constructor performance
		Hicks LT9
	Abstract: Dr Bell will present to us on his paper which uses random-coefficient models and (a) finds rankings of who are the best formula 1 (F1) drivers of all time, conditional on team performance; (b) quantifies how much teams and drivers matter; and (c) quantifies how team and driver effects vary over time and under different racing conditions. The points scored by drivers in a race (standardised across seasons and Normalised) is used as the response variable in a cross-classified multilevel model that partitions variance into team, team-year and driver levels. These effects are then allowed to vary by year, track type and weather conditions using complex variance functions. Juan Manuel Fangio is found to be the greatest driver of all time. Team effects are shown to be more important than driver effects (and increasingly so over time), although their importance may be reduced in wet weather and on street tracks. A sensitivity analysis was undertaken with various forms of the dependent variable; this did not lead to substantively different conclusions. The paper argues that the approach can be applied more widely across the social sciences, to examine individual and team performance under changing conditions.
Nov 24	Fri	Nicola Bellumat	Chromatic homotopy theory reading seminar
14:00		Formal groups and heights
		Hicks Seminar Room J11
Nov 27	Mon	Philip Greulich (Southampton)	Mathematical Biology Seminar
14:00		Mathematical modelling of clonal stem cell dynamics
		Alfred Denny Conference Room
Nov 28	Tue	Carl Wang-Erickson (Imperial)	Number Theory seminar
13:00		The rank of Mazur's Eisenstein ideal
		Hicks Seminar Room J11
	Abstract: In his landmark 1976 paper "Modular curves and the Eisenstein ideal", Mazur studied congruences modulo p between cusp forms and an Eisenstein series of weight 2 and prime level N. He proved a great deal about these congruences, and also posed some questions: how big is the space of cusp forms that are congruent to the Eisenstein series? How big is the extension generated by their coefficients? In joint work with Preston Wake, we give an answer to these questions in terms of cup products (and Massey products) in Galois cohomology. We will introduce these products and explain what algebraic number-theoretic information they encode. Time permitting, we may be able to indicate some partial generalisations to square-free level.
Nov 28	Tue	Emilie Dufresne (Nottingham)	Algebra / Algebraic Geometry seminar
14:00		Separating invariants and local cohomology
		Hicks Seminar Room J11
	Abstract: The study of separating invariants is a new trend in Invariant Theory and a return to its roots: invariants as a classification tool. For a finite group acting linearly on a vector space, a separating set is simply a set of invariants whose elements separate the orbits o the action. Such a set need not generate the ring of invariants. In this talk, we give lower bounds on the size of separating sets based on the geometry of the action. These results are obtained via the study of the local cohomology with support at an arrangement of linear subspaces naturally arising from the action. (Joint with Jack Jeffries)
Nov 28	Tue	Markus Fröb (University of York)	Cosmology, Relativity and Gravitation
16:00		Algebraic quantum field theory, the Hadamard condition and Ward identities
		Hicks Seminar Room J11
	Abstract: In (perturbative) algebraic quantum field theory, the construction of interacting fields, including renormalisation, is done independently of the quantum state of the system. A crucial ingredient in the construction is a Green's function of Hadamard form. For gauge theories, so far one has been restricted to a special gauge (Feynman gauge in Yang-Mills theories), where this Green's function was explicitly known in a general curved background. We show how to construct Green's functions in a general linear covariant gauge, both for Yang-Mills theories and linearised gravity. These functions fulfil certain divergence and trace identities, which can be interpreted as Ward identities in the free theory, and are a prerequisite for the gauge independence of the interacting quantum theory.
Nov 29	Wed	Anna Barbieri (Sheffield)	Pure Maths Colloquium
14:00		Frobenius manifolds
		Hicks Seminar Room J11
	Abstract: The notion of Frobenius structures was introduced by Dubrovin in the '90s as a geometric axiomatization of 2 dimensional Topological Field Theories. A Frobenius manifold is essentially a manifold whose tangent spaces at any point are endowed with the structure of associative Frobenius algebra, varying "smoothly" with respect to a metric. The associativity is encoded in a system of non-linear PDE called WDVV equations. The talk is an introduction to Frobenius manifolds and to their link with the theory of isomonodromic deformations and with WDVV equations.
Nov 29	Wed	Ricardo Garcia-Mayoral (Cambridge)	Applied Mathematics Colloquium
14:00		Alteration of near-wall turbulence by textured surfaces
		Hicks, LT 9
	Abstract: The structure of turbulence near walls can be altered by the presence of surface features such as roughness or texturing, providing opportunities to control the flow passively. The surface texture can induce a coherent component in the flow, as well as a shift in the 'virtual origin' experienced by the overlying turbulence. We will illustrate these mechanisms using the examples of transitionally rough and superhydrophobic textures.
Nov 29	Wed	Rudolf Chow (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		A Tale of Two Sieves
		Hicks Seminar Room J11
	Abstract: Over 300 years ago, the French mathematician Mersenne conjectured that $2^{251} − 1$ was a composite number. This was finally proved 120 years ago, but even 50 years ago the computational load to actually factor the number was considered insurmountable -- the technology and theory at that time would have taken roughly $10^{20}$ years to do so. But this all changed with the advent of accessible and fast computing power as the number was factorised in 1984, merely taking 32 hours. In this talk we will first discuss the method that was used, the quadratic sieve by Pomerance in 1981, before moving on to a more complicated yet powerful version of it, the number field sieve by Pollard in 1996. There'll be plenty of actual numbers and examples!
Nov 30	Thu	Neil Strickland (Sheffield)	Topology Seminar
16:00		Thoughts on the Telescope Conjecture
		Hicks Seminar Room J11
	Abstract: Ravenel's 1984 paper "Localization with respect to certain periodic theories" posed a series of highly prescient conjectures, most of which were later proved by Hopkins, Devinatz and Smith. These results form the heart of chromatic homotopy theory. One conjecture, called the Telescope Conjecture, remained unproven. It can be formulated in many ways, one of which is as follows: if $X$ is a spectrum such that $v_n^{-1}X$ is defined, and $BP_*(v_n^{-1}X)=0$, then already $v_n^{-1}X=0$. This is trivial for $n=0$, and is true for $n=1$ by a theorem of Miller. However, many people including Ravenel came to believe that it is probably false for $n\geq 2$. In 2000 Mahowald, Ravenel and Shick published a paper describing their attempt to disprove the conjecture. They constructed a certain spectral sequence, and showed that the conjecture would imply properties of the spectral sequence that they found implausible, but they were not able to complete the proof of impossibility. This talk will survey this work, and present some small new ideas about properties of certain spectra $T(n,q)$ that play an important role here and in some related areas.
Dec 1	Fri	Dimitar Kodjabachev	Chromatic homotopy theory reading seminar
14:00		The stratification of M_FG
		Hicks Seminar Room J11
Dec 4	Mon	Akos Matszangosz	HHR
16:00		Real bordism
		Hicks Seminar Room J11
Dec 5	Tue	Ariel Weiss (Sheffield)	Number Theory seminar
13:00		Irreducibility of Galois representations associated to low weight Siegel modular forms
		Hicks Seminar Room J11
Dec 5	Tue	Gregory Stevenson (Glasgow)	Algebra / Algebraic Geometry seminar
14:00		A^1-homotopy invariants of singularity categories
		Hicks Seminar Room J11
Dec 5	Tue	Hannah Middleton (University of Birmingham)	Cosmology, Relativity and Gravitation
16:00		Constraints on the gravitational wave background from massive black hole binaries using pulsar timing arrays
		Hicks Seminar Room J11
	Abstract: Pulsar timing arrays are searching for the stochastic gravitational wave background from the merging population of massive black hole binaries. Upper limits on the background are beginning to reach astrophysically interesting sensitivities, however no detection has been reported so far. The recent upper limit from the Parkes Pulsar Timing Array has been interpreted as casting into doubt the standard model of binary assembly through galaxy mergers and hardening via stellar interactions, suggesting that their evolution must be accelerated or stalled. We use a Bayesian analysis to consider the implications of the upper limit for a range of astrophysical scenarios. Weak constraints can be placed on the population parameters, however we find that these astrophysical scenarios are as yet fully consistent with the current observations.
Dec 6	Wed	Vladislav Vysotsky (University of Sussex)	Pure Maths Colloquium
14:00		Convex hulls of random walks
		Hicks Seminar Room J11
	Abstract: Random convex polytopes have been extensively studied over the last decades. A popular model of such polytope is the convex hull of a random walk (which is a random sequence whose increments are independent random vectors with identical distribution). I will present a problem on such convex hulls with notable connections to conic geometry and combinatorics. This is a joint work with Zakhar Kabluchko (Munster) and Dmitry Zaporozhets (St. Petersburg). Consider the probability that the convex hull of an n-step random walk in R^d does not absorb the origin, which in dimension one means that the trajectory of the walk does not change its sign. The remarkable formula of Sparre Andersen (1949) states that any one-dimensional random walk with symmetric continuous distribution of increments stays positive with probability (2n-1)!!/(2n)!!, which does not depend on the distribution. We prove a multidimensional distribution-free counterpart of this result and give an explicit tractable formula for the absorption probability. Our idea is to show that the absorption problem is equivalent to a geometric problem on counting the number of Weyl chambers of type B_n in R^n intersected by a generic linear subspace of co-dimension d. As the main application of this result, we obtain explicit distribution-free formulas for the expected number of faces and vertices of the convex hulls of the random walk.
Dec 6	Wed	Kenta Ishimoto (Oxford)	Applied Mathematics Colloquium
14:00		Hydrodynamics of sperm rheotaxis and guidance of microswimmers
		Hicks, LT 9
	Abstract: Sperm cells swim against a flow -- just as salmon swimming in the river. This sperm rheotacic behaviour was first observed more than a century ago, and recently, it has been hypothesised to be a mechanism of sperm guidance in female reproductive tract. In this talk, we present simple hydrodynamic simulations and theoretical models that could explain this phenomenon, and proceed to consider mathematical structures of the hydrodynamic interactions of a microswimmer in a flow. Possible engineering applications for guidance of microswimmeres will also be discussed.
Dec 6	Wed	Di Zhang (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		Reciprocity laws and $L$-functions
		Hicks Seminar Room J11
	Abstract: Hilbert's ninth problem was to prove the reciprocity law for $n$-th power residue for an arbitrary number field $K$ and for $n>2$, and it was partially solved by Emil Artin. How did Artin guess his reciprocity law? He was led to the law in trying to show that a new kind of L-function was a generalization of the usual L-function. In today's talk we will see why the factorization of some L-functions can be viewed as some form of ''reciprocity law''.
Dec 7	Thu	Maria Kalli (Kent)	Statistics Seminar
14:00
Dec 8	Fri	Dr David Tsiklauri (Queen Mary's University London )	SP2RC seminar
13:00		Alfven wave phase-mixing in flows: why over-dense solar coronal open magnetic field structures are cool? and phase mixing in ABC magnetic fields.
		LT 11
	Abstract: We include the effect of plasma flow in Alfvén wave (AW) damping via phase mixing and explore the observational implications. We apply our findings [1] to addressing the question why over-dense solar coronal open magnetic field structures (OMFS) are cooler than the background plasma. Observations show that the over-dense OMFS (e.g. solar coronal polar plumes) are cooler than surrounding plasma and that, in these structures, Doppler line-broadening is consistent with bulk plasma motions, such as AW. If over-dense solar coronal OMFS are heated by AW damping via phase-mixing, we show that, co-directional with AW, plasma flow in them reduces the phase-mixing induced-heating, thus providing an explanation of why they appear cooler than the background. Also, briefly 3D MHD simulation of linearly polarised Alfven wave dynamics in Arnold-Beltrami-Childress magnetic field [2] will be discussed. [1] D. Tsiklauri, Astron. Astrophys. 586, A95 (2016) [2] D. Tsiklauri, Phys. Plasmas 21, 052902 (2014)
Dec 12	Tue	Marta Mazzocco (Loughborough)	Algebra / Algebraic Geometry seminar
14:00		Colliding holes in Riemann surfaces
		Hicks Seminar Room J11
	Abstract: In 1997 Hitchin proved that the Riemann Hilbert correspondence between Fuchsian systems and conjugacy classes of representations of the fundamental group of the punctured sphere is a Poisson map. Since then, some generalisations of this result to the case of irregular singularities have been proposed by Boalch and by Gualtieri, Li and Pym. In this talk we interpret irregular singularities as the result of collisions of boundaries in a Riemann surface and show that the Stokes phenomenon corresponds to the presence of "bordered cusps". We introduce the concept of decorated character variety of a Riemann surface with bordered cusps and construct a generalised cluster algebra structure and cluster Poisson structure on it. We define the quantum cluster algebras of geometric type and show that they provide an explicit canonical quantisation of this Poisson structure.
Dec 12	Tue	Lucas Lombriser (Royal Observatory Edinburgh)	Cosmology, Relativity and Gravitation
16:00		Cosmic Self-Acceleration from Modified Gravity before/after GW170817
		Hicks Seminar Room J11
	Abstract: Scalar-tensor modifications of gravity have long been considered as an alternative explanation for the late-time accelerated expansion of our Universe. I will first show that a rigorous discrimination between acceleration from modified gravity and from a cosmological constant or dark energy was not possible with observations of the large-scale structure alone. I will then demonstrate how the measurement of the cosmological speed of gravitational waves with GW170817 breaks this dark degeneracy and how the combination of the two challenges the concept of cosmic acceleration from one of the most general scalar-tensor modifications of gravity. Even more general theories, however, reintroduce the dark degeneracy and I will show how a more conclusive result will only be possible with a large number of Standard Sirens. (Refs: 1509.08458; 1602.07670; https://arstechnica.com/science/2017/02/theoretical-battle-dark-energy-vs-modified-gravity).
Dec 13	Wed	Marco Schlichting (University of Warwick)	Pure Maths Colloquium
14:00		The Euler class of a projective module
		Hicks Seminar Room J11
	Abstract: In topology, the existence of a nowhere vanishing section of an oriented vector bundle is detected by its Euler class (in case rank of vector bundle equals dimension of base). This is classical and goes back to at least the 1950s. The analogous story in algebra is less classical and has led to deep questions and results in algebraic K-theory, algebraic cycles, A1-homotopy and group homology. After recalling the topological story, I will give a survey of the algebraic side.
Dec 13	Wed	Ed Pearce (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		Jacobi's Identity and the Dirac Sea
		Hicks Seminar Room J11
	Abstract: The Jacobi Triple Product identity was first introduced in 1829 by Carl Jacobi in his works on the theory of elliptic functions. The identity also arises in the study of affine Kac-Moody Lie algebras. In this talk we will give a physical interpretation of the identity using the electron sea model introduced by Paul Dirac in 1930, which as a by-product theorised the antimatter particle, the positron, years before its experimental discovery. We further provide a combinatorial proof of the identity, where the techniques and concepts involved have applications in the theory of partitions, and interest beyond in the fields of algebraic geometry and number theory.
Dec 14	Thu	Ostap Hryniv (Durham)	Probability seminar
14:00		Limiting behaviour of self-avoiding polygons
		LT 3
	Abstract: In the ensemble of two-dimensional self-avoiding polygons enclosing a fixed area (and centred at the origin), consider a probability distribution whose weights decay exponentially in polygon length. We study statistical properties of these polygons in the limit of large values of the enclosed area. Under a natural sub-criticality condition, we show that this probability distribution concentrates on a deterministic Wulff shape, derive a sharp asymptotics of the corresponding partition function, and describe the normal fluctuations of these polygons around the average profile.
Dec 14	Thu	Danny Sugrue (Queens University Belfast)	Topology Seminar
16:00		The title is Rational Mackey functors of profinite groups.
		Hicks Seminar Room J11
	Abstract: Rational Mackey functors for a compact topological group G are a useful tool for modelling rational G equivariant cohomology theories. Having a better understanding of Mackey functors will enhance our understanding of G-cohomology theories and G-equivariant homotopy theory in general. In the compact Lie group case, rational Mackey functors have been studied extensively by John Greenlees (and others). In this talk we will discuss what can be shown in the case where G is profinite (an inverse limit of finite groups).
Jan 23	Tue	Jordan Williamson	Chromatic homotopy theory reading seminar
14:00		The classification of formal groups
		Hicks Seminar Room J11
Jan 26	Fri	Mihai Barbulescu (Sheffield)	SP2RC seminar
13:00		Periodic Counter Streaming Flows as a Model of Transverse Coronal Loop Oscillations
		LT 11
	Abstract: Recent numerical simulations have demonstrated that non-linear transverse coronal loop oscillations are susceptible to the Kelvin-Helmholtz instability (KHI) due to the counter streaming motions at the boundaries of the loop. We present the first study of this mechanism using an analytical model. The region at the loop boundary where the shearing motions are greatest is treated as a straight interface separating periodic counter-streaming flows. We derive the governing equations for both a straight and a twisted flux tube model, and find that the magnetic twist contributes significantly towards stabilising the system. Establishing the necessary conditions for coronal loops to become unstable due to shearing is important since, it has been shown, the turbulent behaviour due to the instability may lead to heating of the exterior via Ohmic dissipation.
Jan 30	Tue	Yu Qiu (Chinese University of Hong Kong)	Algebra / Algebraic Geometry seminar
14:00		Q-stability conditions on Calabi-Yau-X categories of quivers with superpotential
		Hicks Seminar Room J11
	Abstract: We introduce X-stability conditions on Calabi-Yau-X categories and spaces of their specializations, the q-stability conditions. The motivating example comes from the Calabi-Yau-X category D(S) associated to a graded marked surface S, constructed from quivers with superpotential. We show that the cluster category of D(S) is Haiden-Katzarkov-Kontsevich's topological Fukaya category C(S) and Bridgeland-Smith type Calabi-Yau-N categories are the orbit quotients of D(S). Moreover, we show that stability conditions on C(S) induce q-stability conditions on D(S). Finally, we are constructing moduli space to realize the fiber of the spaces of q-stabilty conditions for given complex number s.
Feb 1	Thu	Scott Balchin	Chromatic homotopy theory reading seminar
14:00		Flat modules over M_FG
		Hicks Seminar Room J11
Feb 2	Fri	Dr Jie Chen (National Astronomical Observatories)	SP2RC seminar
13:00		Study of solar coronal jets
		LT 11
Feb 6	Tue	Simon Willerton (Sheffield)	Magnitude Homology
13:00		Graph magnitude homology + organization
		Hicks Seminar Room J11
Feb 6	Tue	Timothy Logvinenko (University of Cardiff)	Algebra / Algebraic Geometry seminar
14:00		P^n-functors and cyclic covers
		Hicks Seminar Room J11
	Abstract: I will begin by reviewing the geometry of a cyclic cover branched in a divisor. I will then explain how it gives the first ever example of a non-split P^n-functor. This is a joint work with Rina Anno (Kansas).
Feb 7	Wed	Ben Ashby (Bath)	Mathematical Biology Seminar
13:00
		Hicks F20
Feb 7	Wed	Dan Lucas (Keele)	Applied Mathematics Colloquium
14:00		A dynamical systems perspective on layers and mixing in stratified turbulence
		Hicks, LT 9
	Abstract: Stably stratified flows, with dense fluid underlying lighter fluid, are commonly observed in nature and industry. In the oceans the behaviour of turbulence when the fluid is strongly stratified is of great importance if we are to understand fundamental processes such as layer formation and mixing. In this work we approach these issues from the so-called ‘dynamical systems perspective’ where we seek unstable simple solutions, or “exact coherent structures”, which are embedded in the chaos of the turbulent flow. First we show that when forcing the flow with a horizontal shear, spontaneous layers form. We are able to associate the coherent structures responsible for the layers with steady states which a bifurcation analysis shows are the finite amplitude product of a sequence of stratified linear instabilities [1]. Secondly we attack the problem of mixing in stratified turbulence by locating unstable periodic orbits embedded in the turbulence in two parameter regimes; one where the mixing is quite efficient and another where the mixing is weak. The periodic orbits represent a reduced description of the flow which we are able to examine in detail, and compare the processes involved in rearranging the buoyancy field in each case [2]. [1] Lucas, Caulfield & Kerswell 2017 J. Fluid Mech. 832 pp 409-437 [2] Lucas & Caulfield 2017 J. Fluid Mech. 832 R1,
Feb 8	Thu	Christopher Williams (Imperial)	Number Theory seminar
14:00		p-adic Asai L-functions of Bianchi modular forms
		F24
	Abstract: The Asai (or twisted tensor) L-function attached to a Bianchi modular form is the 'restriction to the rationals' of the standard L-function. Introduced by Asai in 1977, subsequent study has linked its special values to the arithmetic of the corresponding form. In this talk, I will discuss joint work with David Loeffler in which we construct a p-adic Asai L-function -- that is, a measure on Z_p* that interpolates the critical values L^As(f,chi,1) -- for ordinary weight 2 Bianchi modular forms. The method makes use of techniques from the theory of Euler systems, namely Kato's system of Siegel units, building on the rationality results of Ghate. I will start by giving a brief introduction to p-adic L-functions and Bianchi modular forms.
Feb 12	Mon	Malte Heuer (Sheffield)
14:00		Decompositions of Triple Vector Bundles
		LT 11
	Abstract: I will prove that any triple vector bundle is non-canonically isomorphic to a decomposed one. The method relies on del Carpio-Marek's construction of local splittings of double vector bundles. Our method yields a useful definition of triple vector bundles via atlases of triple vector bundle charts. This is joint work with Madeleine Jotz Lean.
Feb 13	Tue	Scott Balchin (Sheffield)	Magnitude Homology
13:00		Magnitudes of enriched categories and metric spaces
		Hicks Seminar Room J11
Feb 13	Tue	Tommi Tenkanen (Queen Mary UL)	Cosmology, Relativity and Gravitation
16:00		Primordial Black Holes as Dark Matter
		Hicks Seminar Room J11
	Abstract: I revisit the cosmological and astrophysical constraints on the fraction of dark matter (DM) in primordial black holes (PBHs). I consider a variety of production mechanisms and mass functions for PBHs and discuss whether they can constitute the observed DM abundance or not. I also discuss how one can constrain the physics of the early Universe with the constraints on PBHs, presenting e.g. constraints on the running of the inflaton spectral index which are comparable to those from the Planck satellite.
Feb 14	Wed	Lassina Dembele (University of Sheffield)	Pure Maths Colloquium
14:00		Hilbert modular forms and arithmetic applications
		Hicks Seminar Room J11
	Abstract: Hilbert modular forms were introduced by David Hilbert in 1892 in an attempt to generalise so called elliptic modular forms to other settings. Considered to be a notoriously difficult topic, it wasn't until the mid 1970s that they were seriously studied, notably by Goro Shimura. Since then, they have become very central objects to modern number theory. In this talk, we will start with a gentle introduction to Hilbert modular forms. Then, we will discuss various applications to number theory and arithmetic geometry.
Feb 15	Thu	Neil Dummigan (Sheffield)	Number Theory seminar
14:00		Automorphic forms on Feit's Hermitian lattices
		Hicks Seminar Room J11
	Abstract: This is joint work with Sebastian Schoennenbeck. Feit showed, in 1978, that the genus of unimodular hermitian lattices of rank 12 over the Eisenstein integers contains precisely 20 classes. Complex-valued functions on this finite set are automorphic forms for a unitary group. Using Kneser neighbours, we find a basis of Hecke eigenforms, for each of which we propose a global Arthur parameter. This is consistent with several kinds of congruences involving classical modular forms and critical L-values, and also produces some new examples of Eisenstein congruences for U(2,2).
Feb 15	Thu	Jeremy Colman (Sheffield)	Statistics Seminar
15:00		Stan: better faster MCMC - A user review
		F41
Feb 15	Thu	David Barnes (Queen's University Belfast)	Topology Seminar
16:00		Cohomological dimension of profinite spaces
		Hicks Seminar Room J11
	Abstract: I will introduce the notion of rational cohomological dimension of topological spaces and show a simple way to calculate it when we restrict ourselves to a certain class of topological spaces. Very roughly, the r.c.d of a space X is the largest p such that the pth rational cohomology of X is non-zero. This invariant can be calculated in terms of the more geometric notion of sheaves on X. The category of sheaves on X is an abelian category and the injective dimension of this category is the r.c.d of X. This is a standard way to calculate the the r.c.d. of a space, but can be rather difficult. In this talk, I will describe how for profinite spaces, this injective dimension is related to a simpler notion: the Cantor-Bendixson dimension of the space. There will be a number of pictures and some nice examples illustrating the calculations.
Feb 19	Mon	David Miller (St Andrews)	Mathematical Biology Seminar
14:00		Accounting for detectability in spatially-explicit abundance models of cetaceans
		Hicks F41
Feb 20	Tue	Daniel Graves (Sheffield)	Magnitude Homology
13:00		Hochschild homology of enriched categories
		Hicks Seminar Room J11
Feb 20	Tue	Thanasis Bouganis (Durham)	Number Theory seminar
14:00		On the standard L function attached to Siegel-Jacobi modular forms of higher index
		F24
	Abstract: The standard L function attached to a Siegel modular form is one of the most well-studied L functions, both with respect to its analytic properties and to the algebraicity of its special L-values. Siegel-Jacobi modular forms are closely related to Siegel modular forms, and it was Shintani who first studied the standard L function attached to them. In this talk, I will start by introducing Siegel-Jacobi modular forms and then discuss joint work with Jolanta Marzec on the analytic properties of their standard L function, extending results of Murase and Sugano, and on the algebraicity of its special L values. I will also discuss some open questions.
Feb 20	Tue	RSS Local Group / Michael Wallace (Sheffield)	RSS Seminar
16:30		A tribute to the life and work of Nick Fieller
		Hicks Room I19
	Abstract: Join the Sheffield Local Group in a tribute to Nick Fieller, a member of staff at the University of Sheffield from 1974 until his retirement in 2012, a long-standing fellow of the RSS, and an active member of the local RSS committee until just prior to his death in 2017. The meeting will start with memories of Nick, continue with a seminar given by Dr Michael Wallace from the Department of Archaeology at The University of Sheffield, and end with a drinks reception. A geometric morphometric view of early agriculture - Michael Wallace Nick Fieller had a long and rich history of collaboration with several colleagues in the Department of Archaeology, and Michael was fortunate enough to work with him on the ERC project 'The Evolutionary Origins of Agriculture' (PI: Prof. Glynis Jones). The switch from a mobile hunter-gatherer way of life to one based on settled agriculture was perhaps the most fundamental change in the development of our species, and the subsequent spread of agriculture required the use of crops in environments far outside their natural distribution. A key element of the ERC project was to pioneer the use of geometric modern morphometrics (GMM) for the study of ancient crop remains (primarily cereal grains). GMM allows us to enhance our exploration of past crop remains by quantifying the variation within a crop species, which in turn can offer new insights into ancient crop selection. In this seminar, Michael will discuss some of the key research themes to which GMM can contribute in archaeobotany, the implementation of morphometrics using Vincent Bonhomme's "Momocs' (which was expanded as part of the ERC project), and some of the ongoing research that explores the origins and spread of agriculture.
Feb 21	Wed	Scott Balchin, Caitlin McAuley, Ariel Weiss	ShEAF: postgraduate pure maths seminar
16:00		What is...?
		Hicks Seminar Room J11
	Abstract: Three fifteen minute introductory talks on some important themes from different areas of pure maths, namely Tiling Spaces, Mirror Symmetry, and the Langlands Program.
Feb 22	Thu	Adel Betina (Sheffield)	Number Theory seminar
14:00		Classical and overconvergent modular forms - CANCELLED
		F24
	Abstract: I will explain the proof of Kassaei of Coleman’s theorem via analytic continuation on the modular curve.
Feb 22	Thu	Luca Pol (Sheffield)	Topology Seminar
16:00		On the geometric isotropy of a compact rational global spectrum
		Hicks Seminar Room J11
	Abstract: In this talk I will explain a way to detect groups in the geometric isotropy of a compact rational global spectrum. As an application, I will show that the Balmer spectrum of the rational global stable homotopy category exhibits at least two different types of prime: group and multiplicative primes.
Feb 26	Mon	Dwight Barkley (Warwick)	Applied Mathematics Colloquium
15:00		Recent Advances in the subcritical transition to turbulence
		Hicks, LT E
	Abstract: Explaining the route to turbulence in wall-bounded shear flows has been a long and tortuous journey. After years of missteps, controversies, and uncertainties, we are at last converging on a unified and fascinating picture of transition in flows such as pipes, channels, and ducts. Classically, subcritical transition (such as in a pipe), was thought to imply a {\em discontinuous} route to turbulence. We now know that this is not the case -- subcritical shear flows may, and often do, exhibit continuous transition. I will discuss recent developments in experiments, simulations, and theory that have established a deep connection between transition in subcritical shear flows and a class of non-equilibrium statistical phase transitions known as directed percolation. From this we understand how to define precise critical points for systems without linear instabilities and how to characterize the onset of turbulence in terms of non-trivial, but universal power laws. I will discuss the physics responsible for the complex turbulent structures ubiquitously observed near transition and end with thoughts on outstanding open questions.
Feb 26	Mon	Laurette Tuckerman (ESPCI Paris)	Applied Mathematics Colloquium
15:45		Exotic patterns of Faraday waves
		Hicks, LT E
	Abstract: When a fluid layer is vibrated at a sufficiently high amplitude, a pattern of standing waves appears at its surface. Because of the imposed periodicity, this is a Floquet problem, but we explain how to easily solve it. Classically, the pattern takes the form of stripes, squares or hexagons, but we also look at more exotic patterns like quasipatterns, heteroclinic orbits, supersquares, and Platonic polyhedra. (Longer version) A standing wave pattern appears on the free surface of a fluid layer when it is subjected to vertical oscillation of sufficiently high amplitude. Like Taylor-Couette flow (TC) and Rayleigh-Benard convection (RB), the Faraday instability is one of the archetypical pattern-forming systems. Unlike TC and RB, the wavelength is controlled by the forcing frequency rather than by the fluid depth, making it easy to destabilize multiple wavelengths everywhere simultaneously. Starting in the 1990s, experimental realizations using this technique produced fascinating phenomena such as quasipatterns and superlattices which in turn led to new mathematical theories of pattern formation. Another difference is that the Faraday instability has been the subject of surprisingly little numerical study, lagging behind TC and RB by several decades. The first 3D simulation reproduced hexagonal standing waves, which were succeeded by long-time recurrent alternation between quasi-hexagonal and beaded striped patterns, interconnected by spatio-temporal symmetries. In a large domain, a supersquare is observed in which diagonal subsquares are synchronized. A liquid drop subjected to an oscillatory radial force comprises a spherical version of the Faraday instability. Simulations show Platonic solids alternating with their duals while drifting.
Feb 27	Tue	Alice Rizzardo (University of Liverpool)	Algebra / Algebraic Geometry seminar
14:00
		Hicks Seminar Room J11
Feb 27	Tue	Christos Aravanis (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		Hopf algebras in categories of complexes
		Hicks Seminar Room J11
	Abstract: I will discuss about a generalization of the notion of a Hopf algebra in monoidal categories due to Brugieres and Virelizier. Of particular interest will be the derived category of coherent sheaves on a smooth complex projective variety.
Feb 28	Wed	Peter Millington (Nottingham)	Applied Mathematics Colloquium
14:00		Energy-parity from a bicomplex algebra
		Hicks, LT 9
	Abstract: There is a long history of attempts to alleviate the sensitivity of quantum field theory to vacuum fluctuations and ultraviolet divergences by introducing states of negative norm or states of negative energy. This history involves early works by Dirac, Pauli, Pontrjagin and Krein, as well as more recent suggestions by Linde, Kaplan and Sundrum, and ‘t Hooft and Nobbenhuis. In this talk, we will attempt to construct viable scalar quantum field theories that permit positive- and negative-energy states by replacing the field of complex numbers by the commutative ring of bicomplex numbers. The two idempotent zero divisors of the bicomplex numbers partition the algebra into two ideal subalgebras, and we associate one with positive-energy modes and the other with negative-energy modes. In so doing, we avoid destabilising, negative-energy cascades, while realising a discrete energy-parity symmetry that eliminates the vacuum energy. The probabilistic interpretation is preserved by associating expectation values with the Euclidean inner product of the bicomplex numbers, and both the positive- and negative-energy Fock states have positive-definite Euclidean norms. We consider whether this construction can yield transition probabilities consistent with the usual scattering theory and highlight potential limitations. We conclude by commenting on the extension to spinor, vector and tensor fields.
Mar 1	Thu	Mladen Dmitrov (Université de Lille )	Pure Maths Colloquium
14:00		L-functions of GL(2n): p-adic properties and nonvanishing of twists
		Hicks Seminar Room J11
	Abstract: A crucial result in Shimura's work on the special values of L-functions of modular forms concerns the existence of a twisting character to ensure that a twisted L-value is nonzero at the center of symmetry. Even for simple situations involving L-functions of higher degree this problem is open: for example, if $\pi$ is the automorphic representation attached to a holomorphic cusp form, then it has been an open problem to find a character such that the twisted symmetric cube L-function of $\pi$ does not vanish at the center. We will present a recent joint work with F. Januszewski and A. Raghuram in which purely arithmetic methods involving studying p-adic distributions on Galois groups are used to tackle this problem. Given a cohomological unitary cuspidal automorphic representation $\Pi$ on GL(2n) over a totally real field, under a very mild regularity assumption on the infinity type that ensures two critical points for the standard L-function of $\Pi$, supposing $\Pi$ admits a Shalika model, then for any ordinary prime p for $\Pi$, we prove that for all but finitely many Hecke characters the twisted central L-value of $\Pi$ does not vanish. For example, with a classical normalization of $L$-functions, it follows from our results that there are infinitely many Dirichlet characters $\chi$ such that $L(6, \Delta \otimes \chi) L(17, {\rm Sym}^3\Delta \otimes \chi) \neq 0$ for the Ramanujan $\Delta$-function.
Mar 1	Thu	Christian Wimmer (Bonn)	Topology Seminar
16:00		A model for equivariant commutative ring spectra away from the group order
		Hicks Seminar Room J11
	Abstract: Stable homotopy theory simplifies drastically if one consider spectra up to rational equivalence. It is a classical result that taking homotopy groups induces an equivalence $$G \text{-} \mathcal{SHC} \simeq_{\mathbb{Q}} \text{gr.} \prod_{(H \leq G)} \mathbb{Q} [WH] \text{-mod}$$ between the genuine $G$-equivariant stable homotopy category ($G$ finite) and the category of graded modules over the Weyl groups $WH$ indexed by the conjugacy classes of subgroups of $G$. However, this approach is too primitive to be useful for the comparison of highly structured ring spectra in this setting. Let $R \subset \mathbb{Q}$ be a subring such that $|G|$ is invertible in $R$. I will explain how geometric fixed points equipped with additional norm maps related to the Hill-Hopkins-Ravenel norms can be used to give an $R$-local model: They induce an equivalence $$\text{Com}(G\text{-Sp}) \simeq_R \text{Orb}_G \text{-Com}(\text{Sp})$$ between the $R$-local homotopy theories of genuine commutative $G$-ring spectra and $\text{Orb}_G$-diagrams in non-equivariant commutative ring spectra, where $\text{Orb}_G$ is the orbit category of the group $G$. As a corollary this gives an algebraic model $$\text{Com}(G\text{-Sp})_\mathbb{Q} \simeq \text{Orb}_G \text{-CDGA}_\mathbb{Q}$$ for rational ring spectra in terms of commutative differential algebras. I will also try to indicate the analogous global equivariant statements.
Mar 2	Fri	Dr. Jiajia Liu (University of Sheffield)	SP2RC seminar
12:00		A New Tool for CME Arrival Time Prediction Using Machine Learning Algorithms: CAT-PUMA
		LT 11
	Abstract: Coronal Mass Ejections (CMEs) are arguably the most violent eruptions in the Solar System. CMEs can cause severe disturbances in the interplanetary space and even affect human activities in many respects, causing damages to infrastructure and losses of revenue. Fast and accurate prediction of CME arrival time is then vital to minimize the disruption CMEs may cause when interacting with geospace. In this paper, we propose a new approach for partial-/full-halo CME Arrival Time Prediction Using Machine learning Algorithms (CAT-PUMA). Via detailed analysis of the CME features and solar wind parameters, we build a prediction engine taking advantage of 182 previously observed geo-effective partial-/full-halo CMEs and using algorithms of the Support Vector Machine (SVM). We demonstrate that CAT-PUMA is accurate and fast. In particular, predictions after applying CAT-PUMA to a test set, that is unknown to the engine, show a mean absolute prediction error ~5.9 hours of the CME arrival time, with 54% of the predictions having absolute errors less than 5.9 hours. Comparison with other models reveals that CAT-PUMA has a more accurate prediction for 77% of the events investigated; and can be carried out very fast, i.e. within minutes after providing the necessary input parameters of a CME. We have also designed a publicly free User Interface (https://github.com/PyDL/cat-puma), allowing the community to perform their own applications for prediction using CAT-PUMA.
Mar 2	Fri	Mladen Dimitrov (Lille)	Number Theory seminar
14:00		$p$-adic L-functions for nearly finite slope Hilbert modular forms and the Exceptional Zero Conjecture
		LT-5
	Abstract: We attach $p$-adic L-functions and improved variants theoreof to families of nearly finite slope cohomological Hilbert modular forms, and use them to prove the Greenberg-Benois exceptional zero conjecture at the central point for forms which are Iwahori spherical at $p$. This is a joint work with Daniel Barrera and Andrei Jorza.
Mar 5	Mon	Justin Travis (Aberdeen)	Mathematical Biology Seminar
14:00
		Hicks F41
Mar 8	Thu	Dr Krishna Prasad (Queen's University, Belfast)
10:00		Frequency-dependent Damping of Slow Magneto-acoustic Waves in Sunspots
		LT 6
	Abstract: Propagating slow magneto-acoustic waves are regularly observed in the solar corona, particularly in sunspot related loop structures. These waves exhibit rapid damping as they propagate along the loops. Several physical and geometrical effects were found to produce the observed decay in the wave amplitude. It has also been shown that the damping is frequency dependent. A majority of the observed characteristics have been attributed to damping by thermal conduction in the solar corona. Although it is believed that these waves originate in the photosphere, their damping behaviour in the sub-coronal layers is relatively less studied. Using high spatial and temporal resolution images of a sunspot, we investigated propagation and damping characteristics of slow magnetoacoustic waves up to transition region heights. The major conclusions from this study will be discussed in the talk which include: 1) The energy flux in slow waves estimated from the relative amplitudes decays gradually right from the photosphere even when the oscillation amplitude is increasing. 2) The damping displayed by slow waves is frequency dependent well below coronal heights. 3) A spatial comparison of power spectra across the umbra highlights enhancement of high-frequency waves near the umbral center.
Mar 8	Thu	David Spencer (Sheffield)	Number Theory seminar
14:00		Congruences of local origin for higher levels- CANCELLED
		F35
	Abstract: There are many kinds of congruences between different types of modular forms. The most well known of which is Ramanujan's mod 691 congruence. This is a congruence between the Hecke eigenvalues of the weight 12 Eisenstein series and the Hecke eigenvalues of the weight 12 cusp form (both at level 1). This type of congruence can be extended to give congruences of ''local origin''. In this talk I will explain what is meant by such a congruence while focusing on the case of weight 1. The method of proof in this case is very different to that of higher weights and involves working with Galois representations and ray class characters.
Mar 14	Wed	Igor Sikora (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		Could the Philosophy of Mathematics be interesting for mathematicians
		Hicks Seminar Room J11
	Abstract: Philosophical reflections of mathematics are concerned with the fundamental problems about mathematics, such as existence of mathematical objects, subject of research of mathematics, how do we extend our mathematical knowledge, what are relations of mathematics with other sciences etc. In this talk I will attempt to describe several classical and modern problems in philosophy an approaches to solve them.
Mar 15	Thu	Matthew Bisatt (King's College)	Number Theory seminar
14:00		The generalised Birch--Swinnerton-Dyer conjecture and twisted L-functions- CANCELLED
		LT A
	Abstract: The Birch and Swinnerton-Dyer conjecture famously connects the rank of an elliptic curve to the order of vanishing of its L-function. We combine this with a conjecture of Deligne to study twisted L-functions and derive several interesting properties of them using tools from representation theory. We show that, under certain conditions, these conjectures predict that the order of vanishing of the twisted L-function is always a multiple of a given prime and provide analogous statements for L-functions of modular forms.
Mar 15	Thu	Dr Robert Massey (Royal Astronomical Society)
15:00		Funding Blue Skies Research In The Age Of Austerity
		Hicks LT A
Mar 15	Thu	Simon Wood (Cardiff)	Topology Seminar
16:00		Questions in representation theory inspired by conformal field theory
		Hicks Seminar Room J11
	Abstract: Two dimensional conformal field theories (CFTs) are conformally invariant quantum field theories on a two dimensional manifold. What distinguishes two dimensions from all others is that the (Lie) algebra of local conformal transformations become infinite dimensional. This extraordinary amount of symmetry allows certain conformal field theories to be solved by symmetry considerations alone. The most intensely studied type of CFT, called a rational CFT, is characterised by the fact that its representation theory is completely reducible and that there are only a finite number isomorphism classes of irreducibles. The representation categories of these CFTs form so called modular tensor categories which have important applications in the construction of 3-manifold invariants. In this talk I will discuss recent attempts at generalising this very rich structure to CFTs whose representation categories are neither completely reducible nor finite.
Mar 19	Mon	Cameline Orlendo (Glasgow)	Mathematical Biology Seminar
14:00
		Hicks F41
Mar 20	Tue	Igor Sikora (Sheffield)	Magnitude Homology
13:00		Euler characteristics
		Hicks Seminar Room J11
Mar 21	Wed	Evgeny Shinder (Sheffield)	Pure Maths Colloquium
14:00		Rationality in families of algebraic varieties
		Hicks Seminar Room J11
	Abstract: I will talk about the following problem in algebraic geometry: given a family of algebraic varieities, if general fibers are rational, are all fibers rational? The talk will be based on recent joint work of myself and Nicaise, and a development by Kontsevich and Tschinkel.
Mar 21	Wed	Sam Morgan (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		Lie groupoids and their application in symplectic geometry
		F20
	Abstract: The aim of this talk is to introduce the theory of Lie groupoids and Lie algebroids to a broad audience. It is hoped that the subject can be well motivated, without many prerequisites. In the second part of the talk, we will see why Lie groupoids were first introduced into symplectic and Poisson geometry, and what role they play here.
Mar 22	Thu	Petros Syntelis (ESPOS Seminar) (University of St Andrews)	SP2RC seminar
10:00		Recurrent CME-like Eruptions in Flux Emergence Simulations
		E39
	Abstract: We report on three-dimensional MHD simulations of recurrent small-scale Coronal Mass Ejection (CME)-like eruptions using flux-emergence simulations and study their formation and eruption mechanism. These eruptions have the size and energies of small prominence eruptions. The erupting flux ropes are formed due to the reconnection of J-loops (formed by shearing and rotation) and are located inside magnetic envelope field favouring torus instability. The flux rope eruptions are triggered by the action of a tension removal mechanism, such as the typical tether-cutting where the envelope field reconnects with itself. Another side tether-cutting is also found. There, the envelope field reconnected with the J-loops. The two tether-cutting mechanisms transfer hot plasma differently inside the erupting structures. We report similar mechanisms creating three more eruptions in a recurrent manner.
Mar 22	Thu	Netan Dogra (Imperial)	Number Theory seminar
14:00		Unlikely intersections and the Chabauty-Kim method over number fields
		Hicks Seminar Room J11
	Abstract: Chabauty's method is a method for proving finiteness of rational points on curves under assumptions on the rank of the Jacobian. Recently, Kim has shown that one can extend this to prove finiteness of rational points on curves over Q, under slightly weaker assumptions on the dimension of certain Galois cohomology groups. A conjecture of Beilinson-Bloch-Kato implies these assumptions are always satisfied. In this talk I will explain Kim's construction, and how to extend his results to general number fields by proving an 'unlikely intersection' result for the zeroes of p-adic iterated integrals.
Mar 26	Mon	Hans Werner Henn (Strasbourg)	Topology Seminar
16:00		The centralizer resolution of the K(2)-local sphere at the prime 2.
		Hicks Seminar Room J11
	Abstract: In the last few years two different resolutions of the K(2)-local sphere at the prime 3 have been used very successfully to settle some basic problems in K(2)-local stable homotopy theory like the chromatic splitting conjecture, the calculation of Hopkins' K(2)-local Picard group and determining $K(2)-local Brown-Comentz duality. The focus is now moving towards the prime 2 where one can hope for similar progress. In this talk we concentrate on one of these two resolutions, the centralizer resolution at the prime 2.
Mar 27	Tue	Prof. Manolis Georgoulis (Academy of Athens)	SP2RC seminar
13:00		From Physical Understanding to Forecasting of Solar Flares and Coronal Mass Ejections
		LT 10
	Abstract: The imperative and pressing nature of an efficient space weather forecasting has spurred multiple efforts around the world to address this problem. A recent realization is that the problem's tackling should not be restricted to heliophysics, but should utilize help provided by the big data and machine learning communities, in a complementary and reinforcing role. This said, we argue that without the lead of solar and heliospheric physicists, these interdisciplinary efforts would be ill-fated. This is because a successful forecasting effort should be driven by an in-depth understanding of the solar pre-eruption phase(s) and evolution of solar source regions. We will provide a few examples of this enhanced-understanding process put to work in the framework of the EU FLARECAST project on solar flare prediction. From flares, we will then take a conceptual step toward an efficient CME forecasting that can be facilitated by what has been already achieved through FLARECAST and other EU projects. Concluding, we will touch on another necessary aspect of efficient space weather forecasting, namely, the input data from solar monitoring. With continuous, near-realtime monitoring of the Sun attempted predominantly from satellites and spacecraft, we discuss a potentially viable, longer-term and better managed alternative such as a strategically built network of ground-based monitoring stations. Such networks can be served, maintained, and expanded / upgraded at will, better adapting to the problem at hand while reflecting progress in its physical understanding.
Apr 16	Mon	Natasha Savage (Liverpool)	Mathematical Biology Seminar
14:00		Where to draw one’s theoretical boundary: One closed question, one experimental data set, two published models, two opposing answers.
		Hicks LT6
Apr 17	Tue	Igor Sikora (Sheffield)	Magnitude Homology
13:00		Euler Characteristic II
		Hicks Seminar Room J11
Apr 18	Wed	Ilke Canakci (University of Newcastle)	Pure Maths Colloquium
14:00		Cluster algebras and continued fractions
		Hicks Seminar Room J11
	Abstract: I will report on a new connection between cluster algebras and continued fractions given in terms of so-called 'Snake graphs'. Snake graphs are planar graphs first appeared in the context of cluster algebras associated to marked surfaces. In their first incarnation, they were used to give formulas for generators of cluster algebras. Along with further investigations and several applications, snake graphs were also studied from a more abstract point of view as combinatorial objects. This talk will focus on a combinatorial realisation of continued fractions in terms of 'perfect matchings' of snake graphs. I will also discuss applications to Cluster algebras, to elementary Number theory and, time permitting, to Knot theory. This is joint work with Ralf Schiffler.
Apr 18	Wed	Elena Marensi (Sheffield)	Applied Mathematics Colloquium
14:00		Calculation of minimal seeds in stabilised pipe flows
		Hicks, LT 9
	Abstract: Turbulent wall flows exert a much higher friction drag than laminar flows, with consequent increase in energy consumption and carbon emissions. Considerable research effort is thus directed towards the design of control strategies to reduce the turbulent drag or delay the transition to turbulence. Of fundamental interest from this viewpoint is the so-called minimal seed, i.e. the initial perturbation of lowest energy capable to trigger transition. In this talk, variational methods are used to construct fully nonlinear optimisation problems that seek the minimal seed in stabilised pipe flows. The question of how representative the minimal seed is of typical ambient disturbances is addressed here for the first time by performing a statistical study of the critical initial energies for transition with different initial perturbations. A set of initial conditions are thus generated to investigate the stabilising effect of a simple model for the presence of a baffle in the core of the flow. Significant increases in the critical energy and drag reductions are found to be possible. The relevance of the minimal seed in realistic scenarios will be further discussed, as well as a closely-related variational problem for the control of transition.
Apr 18	Wed	David Spencer (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		Visualising the values of a binary quadratic form
		Hicks Seminar Room J11
	Abstract: The solution of Diophantine equations is still a thriving area in number theory. In this talk I will consider binary quadratic forms, those of the form $ax^2 + bxy + cy^2$ with $a,b,c \in\mathbb Z$. I will show how to construct a graph which allows us to see the possible values such a quadratic form can take. This will allow us to determine when the Diophantine equation $ax^2 + bxy + cy^2 = k$ is solvable in integers $(x,y)$, and to find such integers when it is solvable.
Apr 19	Thu	Martine Barrons (Warwick)	Statistics Seminar
14:00
		LT3
Apr 19	Thu	Gary McConnell (Imperial)	Number Theory seminar
14:00		Empirical connections between "crystals" of complex equiangular lines and Hilbert's twelfth problem for real quadratic fields
		Hicks Seminar Room J11
	Abstract: Let K be a real quadratic field of discriminant D or 4D, and set d to be one of the infinitely many integers for which the square-free part of $(d-1)^2 - 4$ is D. Over the past ten years it has become evident from many calculations that there is a profound connection between certain maximal sets of equiangular lines in complex d-dimensional Hilbert space on the one hand, and the ray class field of K of conductor d on the other. I will give a short outline of what has been discovered and where we believe it may be heading.
Apr 24	Tue	Jordan Williamson (Sheffield)	Magnitude Homology
13:00		Magnitude homology equals Hochschild homology I
		Hicks Seminar Room J11
Apr 25	Wed	Andrew Granville (University College London)	Pure Maths Colloquium
14:00		An alternative approach to analytic number theory
		Hicks Seminar Room J11
	Abstract: Ever since Riemann's seminal paper in 1859, analytic approaches to number theory have developed out of an understanding of the zeros of the Riemann zeta-function. In 2009, Soundararajan and I proposed an alternative approach (the "pretentious approach"), piecing together many "ad hoc" ideas from the past into a coherent theory. This new theory has taken on a life of its own in the last few years, providing the framework for some impressive new results by Matomaki, Radziwill, Tao and others. In this talk we will explain the main ideas and try to give some sense of how these new works fit in.
Apr 25	Wed	Caitlin McAuley (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		Introducing stability conditions
		Hicks Seminar Room J11
	Abstract: The space of stability conditions is a complex manifold associated to a triangulated category. The definition of a stability condition was motivated by work in string theory and as such, an understanding of the stability manifold will have important consequences in mirror symmetry. I'll introduce stability conditions on an arbitrary triangulated category and discuss some of their most important features, as well as discussing some examples.
Apr 26	Thu	Emmanuel Lecouturier (Paris)	Number Theory seminar
14:00		Higher Eisenstein elements in weight 2 and prime level
		LT 6
	Abstract: In his classical work, Mazur considers the Eisenstein ideal $I$ of the Hecke algebra $T$ acting on cusp forms of weight $2$ and level $\Gamma_0(N)$ where $N$ is prime. When $p$ is an Eisenstein prime, i.e. $p$ divides the numerator of $\frac{N−1}{12}$, denote by $\mathbf{T}$ the completion of $T$ at the maximal ideal generated by $I$ and $p$. This is a $\mathbb{Z}_p$-algebra of finite rank $g_p ≥ 1$ as a $\mathbb{Z}_p$-module. Mazur asked what can be said about $g_p$. Merel proved a criterion for when $g_p \geq 2$. We will give criteria for $g_p \geq 3, 4$ and prove higher Eichler formulas.
May 1	Tue	Jordan Williamson (Sheffield)	Magnitude Homology
13:00		Magnitude homology equals Hochschild homology II
		Hicks Seminar Room J11
May 2	Wed	Owen Jones (Cardiff)	Probability in the North East
13:30		Runoff processes on trees
		LT D
	Abstract: The volume of catchment discharge that reaches a stream via the overland flow path is critical for water quality prediction, because it is via this pathway that most particulate pollutants are generated and transported to the stream channel, via surface erosion processes. When it rains, spatial variation in the soil infiltration rate leads to the formation and reabsorption of rivulets on the surface, and local topography determines the coalescence of rivulets. We consider the question of how coalescence facilitates overland flow using a highly abstracted version of the problem, in which the drainage pattern is represented by a Galton-Watson tree. We show that as the rate of rainfall increases there is a distinct phase-change: when there is no stream coalescence the critical point occurs when the rainfall rate equals the infiltration rate, but when we allow coalescence the critical point occurs when the rainfall rate is less than the infiltration rate, and increasing the amount of coalescence increases the total expected runoff.
May 2	Wed	David O'Sullivan (Sheffield Hallam University)	Pure Maths Colloquium
14:00		Isomorphism conjectures and assembly maps via topological categories
		Hicks Seminar Room J11
	Abstract: The Baum-Connes conjecture is the "commutative" part of Alain Connes' noncommutative geometry programme, since it forms the bridge to classical geometry and topology. In its classical form, the conjecture identifies two object associated with a countable discrete group: one analytical and one topological. In their 1997 paper, Davis and Lück utilised a (then little known) category theoretic variant of an operator algebra to present a unified approach to this conjecture, and to the Isomorphism Conjecture of Farrell and Jones on the algebraic K- and L-theory of integral group rings. In this talk we will look at how this machinery fits together, what information the machinery gives us about the identifying maps, and how we might go about extending the scope of the techniques to topological groups and groupoids.
May 2	Wed	Vittoria Silvestri (Cambridge)	Probability in the North East
14:20		Recent progress on Laplacian growth models
		LT D
	Abstract: The Hastings-Levitov planar aggregation models describe growing random clusters on the complex plane, built by iterated composition of random conformal maps. A striking feature of these models is that they can be used to define natural off–lattice analogues of several fundamental discrete models, such as the Eden model or Diffusion Limited Aggregation, by tuning the correlation between the defining maps appropriately. In this talk I will discuss shape theorems and fluctuations of large clusters in the weak correlation regime. Joint work with James Norris and Amanda Turner.
May 2	Wed	David Penman (Essex)	Probability in the North East
15:30		Probabilistic aspects of comparable pairs and linear extensions of partial orders
		LT D
	Abstract: Given a finite partially ordered set $(P,\prec)$, a linear extension of it is a total order on the set which is compatible with the original partial order. A comparable pair of elements is two elements $x,y\in P$ for which we have $x\prec y$ or $y\prec x$. It is reasonable to ask about the extent of any relationship between the number of comparable pairs and the number of linear extensions, with an initial rough intuition being that fewer comparable pairs should correspond to more linear extensions. We will focus in this talk on the case of dense posets where a strictly positive proportion of pairs are comparable, though other cases will be considered as well. I shall focus on probabilistic aspects in this version of the talk, including the original motivating problem of estimating how many linear extensions a random interval order (which has roughly two-thirds of pairs comparable) possesses. This talk is based on joint work with Vasileios Iliopoulos and Colin McDiarmid.
May 2	Wed	*No talk*	ShEAF: postgraduate pure maths seminar
16:00
		Hicks Seminar Room J11
May 2	Wed	Andreas Kyprianou (Bath)	Probability in the North East
16:20		Entrance and exit at infinity for stable jump diffusions
		LT D
	Abstract: In a seminal work from the 50s of the last century, William Feller classified all one-dimensional diffusions on $-\infty\leq a1$ and $\alpha= 1$ differ significantly in the details by virtue of non-existence of local times for $\alpha=1$.
May 3	Thu	Salvo Guglielmino (Osservatorio Astrofisico di Catania)	SP2RC seminar
10:00		Interactions between pre-existing and emerging magnetic flux systems observed with IRIS
		K14
	Abstract: We report multi-wavelength ultraviolet observations taken with the IRIS satellite, concerning the emergence phase in the upper chromosphere and transition region of an emerging flux region (EFR) embedded in the unipolar plage of active region NOAA 12529. IRIS data are complemented by full-disk, simultaneous observations of the Solar Dynamics Observatory satellite, relevant to the photosphere and the corona. The photospheric configuration of the EFR is also analysed by measurements taken with the spectropolarimeter onboard the Hinode satellite, when the EFR was fully developed. Recurrent intense brightenings that resemble UV bursts, with counterparts in all coronal passbands, are identified at the edges of the EFR. Jet activity is also found at chromospheric and coronal levels, near the observed brightness enhancement sites. Analysis of the IRIS line profiles reveals heating of dense plasma in the low solar atmosphere and the driving of bi-directional, high-velocity flows with speeds up to 100 km/s at the same locations. Comparing these signatures with previous observations and numerical models, we suggest evidence of several long-lasting, small-scale magnetic reconnection episodes between the emerging bipole and the ambient field. This process leads to the cancellation of a pre-existing photospheric flux concentration of the plage with the opposite polarity flux patch of the EFR. Moreover, the reconnection appears to occur higher in the atmosphere than usually found in UV bursts, explaining the observed coronal counterparts.
May 3	Thu	Abhishek Saha (Queen Mary)	Number Theory seminar
14:00		On the critical values for the standard L-function of a Siegel modular form
		Hicks Seminar Room J11
	Abstract: I will talk about some joint work with Pitale and Schmidt where we prove an explicit pullback formula that gives an integral representation for the twisted standard L-function for a holomorphic vector-valued Siegel cusp form of degree n and arbitrary level. In contrast to all previously proved pullback formulas in this situation, our formula involves only scalar-valued functions despite being applicable to L-functions of vector-valued Siegel cusp forms. Further, by specializing our integral representation to the case n=2, we prove an algebraicity result for the critical L-values in that case (generalizing previously proved critical-value results for the full level case). Time permitting, I will also talk of some further applications and works in progress.
May 4	Fri	Mathew Owens (University of Reading)	SP2RC seminar
13:00		The changing heliosphere.
		LT 09
	Abstract: Knowledge of long-term solar variability underpins understanding of the solar dynamo and quantification of potential climate and space weather implications. Prior to direct spacecraft measurements of the heliospheric magnetic field (HMF) and solar wind, accurate annual reconstructions are possible using geomagnetic and sunspot records. On longer timescales, information about the HMF can be extracted from cosmogenic radionuclide records, particularly 14C in ancient trees and 10Be in ice sheets. I'll discuss these proxies and what they reveal about the HMF and solar wind, both in terms of space climate and space weather.
May 8	Tue	Johannes Nicaise (Imperial College (London))	Algebra / Algebraic Geometry seminar
14:00		A motivic Fubini theorem for the tropicalization map
		Hicks Seminar Room J11
	Abstract: Abstract: This talk is based on joint work with Sam Payne (arXiv:1703.10228). Kontsevich and Soibelman's motivic upgrade of Donaldson-Thomas theory produces refined curve counting invariants by means of motivic vanishing cycles of potential functions. In order to get a coherent theory, Kontsevich-Soibelman and Davison-Meinhardt have conjectured formulas for the motivic vanishing cycles of special types of functions. I will explain how one can deduce these formulas from a combination of Hrushovski-Kazhdan motivic integration and tropical geometry.
May 9	Wed	Shunsuke Takagi (University of Tokyo)	Pure Maths Colloquium
14:00		General hyperplane sections of 3-folds in positive characteristic
		Hicks Seminar Room J11
	Abstract: Miles Reid proved that in characteristic zero, a general hyperplane section of a canonical (resp. klt) 3-hold has only rational double points (resp. klt singularities). His proof heavily depends on the Bertini theorem for free linear series, which fails in positive characteristic. Thus, it is natural to ask whether the same statement holds in positive characteristic or not. In this talk, I will present an affirmative answer to this question when the characteristic is larger than 5. This is joint work with Kenta Sato.
May 9	Wed	Riccardo Vanon (Sheffield)	Applied Mathematics Colloquium
14:00		The role of zonal flows in self-gravitating astrophysical disc turbulence
		Hicks, LT 9
	Abstract: Astrophysical discs whose mass is not negligible compared to their central object (ie. self-gravitating discs) can be induced to fragment or settle into a turbulent-like state due to the de-stabilising action of self-gravity. Although the fragmentation process is well studied, the mechanism allowing the gravitational turbulent state to sustain itself is poorly understood, as this requires a continuous extraction of energy from the background flow to prevent its decay. In this talk I will present numerical simulations, carried out using a bespoke pseudo-spectral code, that will show how the gravitational turbulent state and the formation of zonal flows in the disc are strongly connected thanks to the action of axisymmetric and non-axisymmetric instabilities.
May 9	Wed	Matthew Bisatt (King's College)	Number Theory seminar
15:00		The generalised Birch--Swinnerton-Dyer conjecture and twisted L-functions
		LT 9
	Abstract: The Birch and Swinnerton-Dyer conjecture famously connects the rank of an elliptic curve to the order of vanishing of its L-function. We combine this with a conjecture of Deligne to study twisted L-functions and derive several interesting properties of them using tools from representation theory. We show that, under certain conditions, these conjectures predict that the order of vanishing of the twisted L-function is always a multiple of a given prime and provide analogous statements for L-functions of modular forms.
May 9	Wed	Davide Spriano (ETH Zurich)	ShEAF: postgraduate pure maths seminar
16:00		What is geometric group theory (and why people care about it)
		Hicks Seminar Room J11
	Abstract: Geometric group theory is an area of mathematics that focuses on understanding a group by understanding its geometric properties, which are typically expressed in terms of actions on metric spaces. The advantage of the geometric group theory approach is that it provides a better understanding of groups of great interest on which more classical approach would fail. A prominent example is given by "automorphism groups of certain objects". They can be easily defined, but it is not at all clear when they are, for instance, finitely generated. The first part of the talk will be concerned in providing example of such groups motivating why are they interesting and which are the main difficulties that arises in the study of them. In the second part, we will introduce some of the fundamental concepts and tools of geometric group theory and coarse geometry.
May 10	Thu	Fredrik Stromberg (Nottingham)	Number Theory seminar
14:00		Spectral theory and Maass forms for noncongruence subgroups
		F24
	Abstract: The spectral theory for congruence subgroups of the modular group is fairly well understood since Selberg and the development of the Selberg trace formula. In particular it is known that congruence subgroups has an infinite number of discrete eigenvalues (corresponding to Maass cusp forms) and there is extensive support towards Selberg’s conjecture that there are no small eigenvalues for congruence subgroups. In contrast to this setting, much less is known for noncongruence subgroups of the modular group even though these groups are clearly arithmetic. In fact, it can be shown that under certain circumstances small eigenvalues must exist. And even the existence of infinitely many “new” discrete eigenvalues is not known for these groups. The main obstacle for developing the spectral theory here is that there is in general no explicit formula for the scattering determinant. In this talk I will present sufficient conditions for an “odd” discrete spectrum to exist and I will also give experimental support for the conjecture that these conditions are also necessary. I will also present an experimental version of Turing’s method for certifying correctness of the spectral counting.
May 11	Fri	Siung Ghai (University of Sheffield)	SP2RC seminar
12:00		A statistical study of ionopause perturbation and associated boundary wave formation at Venus.
		LT 11
May 14	Mon	Kayla King (Oxford)	Mathematical Biology Seminar
13:00
		Alfred Denny LT1
May 15	Tue	Simon Willerton (Sheffield)	Magnitude Homology
13:00		A graph with torsion in magnitude homology (after Kaneta and Yoshinaga)
		Hicks Seminar Room J11
May 15	Tue	Damiano Testa (University of Warwick)	Algebra / Algebraic Geometry seminar
14:00		Plane quartics and their inflection lines
		Hicks Seminar Room J11
	Abstract: Let C be a general plane quartic curve. It follows from the Plücker formulas that C admits 24 inflection lines. We address the question of finding all the plane quartics D, having the same 24 inflection lines as C. In joint work with Marco Pacini, we show that, over fields of characteristic coprime with 6, the curve C is uniquely determined by its configuration of inflection lines.
May 15	Tue	Damien Trinh (Manchester)	Cosmology, Relativity and Gravitation
16:00		The dark sector in light of GW170817
		Hicks Seminar Room J11
	Abstract: Recent observations in the propagation of gravitational waves have seemingly severely restricted viable alternatives to the cosmological constant. Indeed, the stringent constraint that gravitational waves must propagate at the speed of light is not something which many modified gravity theories predict. Using the Equation of State approach, I will discuss its implications to some theories and also highlight some caveats to the recent observations which may yield a slightly more optimistic outlook for this field.
May 16	Wed	Shaun Stevens (University of East Anglia)	Pure Maths Colloquium
14:00		Towards an explicit local Langlands correspondence for classical groups
		Hicks Seminar Room J11
	Abstract: The local Langlands correspondence is a web of sometimes conjectural correspondences between, on the one hand, irreducible representations of reductive groups over a p-adic field F and, on the other hand, certain representations of the absolute Weil group of F (which is almost the absolute Galois group). I will try to explain what the objects involved here are, some of what the correspondence predicts and what is known/unknown, as well as work (particularly due to Bushnell and Henniart for general linear groups) towards making the correspondence explicit. Hopefully I will also explain some joint work (with Blondel and Henniart) where we describe the "wild part'' of the correspondence for symplectic groups.
May 16	Wed	Ati Sharma (Southampton)	Applied Mathematics Colloquium
14:00		Some recent developments in the low-order modelling of fluid flows
		Hicks, LT 9
	Abstract: Modelling fluid flows is a difficult problem. Fluid flows are well described by the Navier-Stokes equations, but these are nonlinear PDEs, which are difficult to solve in a general way. Much recent work has focused on finding low-dimensional approximations to fluid flow systems, either by abstracting them from data generated from experiment and simulation or by finding suitable approximations to the equations. This talk will discuss two such approaches, Dynamic Mode Decomposition (DMD) and resolvent analysis. The approaches will be explained, and a variety of recent applications to flow analysis and estimation will be presented.
May 16	Wed	Arend Bayer (University of Edinburgh)	Algebra / Algebraic Geometry seminar
15:30		Families of Hyperkaehler varieties via families of stability conditions
		Hicks Seminar Room J11
	Abstract: Abstract: Stability conditions on derived categories of algebraic varieties and their wall-crossings have recently been used extensively to study the geometry of moduli spaces of stable sheaves. In work in progress with Macri, Lahoz, Nuer, Perry and Stellari, we are extending this toolkit to the "relative" setting, i.e. for a family of varieties. Our construction comes with relative moduli spaces of stable objects; this gives additional ways of constructing new families of varieties from a given family, thereby potentially relating different moduli spaces of varieties. Our main application is for families of cubic fourfolds; in particular, this produces many new examples of algebraically constructed families of Hyperkaehler varieties over a base of maximal dimension 20.
May 16	Wed	*No talk*	ShEAF: postgraduate pure maths seminar
16:00
		Hicks Seminar Room J11
May 17	Thu	Frazer Jarvis (Sheffield)	Number Theory seminar
14:00		$p$-adic periods of genus 2 curves via the AGM
		F24
	Abstract: The arithmetic-geometric mean provides the fastest way to compute periods of elliptic curves, both over the complex and $p$-adic numbers. There is an isogeny of genus 2 curves which looks like it might play the same role to compute periods for curves of genus 2. In this talk, we will discuss progress in developing an algorithm for the $p$-adic case, where $p$-adic periods were defined and first investigated in Teitelbaum's thesis. It is as yet incomplete, but the only missing step is an explicit Tate uniformisation for genus 2 curves. This is joint work with Rudolf Chow, and relates to the final chapter of his PhD thesis.
May 21	Mon	Angelo Rendina (Sheffield)	Number Theory Learning Seminar
14:00		Geometric definition of modular forms
		Hicks Seminar Room J11
May 22	Tue	Paolo Stellari (Universita' degli studi di Milano)	Algebra / Algebraic Geometry seminar
14:00		TBA
		Hicks Seminar Room J11
	Abstract: TBA
May 22	Tue	Joseph Fernandez (Liverpool John Moores)	Cosmology, Relativity and Gravitation
16:00		Tidal encounters of compact binaries with massive black holes as a source of gravitational waves
		Hicks Seminar Room J11
	Abstract: Massive black holes (MBHs) are ubiquitous in galactic centres. The extreme potential due to these objects dominates the surrounding dynamics, giving rise to physics not possible in other regions. These regions are of particular interest for gravitational wave astronomy, as several dynamical processes which can give rise to black hole (BH) binary mergers have been postulated. We show that compact binaries can survive close encounters with the MBH without being disrupted, and that they tend to become hard and eccentric. Since the GW merger time of binaries is sensitive to the semi-major axis length and eccentricity, we find that this leads to a reduction of the merger time by several orders of magnitude in some cases. Therefore, tidal encounters of stellar mass BH binaries with a MBH at the centre of galaxies can provide a new formation channel of BH mergers. We use Monte Carlo simulations to evaluate the effective spin of the binaries after the encounter We also provide a description of a simple scenario to understand how this process could take place the a larger astrophysical context.
May 23	Wed	Ciaran Meachan (University of Glasgow)	Algebra / Algebraic Geometry seminar
13:00		Derived equivalent Hilbert schemes of points on K3 surfaces which are not birational
		Hicks LT09
	Abstract: Starting with two non-birational derived equivalent K3 surfaces, one can ask whether their Hilbert schemes of points are birational. In this talk, we will show that in some cases they are but in most cases they are not. This is joint work with Giovanni Mongardi and Kota Yoshioka.
May 23	Wed	Daniil Proskurin (Kiev Taras Shevchenko University)	Pure Maths Colloquium
14:00		$C^*$-algebras generated by quonic commutation relations and extensions of non-commutative tori
		Hicks Seminar Room J11
	Abstract: We consider $C^*$-algebras $A_{q_i}\Theta$ generated by relations of the following form $$a_i^*a_i=1+q_i a_ia_i^* a_i^*a_j=e^{2\pi\theta_{ij}} a_ja_i^*, \quad i\ne j i, \quad j=1,\ldots,d $$ where $-1 \lt q_i \lt 1$, $\theta_{ij}=-\theta_{ji}$, $i\ne j$. We show that $A_{q_i}\Theta \simeq A_{0}\Theta$ is an extension of higher-dimensional non-commutative tori and study its properties.
May 23	Wed	Xiaolei Zhao (Northeastern University)	Algebra / Algebraic Geometry seminar
15:00		Twisted cubics on cubic fourfolds and stability conditions
		Hicks LT09
	Abstract: It is a classical result of Beauville and Donagi that Fano varieties of lines on cubic fourfolds are hyper-Kahler. More recently, Lehn, Lehn, Sorger and van Straten constructed a hyper-Kahler eightfold out of twisted cubics on cubic fourfolds. In this talk, I will explain a new approach to these hyper-Kahler varieties via moduli of stable objects on the Kuznetsov components. Along the way, we will derive several properties of cubic fourfolds as consequences. This is based on a joint work with Chunyi Li and Laura Pertusi.
May 23	Wed	Chunyi Li (University of Warwick)	Algebra / Algebraic Geometry seminar
16:15		Bogomolov type inequality for Fano varieties with Picard number 1
		Hicks LT09
	Abstract: I will talk about some basic facts about slope stable sheaves and the Bogomolov inequality. New techniques from stability conditions will imply new stronger bounds on Chern characters of stable sheaves on some special varieties, including Fano varieties, quintic threefolds and etc. I will discuss the progress in this direction and some related open problems.
May 24	Thu	Adel Betina (Sheffield)	Number Theory Learning Seminar
14:00		The modular curve
		Hicks Seminar Room J11
May 29	Tue	Scott Balchin (Sheffield)	Magnitude Homology
13:00		Mangitude homology and persistent homology??
		Hicks Seminar Room J11
May 29	Tue	Elisa Postinghel (University of Loughborough)	Algebra / Algebraic Geometry seminar
14:00
		Hicks Seminar Room J11
May 29	Tue	Jessie Durk (Queen Mary UL)	Cosmology, Relativity and Gravitation
16:00		Black hole lattices as inhomogeneous cosmological models
		LT09, Hicks
	Abstract: The standard model of cosmology, ΛCDM, is based on the assumption that the Universe can be described by the homogeneous and isotropic FLRW solution to the Einstein field equations. The need to test whether the large-scale expansion of space is that of FLRW, or is instead modified by the presence of inhomogeneities, has lead to this assumption being relaxed. An interesting subset of inhomogeneous cosmologies include those dubbed black hole lattices. These are exact, fully-relativistic treatments of universes with a discretised matter content. We generalise an existing family of these to include a cosmological constant, structure formation and electric charge. For each new generalisation, we find a common behaviour of tending towards FLRW-like as the number of masses is increased, and for the addition of structures, we investigate the effect of gravitational interaction energies between clustered masses.
May 30	Wed	Nebojsa Pavic (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		Intersection theory in algebraic geometry: History and motivation.
		Hicks Seminar Room J11
	Abstract: In this talk I'm going to motivate the notion of intersection theory in algebraic geometry by considering the example of Riemannian surfaces and only requiring a basic knowledge of complex analysis and a little bit of complex differential geometry. If time permits, I will give a rigorous definition of intersection groups, so called Chow groups, and relate them to the example.
May 31	Thu	S. Shelyag (Northumbria University)
10:00		Do photospheric non-magnetic bright points exist?
		LT 10
	Abstract: Recent high-resolution simulations of non-magnetic solar photospheric convection suggest the presence of a separate class of small-scale photospheric brightenings, which coincide with intergranular vortex tubes. In contrast to well-known magnetic bright points, these brightenings are not related to magnetic fields. In our presentation, using high-resolution simulations with MURaM and detailed radiative diagnostics of the simulated models, I will analyse the physical characteristics of these brightenings and their observability with current and future instruments for solar observations.
May 31	Thu	Adel Betina (Sheffield)	Number Theory Learning Seminar
14:00		Modular curve- Part 2
		Hicks Seminar Room J11
Jun 4	Mon	Ariel Weiss (Sheffield)	Number Theory Learning Seminar
14:00		Hasse invariant
		Hicks Seminar Room J11
Jun 6	Wed	Ciaran Schembri (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		Fuchsian group
		Hicks Seminar Room J11
	Abstract: Fuchsian groups are discrete subgroups of the special projective linear group. They act as isometries on the hyperbolic plane and are studied because of their role in generating Riemann surfaces among other things. In this talk I will outline their geometric properties and if time permits will discuss how they relate to modern number theory.
Jun 7	Thu	Adel Betina (Sheffield)	Number Theory Learning Seminar
14:00		Introduction to rigid analytic geometry- Part (1)
		Hicks Seminar Room J11
Jun 11	Mon	Adel Betina (Sheffield)	Number Theory Learning Seminar
14:00		Introduction to rigid analytic geometry- Part (2)
		Hicks Seminar Room J11
Jun 14	Thu	Adel Betina (Sheffield)	Number Theory Learning Seminar
14:00		Introduction to rigid analytic geometry- Part (3)
		Hicks Seminar Room J11
Jun 18	Mon	Adel Betina (Sheffield)	Number Theory Learning Seminar
14:00		The canonical subgroup
		Hicks Seminar Room J11
Jun 21	Thu	Adel Betina (Sheffield)	Number Theory Learning Seminar
14:00		Classicality
		Hicks Seminar Room J11
Jun 25	Mon	Adel Betina (Sheffield)	Number Theory Learning Seminar
14:00		Classicality of overconvergent modular forms
		Hicks Seminar Room J11
Jun 27	Wed	Ariel Weiss (Sheffield)	Number Theory Learning Seminar
14:00		Hida families (classical treatment)
		Hicks Seminar Room J11
Jun 28	Thu	Adel Betina (Sheffield)	Number Theory Learning Seminar
14:00		Hida families (a la Pilloni)
		Hicks Seminar Room J11
Jul 3	Tue	Bram Mesland (MPIM Bonn)	K-Theory, Hecke Algebras and Representation Theory
14:30		A Hecke module structure on the KK-theory of arithmetic groups
		Lecture Theatre C
	Abstract: Let G be a locally compact group, H a discrete subgroup and C(G,H) the commensurator of H in G. The cohomology of H is a module over the Shimura Hecke ring of the pair (H,C(G,H)). This construction recovers the action of the Hecke operators on modular forms for SL(2,Z) as a particular case. In this talk I will discuss how the Shimura Hecke ring of a pair (H, C(G,H)) maps into the KK-ring associated to an arbitrary H-C*-algebra. From this we obtain a variety of K-theoretic Hecke modules. In the case of manifolds the Chern character provides a Hecke equivariant transformation into cohomology, which is an isomorphism in low dimensions. We discuss Hecke equivariant exact sequences arising from possibly noncommutative compactifications of H-spaces. Examples include the Borel-Serre and geodesic compactifications of the universal cover of an arithmetic manifold, and the totally disconnected boundary of the Bruhat-Tits tree of SL(2,Z). This is joint work with M.H. Sengun (Sheffield).
Jul 3	Tue	Heath Emerson (Victoria)	K-Theory, Hecke Algebras and Representation Theory
16:00		Noncommutative Lefshetz fixed-point formulas via KK-theory
		Lecture Theatre C
	Abstract: Using the idea of K-theoretic Poincaré duality, it is possible to formulate an analogue of the classical Lefschetz fixed-point formula from basic algebraic topology, which applies to KK-endomorphisms (e.g. ordinary C*-algebra endomorphisms) of a C*-algebra equipped with such a duality. We discuss the general methodology and apply it in the example of the C*-algebra crossed-product of a discrete group acting properly, smoothly and co-compactly on a smooth manifold. The result is an `orbifold' Lefschetz formula of some interest; our hope is that many other examples should exist.
Jul 4	Wed	Hang Wang (Adelaide / East China Normal)	K-Theory, Hecke Algebras and Representation Theory
09:30		Role of local Langlands correspondence in K-theory of group C*-algebras
		Lecture Theatre C
	Abstract: K-theory of C*-algebras associated to a Lie group can be understood both from the geometric point of view via Baum-Connes assembly map and from the representation theoretic point of view via harmonic analysis of Lie groups. Inspired by the local Langlangds correspondence and work by Plymen and collaborators, one can study relations between two groups, where their L-parameters are related in a nice way, from the aspects of K-theory and index theory of invariant elliptic operators. I will introduce two examples I investigated with Peter Hochs (when the two groups are inner forms to each other) and with Kuok Fai Chao (when there is a base change involved between the L-parameters of the two groups).
Jul 4	Wed	Alexandre Afgoustidis (Paris 9)	K-Theory, Hecke Algebras and Representation Theory
11:00		On the tempered dual of a real reductive group and that of its Cartan motion group
		Lecture Theatre C
	Abstract: Given a reductive Lie group G and a maximal compact subgroup K, one can consider the isometry group of the (flat) tangent space to G/K at the identity coset: this is a first-order approximation of G near K, called the Cartan motion group of G. George Mackey’s early work on semi-direct products describes its unitary representations in very simple and concrete terms. In the 1970s, Mackey noticed that his parametrization for the representations of the motion group showed unexpected similarities with Harish-Chandra’s more subtle parametrization for the tempered representations of G. Motivated by quantum-mechanical considerations related with the existence of a one-parameter family of Lie groups interpolating between both groups, he suggested that a kind of rigidity of representation theory along the deformation may be observed in general. Alain Connes and Nigel Higson later pointed out that the Baum-Connes-Kasparov isomorphism in operator K-theory can be viewed, for real reductive groups, as a cohomological reflection of Mackey’s ideas. For the special case of complex semisimple groups, Nigel Higson gave in 2008 a precise form to Mackey’s analogy and its relationship with the Baum-Connes-Kasparov isomorphism. For real reductive groups, I will describe a natural one-to-one correspondence between the tempered and admissible duals of both groups, and discuss some geometrical (or topological) aspects of the rigidity revealed by the correspondence along the deformation from one group to the other.
Jul 4	Wed	Pierre Clare (William&Mary)	K-Theory, Hecke Algebras and Representation Theory
14:00		On the reduced C*-algebra of real reductive groups
		Lecture Theatre C
	Abstract: I will report on joint work with Nigel Higson regarding the description up to Morita equivalence of the reduced C*-algebra of a class of real reductive groups. The results build on previous work, joint with Tyrone Crisp, and are related to the approach to the Connes-Kasparov isomorphism promoted by Roger Plymen and others.
Jul 4	Wed	Nigel Higson (PennState)	K-Theory, Hecke Algebras and Representation Theory
15:30		On (some of) the work of Roger Plymen
		Lecture Theatre C
	Abstract: I shall give an appreciation of some of the fundamental contributions of Roger Plymen to the themes of this conference, focusing on his studies of the C*-algebras of real and p-adic groups, and their K-theory groups.
Jul 5	Thu	Peter Hochs (Adelaide)	K-Theory, Hecke Algebras and Representation Theory
09:30		K-types of tempered representations and index theory
		Lecture Theatre C
	Abstract: Let G be a semisimple Lie group. Tempered representations of G are the ones occurring in the Plancherel decomposition of $L^2$(G). They are also relevant to the Langlands classification of the more general admissible representations. In joint work with Yanli Song and Shilin Yu, we realise the restriction of any tempered representation to a maximal compact subgroup K as an equivariant index. This is a concrete expression of Kirillov's orbit method. A consequence of this realisation is a geometric expression for the multiplicities of the irreducible representations of K in that restriction. (The irreducible representations that occur are the K-types of the representation.) This helps to study the general behaviour of those multiplicities. As an example, we show that admissible representations of SU(p,1) and SO_0(p,1) restrict multiplicity-freely to maximal compact subgroups. That was proved earlier by Koornwinder, but now illustrates our multiplicity formula.
Jul 5	Thu	Henrik Schlichtkrull (Copenhagen)	K-Theory, Hecke Algebras and Representation Theory
11:00		Harmonic analysis on real spherical spaces
		Lecture Theatre C
	Abstract: Let G be a real reductive Lie group. A homogeneous space Z of G is called real spherical if the minimal parabolic subgroups of G have only finitely many orbits on Z. For example, the Bruhat decomposition of G implies that Z=G is real spherical for the two-sided action of G$\times$G. A survey will be given of some recent progress (by F. Knop, B. Krötz, and others) on the generalization of Harish-Chandra's harmonic analysis to such spaces.
Jul 5	Thu	Beth Romano (Cambridge)	K-Theory, Hecke Algebras and Representation Theory
14:00		The local Langlands correspondence in small residue characteristic
		Lecture Theatre C
	Abstract: Through explicit examples, I'll discuss why the local Langlands correspondence becomes mysterious for small residue characteristic. I'll focus on examples and conjectures related to ``epipelagic" representations, which have minimal positive depth.
Jul 5	Thu	Tyrone Crisp (Nijmegen)	K-Theory, Hecke Algebras and Representation Theory
15:30		Parabolic induction over the p-adic integers
		Lecture Theatre C
	Abstract: For p-adic reductive groups like GL(n,Q_p), the right-hand side of the Baum-Connes conjecture --- i.e., the K-theory of the group C*-algebra --- is in many respects better understood than the left-hand side. This unusual state of affairs is due to the extremely complicated representation theory of compact p-adic groups like GL(n,Z_p). In this talk I shall present an ongoing program, joint with Ehud Meir and Uri Onn, that aims to understand the representations of these compact groups in terms of parabolic induction from Levi subgroups, analogously to the way one usually studies representations of real, complex, p-adic, and finite reductive groups.
Jul 6	Fri	Christian Voigt (Glasgow)	K-Theory, Hecke Algebras and Representation Theory
09:30		Categorification and Hecke algebras
		Lecture Theatre C
	Abstract: The idea of categorification is to replace set theoretic constructions and theorems by category theoretic analogues, recovering the original constructions via taking isomorphism classes or K-groups. In this talk I’ll discuss some examples of this procedure related to Hecke algebras and connections to noncommutative geometry.
Jul 6	Fri	Maarten Solleveld (Nijmegen)	K-Theory, Hecke Algebras and Representation Theory
11:00		Topological K-theory of affine Hecke algebras
		Lecture Theatre C
	Abstract: An affine Hecke algebra can be completed to a C*-algebra. These algebras appear in the theory of reductive p-adic groups, and they are of interest in representation theory and in relation with the Baum--Connes conjecture.They provide typical examples of C*-algebras which are close to commutative. In this talk I will discuss results about the K-theory of such C*-algebras, and techniques used to study it. In particular, I will show that the K-theory does not depend on the deformation parameter of the Hecke algebra. In the end all calculations will be reduced to equivariant K-theory of topological spaces, with respect to certain nice actions of finite groups. I will show that under mild conditions these equivariant K-groups are torsion-free.
Jul 6	Fri	Sergio Mendes (ISCTE Lisbon)	K-Theory, Hecke Algebras and Representation Theory
14:00		On L-packets and depth for SL2(K) and its inner forms
		Lecture Theatre C
	Abstract: An invariant that makes sense on both sides of the local Langlands correspondence is depth. In this talk we survey the notion of depth and study depth-preservation under the local Langlands correspondence. Examples will be provided with special emphasis to the group SL2 over a local field with characteristic 2. This talk is based on joint work with Anne-Marie Aubert, Roger Plymen and Maarten Solleveld.
Jul 6	Fri	Anne-Marie Aubert (Paris 6)	K-Theory, Hecke Algebras and Representation Theory
15:30		Affine Hecke algebras on the Galois side
		Lecture Theatre C
	Abstract: We will explain a way to attach affine Hecke algebras to certain Langlands parameters on Levi subgroups of a given p-adic reductive group in relation with the ABPS-conjecture. This is joint work with Ahmed Moussaoui and Maarten Solleveld.
Jul 17	Tue	David Spencer (Sheffield)	Number Theory seminar
14:00		Congruences of local origin for higher levels
		Hicks Seminar Room J11
	Abstract: There are many kinds of congruences between different types of modular forms. The most well known of which is Ramanujan's mod 691 congruence. This is a congruence between the Hecke eigenvalues of the weight 12 Eisenstein series and the Hecke eigenvalues of the weight 12 cusp form (both at level 1). This type of congruence can be extended to give congruences of ''local origin''. In this talk I will explain what is meant by such a congruence while focusing on the case of weight 1. The method of proof in this case is very different to that of higher weights and involves working with Galois representations and ray class characters.
Aug 7	Tue	Kirill Mackenzie (Sheffield)
14:00		Quotients of Lie algebroids
		LT 7
	Abstract: For a transitive Lie algebroid $A$, and an ideal in the adjoint bundle (= kernel of the anchor), there is a simple construction of a quotient Lie algebroid over the same base, and this has the usual properties. When the base manifold is also quotiented, the situation is more complicated. This talk will describe the general quotient construction, starting with the case of vector bundles. I'll assume a basic familiarity with Lie algebroids. All are welcome.
Sep 26	Wed	Yang Zhang (Sheffield (Mech Eng))	Applied Mathematics Colloquium
14:00		Imaging based flame diagnostics and its quantitative analysis
		Hicks, LT 9
	Abstract: In this talk, a brief history of photography and their application in combustion studies will be given, which actually goes back to the 19th century. Then case studies will be shown on digital flame imaging, especially high speed imaging for the tracking of the fast flame dynamics. It will demonstrate that selective digital imaging enhancement is essential in observing the drastically different flame light intensities of the soot and chemical species. Through digital image processing, quantitative and useful information can be extracted from the flame image database. The simultaneous imaging of visible and infrared light emissions from the ignition of a flame using a single high speed colour digital camera will also be demonstrated which also poses a challenge in spectroscopic study on how to identify this infrared only emissions.
Oct 1	Mon	Rachel Bearon (Liverpool)	Mathematical Biology Seminar
14:00		Revisiting Jeffery orbits; the importance of shape for micro-organism transport
		Hicks F41
Oct 3	Wed	Priya Subramanian (Leeds)	Applied Mathematics Colloquium
14:00		Pattern formation in systems with multiple scales
		Hicks, LT 9
Oct 9	Tue	Angelo Rendina (Sheffield)	Number Theory seminar
14:00		Nearly holomorphic Siegel modular forms and applications
		Hicks Seminar Room J11
	Abstract: Nearly holomorphic modular forms were introduced by Shimura as a generalization of modular forms to study a more general class of Eisenstein series. I will introduce some of the tools that we use to work with them, such as the Shimura-Maass differential operator and holomorphic projection, and present some applications: some formulae for the sum of divisor $s_r$ and Ramanujan $\tau$ functions and then congruences of critical $L$-values attached to Siegel modular forms, the latter being part of my research project.
Oct 10	Wed	Visakan Balakumar & Jake Percival (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Report from QFT Energy Inequalities conference
		Hicks Seminar Room J11
Oct 15	Mon	Helen Kettle (BIOSS)	Mathematical Biology Seminar
14:00
		Hicks F41
Oct 16	Tue	Kohei Kikuta (Osaka)	Algebra / Algebraic Geometry seminar
16:00		On categorical entropy
		Hicks Seminar Room J11
	Abstract: The categorical entropy of triangulated endofunctors was defined by Dimitrov-Haiden-Katzarkov-Kontsevich motivated by classical dynamical theory. In this talk, I'll explain relations to classical entropy theory, basics on categorical entropy, many examples and future directions.
Oct 17	Wed	Jack Morrice (Cape Town)	Cosmology, Relativity and Gravitation
00:00		Streams: a small, mesh-based look at large structure formation
		Hicks Seminar Room J11
	Abstract: Today, cosmology's N-body paradigm looks a bit like a power monopoly. The codes (GADGET, RAMSES...) have huge computational overheads; descriptions of their underlying algorithms are old and hard to find; and the outputs of these codes are very difficult to analyze. These factors make the study of cosmic large scale structure accessible only to those with easy access to a lot of supercomputer cores and a familiarity with old imperative programming languages like C and Fortran. In this talk, we will look at Streams, a modest attempt to address these issues. Streams is a small package written for the Julia programming language that uses Lagrangian perturbation theory to significantly reduce overheads, and is built from a computer geometry (mesh) perspective which, together, make it very well suited to studying the formation of folds and caustics in the dark matter fluid on a personal computer.
Oct 17	Wed	Kevin Buzzard (Imperial)	Pure Maths Colloquium
14:00		Pure mathematics in crisis?
		Hicks Lecture Theatre C
	Abstract: I argue that pure mathematics is walking inexorably towards a cliff edge, and that anyone who believes that current pure mathematics is rigorous, or a science, needs to wake up and look at the facts, which there will be plenty of in this talk, and they are not pretty. Are our results reproducible? Does it matter? What *is* mathematics? Can computer scientists save us? Can *undergraduates* save us? I hope so. This talk is about pure mathematics but will be accessible to undergraduates, mathematicians both pure and applied/applicable and computer scientists.
Oct 18	Thu	Gary Verth (Sheffield)	Plasma Dynamics Group
15:00		Introduction to the Sun
		Room K14 (Hicks Building)
	Abstract: This talk will be an introduction to the science required to understand the Sun and its atmosphere. It is primarily intended for students starting their postgraduate research in plasma, solar, or magnetospheric physics. Due to the introductory nature of the talk, it would also be suitable for any interested non-specialists.
Oct 18	Thu	Simon Willerton (Sheffield)	Topology Seminar
16:00		The Legendre-Fenchel transform from a category theoretic perspective
		Hicks Seminar Room J11
	Abstract: The Legendre-Fenchel transform is a classical piece of mathematics with many applications. In this talk I'll show how it arises in the context of category theory using categories enriched over the extended real numbers $\overline{ \mathbb{R}}:=[-\infty,+\infty]$. It turns out that it arises out of nothing more than the pairing between a vector space and its dual in the same way that the many classical dualities (eg. in Galois theory or algebraic geometry) arise from a relation between sets. I will assume no knowledge of the Legendre-Fenchel transform and no knowledge of enriched categories.
Oct 23	Tue	Kim Klinger-Logan (Minnesota)	Number Theory seminar
14:00		The Riemann Hypothesis and periods of Eisenstein series
		Hicks Seminar Room J11
	Abstract: This summer at Perspectives on the Riemann Hypothesis, Bombieri and Garrett discussed modifications to the invariant Laplacian $\Delta=y^2(\partial_x^2+\partial_y^2)$ on $SL_2(\mathbb{Z})\backslash\mathfrak{H}$ possibly relevant to RH. We will present a $GL(2)$ $L$-function as a period of Eisenstein series which can, in turn, be thought of as a linear functional on an Eisenstein series and we will discuss how such functionals may be use to analyze the zeros of the $L$-function. This idea is an extension of recent work of Bombieri and Garrett and uses techniques from functional analysis and spectral theory of automorphic forms.
Oct 23	Tue	Nebojsa Pavic (Sheffield)	Algebra / Algebraic Geometry seminar
16:00		Grothendieck groups and singularity categories of quotient singularities
		Hicks Seminar Room J11
	Abstract: We study the K-theory of the Buchweitz-Orlov singularity category for quasi-projective algebraic schemes. Particularly, we show for isolated quotient singularities with abelian isotropy groups that the Grothendieck group of the singularity category is finite torsion and that rational Poincare duality is satisfied on the level of Grothendieck groups. We consider also consequences for the resolution of singularities of such quotient singularities and study dual properties in this setting, more concretely we prove a conjecture of Bondal and Orlov in the case of quotient singularities.
Oct 24	Wed	Christian Voigt (Glasgow)	Pure Maths Colloquium
14:00		$C^*$-algebras, the Baum-Connes conjecture and quantum groups
		Hicks Seminar Room J11
	Abstract: A central theme of research in operator algebras is the Baum-Connes conjecture, which predicts the K-theory of group $C^*$-algebras and crossed products. In this talk I will give a leisurely introduction to this conjecture, explain what it is good for, and discuss some recent connections with the theory of quantum groups.
Oct 24	Wed	Istvan Cziegler (York)	Applied Mathematics Colloquium
14:00		Turbulence and phase transitions in tokamak plasmas
		Hicks, LT 11
	Abstract: The transition from the low- to the high-confinement operation is one of the most important phenomena in magnetic confinement fusion. The high-confinement regime, known as H-mode, leads to a vastly increased plasma density and temperature, which equates to a significant gain in fusion power. Since the dominant transport across the confining magnetic field is due to turbulence, the L-H transition can be thought of as a phase transition to suppressed turbulence. It is known that both the quality of global confinement and the threshold of the transition depend on macroscopic parameters, such as plasma density, magnetic topology and geometry near particle exhaust areas called divertors. The talk will connect the various scales of dynamics with this phenomenology and some broader context in physics.
Oct 24	Wed	Elizabeth Winstanley (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Quantum expectation values on black hole space-times
		Hicks Seminar Room J11
	Abstract: The renormalized expectation value of the stress energy tensor (RSET) is an object of central importance in quantum field theory in curved space-time, but calculating this on black hole space-times is far from trivial. The standard methodology was developed in the 1980s and 1990s and successfully applied to a range of quantum fields on Schwarzschild black holes. The subject received an impetus in the last few years with to the development of two novel approaches to computing the RSET and renormalized vacuum polarization (VP). These advances have enabled calculations on a wider range of black hole space-times to be performed. In this talk we will review both the standard and novel methodologies and some results for the RSET and VP on asymptotically flat, de Sitter and anti-de Sitter black holes.
Oct 24	Wed	James Brotherston, Callum Reader, Sadiah Zahoor	ShEAF: postgraduate pure maths seminar
16:00
		Hicks Seminar Room J11
	Abstract: What is Forcing? (Reader) I will give an introduction to the main themes behind Cohen's forcing method in ZFC, as framed by Scott through the lens of Boolean algebras. Given time there will also be some discussion of why, contrary to Godel's belief, forcing shows that the inclusion of large cardinal axioms does not solve the continuum hypothesis A Calculation of Some Group Cohomology (Brotherston) I will give a very brief introduction to group cohomology and why we care in relation to algebraic K-theory. I will then move on to outline a mostly geometric calculation of the former in the case where $G = GL_n(\mathbb{F}_q)$ with coefficients in $\mathbb{Z}/l$ for $l$ coprime to the characteristic of the field $\mathbb{F}_q$. There will hopefully be a little of number theory, algebraic topology and algebraic geometry mentioned. Tate Shafarevich Groups - The mysterious objects attached to Elliptic Curves (Zahoor) One of the main unsolved mystery about elliptic curves is the size of the Tate Shafarevich Group (Sha), that is conjectured to be finite. The lack of proof of this particular fact is one of the main barriers in giving an algorithm to compute rank of an elliptic curve. Intuitively, Sha measures the obstruction to the Hasse (local-global) principle. This talk aims at understanding Tate Shafarevich Groups using torsors of elliptic curves and is deigned for anyone having a first look at the Sha.
Oct 25	Thu	Anna Marie Bohmann (Vanderbilt)	Topology Seminar
16:00		Graded Tambara Functors
		Hicks Seminar Room J11
	Abstract: Let G be a finite group. The coefficients of G-equivariant cohomology theories naturally form a type of structure called a Mackey functor, which incorporates data coming from each subgroup of G. When the cohomology theory is a G-ring commutative spectrum---meaning that is has an equivariant multiplication---interesting new structures arise. In particular, work of Brun and of Strickland shows that the zeroth homotopy groups have norm maps which yield the structure of a Tambara functor. In this talk, I discuss joint work with Vigleik Angeltveit on the algebraic structure induced by norm maps on the higher homotopy groups, which we call a graded Tambara functor.
Oct 29	Mon	Elaine Ferguson (Glasgow)	Mathematical Biology Seminar
14:00
		Hicks F41
Oct 30	Tue	Adel Betina (Sheffield)	Number Theory seminar
14:00		On the p-adic periods of semi-stable modular curves
		Hicks Seminar Room J11
	Abstract: I will present a joint work with E.Lecouturier in which we prove a variant of Oesterlé's conjecture about $p$-adic periods of the modular curve $X_0(p)$, with an additional $Γ(2)$-structure. We use de Shalit's techniques and $p$-adic uniformization of Mumford curves whose reduction is semi-stable.
Oct 31	Wed	Miguel Teixeira (Reading)	Applied Mathematics Colloquium
14:00		A physically-based model for the wind-driven current in the wavy oceanic surface layer
		Hicks, LT 9
	Abstract: A simple analytical model is developed for the current induced by the wind and modified by surface wind-waves in the oceanic surface layer, based on a first-order turbulence closure and including the effect of a vortex force representing the Stokes drift of the waves. The shear stress is partitioned between a component due to shear in the current and a wave-induced component, which decays over a depth proportional to the wavelength. The model reproduces the apparent reduction of the friction velocity and enhancement of the roughness length estimated from current profiles, detected in a number of studies. The current profile becomes flatter for strong wave forcing owing to a smaller fraction of the total shear stress being supported by the current shear. These effects are entirely attributed to non-breaking surface waves, and predicted to increase with wave forcing. A version of the model where the shear stress decays to zero with depth is able to adequately predict the surface current speed.
Nov 1	Thu	David Kuridze (Aberystwyth University)	SP2RC seminar
10:00		Spectropolarimetric Inversions of the Ca II 8542 Å Line in an M-class Solar Flare
		LT 10
	Abstract: We study an M1.9-class solar flare (SOL2015-09-27T10:40 UT) using high-resolution full Stokes imaging spectropolarimetry of the Ca II 8542 Å line obtained with the CRISP imaging spectropolarimeter at the Swedish 1-m Solar Telescope. Spectropolarimetric inversions using the non-LTE code NICOLE are used to construct semi-empirical models of the flaring atmosphere to investigate the structure and evolution of the flare temperature and magnetic field. A comparison of the temperature stratification in flaring and nonflaring areas reveals strong heating of the flare ribbon during the flare peak. The polarisation signals of the ribbon in the chromosphere during the flare maximum become stronger when compared to its surroundings and to pre- and post-flare profiles. Furthermore, a comparison of the response functions to perturbations in the line-of-sight magnetic field and temperature in flaring and nonflaring atmospheres shows that during the flare, the Ca II 8542 Å line is more sensitive to the lower atmosphere where the magnetic field is expected to be stronger. The chromospheric magnetic field was also determined with the weak-field approximation, which led to results similar to those obtained with the NICOLE inversions.
Nov 1	Thu	Sam Marsh and Simon Willerton (Sheffield)	Teaching Lunch
13:00		Things we've tried in 115.
		LT6
	Abstract: In MAS115 Mathematical Investigation Skills -- where the students learn programming and LaTeX amongst other things -- we have experimented with various ideas including peer assessment, video marking, group work, students creating mathematical websites, in-class marking of homework. Usually we try to think of things which will benefit the students, but not increase our workload overly. We will present a smorgasbord of things we've tried and comment on how successful they've been, hopefully giving other people ideas along the way.
Nov 1	Thu	Samuel Skirvin (Sheffield)	Plasma Dynamics Group
15:00		Properties of Alfvénic waves in the solar chromosphere
		Room K14 (Hicks Building)
	Abstract: In the first part of my talk I will discuss the results of investigation of the properties of transverse waves existing in spicules using the automated wave tracking code NUWT. Analysing a distance-time diagram at an altitude of 7 Mm relative to the solar limb produces the measured distribution of properties such as wave amplitude, period and velocity amplitude. In the second part of the talk I will provide an overview of the recent studies on the effect of initial flow profiles on the dynamics of solar jets and introduce the work I will be doing as part of my PhD project
Nov 1	Thu	Markus Szymik (NTNU)	Topology Seminar
16:00		Quandles, knots, and homotopical algebra
		Hicks Seminar Room J11
	Abstract: Knots and their groups are a traditional topic of geometric topology. In this talk I will explain how aspects of the subject can be approached using ideas from Quillen’s homotopical algebra, rephrasing old results and leading to new ones.
Nov 2	Fri	Professor Craig J. Rodger (University of Otago)	SP2RC seminar
14:00		And then the Sun went "Bang": An Overview of Space Weather Research
		Sir Henry Stephenson Building, LT01
	Abstract: The Sun is the main provider of energy for the Earth; without it we would surely die. However, the Sun is not just a huge light bulb sending heat and light to us - it is a gigantic fiery ball of burning gas on which the largest explosions in our solar system take place. The highly dynamic Sun affects the Earth in multiple ways. We are only just starting to understand how the Sun drives "Space Weather" - changes in the environment on and around the Earth which affect our technological systems. In my colloquia I will give an overview of this research field, and provide some specific examples around hazards to Earth-orbiting satellites and electrical transmission networks.
Nov 6	Tue	Vlad Serban (Vienna)	Number Theory seminar
14:00		A finiteness result for families of Bianchi modular forms
		Hicks Seminar Room J11
	Abstract: We develop a p-adic "unlikely intersection” result and show how it can be used to examine which Hida families over imaginary quadratic fields interpolate a dense set of modular forms for GL2 over an imaginary quadratic field. In this way we arrive at the first proven examples where only finitely many classical automorphic forms are on a p-adic family.
Nov 7	Wed	Nicola Rendell (York)	Cosmology, Relativity and Gravitation
15:00		Infrared divergences in cosmological spacetimes
		Hicks Seminar Room J11
	Abstract: We study the infrared divergences of the graviton propagator in FLRW spacetime. We show that, through the use of a 'large' gauge transformation, this divergence is a gauge effect.
Nov 9	Fri	Alexander Shukhobodskiy (Sheffield)	SP2RC seminar
14:00		Kink Oscillations of Expanding Coronal Loops in the Presence of Bulk Flow
		F28
	Abstract: Transverse coronal loop oscillations were first observed by TRACE in 1998 and reported by Aschwanden et al. (1999) and Nakariakov et al. (1999). One important property of transverse coronal loop oscillations is that they are usually strongly damped with the damping time being comparable with the oscillation period. However, sometimes this is not the case. At present, a generally accepted mechanism of this damping is resonant absorption. Observations show that very often oscillating coronal loops are in a highly dynamic state. In particular, they can cool quickly with a characteristic cooling time of the order of a few periods of kink oscillation. It was later showed theoretically that cooling causes amplification and may result in existence of oscillations for which amplitude does not vary in time. Although the coronal loop expansion is relatively small, the ratio of the loop cross-section radii at the apex and at the foot-points still can be about 1.5. These leads to particular interest the effect of expansion on kink oscillations. A coronal loop is modeled as a cylindrical magnetic flux tube. The tube consists of a core region and a thin transitional region at the tube boundary. The plasma density monotonically decreases from its value in the core region to the value outside the tube. Both the plasma density and velocity of background flow vary along the tube and in time. Using multiscale expansions, the system of two equations describing the kink oscillations was derived. This model is then studied both analytically and numerically.
Nov 12	Mon	George Constable (Bath)	Mathematical Biology Seminar
14:00
		Hicks LT10
Nov 13	Tue	Philip G. Judge (High Altitude Observatory )	SP2RC seminar
13:00		Restoring the observational basis for solar physics
		LT 09
	Abstract: SUMMARY: A simple near-UV polarimeter on board a spacecraft that is more than 0.1 radians away from the Earth-Sun line will, with the suite of terrestrial solar observatories, resolve all ambiguities in vector field measurements, permitting us to restore studies of solar magnetic fields to its proper, observationally-based place. I will show how the spectrum of Fe~I at UV and IR wavelengths can strengthen the foundations of solar physics with consequences for all subjects involving magnetic activity. MOTIVATION: In recent years, research in solar physics has arguably become divorced from genuinely penetrating measurements. The idea of refuting theoretical pictures with critical observations seems to be losing ground to the development and application of computer models as a prime tool, indeed some models appear to have superceded the Sun itself in terms of ``reality''. Funding agencies and peer review enable what I call "institutionalized science" which is designed from the outset to optimize the number of publications, leading to vast numbers of, at best, incremental advances. I will argue that our collective "institutions" need to reward bold new ideas that are risky. I will present one such idea that will enable us to place measurements of solar magnetism at stage center, recognizing that the variable magnetism lies at the core of essentially all problems of interest in solar physics.
Nov 14	Wed	Lukasz Grabowski (Lancaster)	Pure Maths Colloquium
14:00		Approximation of groups with respect to the rank metric.
		Hicks Seminar Room J11
	Abstract: I'll talk about an ongoing joint work with Gabor Elek about approximation of groups with respect two the rank metric. The basic question is the following variant of the Halmos problem about commuting matrices: if A and B are large matrices such that the rank of the image of the commutator is small, is it true that A and B can be perturbed with small rank matrices in such a way that the resulting matrices commute? There are interesting connections to classical notions of commutative algebra, in particular we develop what are perhaps some new (or forgotten) variants of Nullstellensatz for primary ideals.
Nov 14	Wed	James McLaughlin (Northumbria)	Applied Mathematics Colloquium
14:00		Modelling Quasi-Periodic Pulsations in Solar and Stellar Flares
		Hicks, LT 9
	Abstract: Solar flare emission is detected in all EM bands and variations in flux density of solar energetic particles. Often the EM radiation generated in solar and stellar flares shows a pronounced oscillatory pattern, with characteristic periods ranging from a fraction of a second to several minutes. These oscillations are referred to as quasi-periodic pulsations (QPPs), to emphasise that they often contain apparent amplitude and period modulation. We review the current understanding of quasi-periodic pulsations in solar and stellar flares. In particular, we focus on the possible physical mechanisms, with an emphasis on the underlying physics that generates the resultant range of periodicities. These physical mechanisms include MHD oscillations, self-oscillatory mechanisms, oscillatory reconnection/reconnection reversal, wave-driven reconnection, two loop coalescence, MHD flow over-stability, the equivalent LCR-contour mechanism, and thermal-dynamical cycles. We also provide a histogram of all QPP events published in the literature at this time. The occurrence of QPPs puts additional constraints on the interpretation and understanding of the fundamental processes operating in flares, e.g. magnetic energy liberation and particle acceleration. Therefore, a full understanding of QPPs is essential in order to work towards an integrated model of solar and stellar flares. Based on McLaughlin et al., 2018, Space Science Review, 214, 45, https://doi.org/10.1007/s11214-018-0478-5
Nov 14	Wed	Eleni Kontou (York)	Cosmology, Relativity and Gravitation
15:00		Strong quantum energy inequality and the Hawking singularity theorem
		Hicks Seminar Room J11
	Abstract: Hawking's singularity theorem concerns matter obeying the strong energy condition (SEC), which means that all observers experience a nonnegative effective energy density (EED), thereby guaranteeing the timelike convergence property. However, for both classical and quantum fields, violations of the SEC can be observed in some of the simplest of cases, like the massive Klein-Gordon field. Therefore there is a need to develop theorems with weaker restrictions, namely energy conditions averaged over an entire geodesic and quantum inequalities, weighted local averages of energy densities. We have derived lower bounds of the EED in the presence of both classical and quantum scalar fields allowing nonzero mass and nonminimal coupling to the scalar curvature. In the quantum case these bounds take the form of a set of state-dependent quantum energy inequalities valid for the class of Hadamard states. Finally, we discuss how these lower bounds are applied to prove Hawking-type singularity theorems asserting that, along with sufficient initial contraction at a compact Cauchy surface, the spacetime is future timelike geodesically incomplete. Talk is based on: DOI:10.1007/s10714-018-2446-5, arXiv:1809.05047 and a manuscript in preparation.
Nov 14	Wed	Jordan Williamson (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		Equivariant Topology and Commutative Algebra
		Hicks Seminar Room J11
	Abstract: Equivariant topology is the study of spaces with a group action, and some invariants for studying these objects are equivariant cohomology theories. In this talk, we will explain how algebraic techniques can be used to study equivariant cohomology theories, and we will give a sketch-proof of a theorem of Greenlees-Shipley which classifies the equivariant cohomology theories on free G-spaces over the rational numbers. This will involve a discussion of Borel cohomology and its relation to representation theory, and the algebraicization theorem of Shipley, which provides a bridge between algebra and topology.
Nov 15	Thu	Matt Allcock (University of Sheffield)	SP2RC seminar
10:00		Asymmetric Solar Waveguides: theory and observations
		LT 10
	Abstract: Are solar MHD waveguides symmetric? It is convenient to assume that they are. The solar physics community is familiar with the traditional notion of sausage and kink waves, which propagate along waveguides in the solar atmosphere that we assume are symmetric. In this talk, we drop this assumption and motivate the study of MHD wave propagation in asymmetric waveguides from theoretical and observational viewpoints. We discuss the implications that asymmetric waveguides have for mode identification, highlighting the observational ambiguity between waves in symmetric and asymmetric waveguides, which becomes a crucial consideration when implementing magneto-seismology diagnostics. We present a novel technique for solar magneto-seismology that utilises the observed asymmetry of MHD waves to diagnose background parameters of the solar atmosphere that are difficult to measure using traditional methods. We present a preliminary application of this technique to chromospheric fibrils as a proof-of-concept and discuss the potential further application to prominences, elongated magnetic bright points, and sunspot light walls.
Nov 15	Thu	Istvan Ballai (Sheffield)	Plasma Dynamics Group
15:00		Introduction to multiple scaling methods to solve differential equations with applications to plasma physics. Part I: Ordinary linear differential equations
		Room K14 (Hicks Building)
	Abstract: Many of the equations we encounter in our research in solar and space plasma physics dynamics contain essential physical constraints (non-linearity, singularities, complex domains of interest, complex boundary conditions, etc.) that makes difficult to find exact solutions. Therefore, in order to obtain information about solutions of governing equations, we are forced to use analytical approximate methods, numerical solutions, or both. The most important analytical approximation methods are perturbation methods, where the solutions are represented by the first few terms of an expansion. In this seminar I will review perturbation methods used to solve ordinary differential equations, highlighting their advantages and shortcomings. The presentation will revolve around simple examples of differential equations, presenting methods of finding approximate analytical solutions of differential equations applicable to plasma physics.
Nov 20	Tue	Eoin Murphy (Sheffield)	Algebra / Algebraic Geometry seminar
16:00		Simultaneous deformations of Hall algebras
		Hicks Seminar Room J11
	Abstract: In this talk, we discuss how Ringel-Hall algebras, an algebra associated to suitably finite Abelian categories, can be viewed in certain cases as simultaneously deforming two simpler algebras. One of these algebras is the universal enveloping algebra of a Lie algebra, while the other is a Poisson algebra. Time permitting we also discuss an analogous deformation picture for a generalization of Ringel-Hall algebras due to Bridgeland.
Nov 21	Wed	Tobias Berger (Sheffield)	Pure Maths Colloquium
14:00		Paramodularity of abelian surfaces
		Hicks Seminar Room J11
	Abstract: The key ingredient in Wiles' proof of Fermat's last theorem was to establish the modularity of elliptic curves. Despite many impressive advances in the Langlands programme the analogous question of modularity for abelian varieties of dimension 2 is still open. I will discuss what we know and present joint work with Kris Klosin (CUNY) on the modularity of abelian surfaces which have a rational torsion point.
Nov 21	Wed	Simon Malham (Herrot-Watt)	Applied Mathematics Colloquium
14:00		Partial differential equations with non-local nonlinearities: Generation and solution
		Hicks, LT 9
	Abstract: We present a programme for generating the solutions of large classes of nonlinear partial differential equations, by pulling the equations back to a linear system of equations. The idea underlying this programme is to lift the standard relation between Riccati equations and linear systems to the infinite dimensional setting. This generalisation is well-known in optimal control theory where the off-line Riccati solution mediates the optimal current state feedback. The solution procedure can be presented at an elementary level and many examples will be included. Such example applications are partial differential equations with nonlocal nonlinearities, for example the nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation and Smoluchowski's coagulation equation and, by association, the inviscid and viscous Burgers equations with local advective nonlinearities.
	Slides
Nov 21	Wed	Konstantinos Dimopoulos (Lancaster)	Cosmology, Relativity and Gravitation
15:00		Cosmic Inflation and Dark Energy from the Electroweak Phase Transition
		Hicks Seminar Room J11
	Abstract: Cosmic inflation is a period of accelerated expansion in the Early Universe. Inflation is the most compelling proposal for the formation of of the observed structures in the Universe like galaxies and galactic clusters. It also makes the Universe uniform and spatially flat in agreement with observations. To drive inflation an exotic substance is needed, with pressure negative enough to cause the expansion of the Universe to accelerate, when this substance is dominant. Observations suggest that the late Universe is also undergoing accelerated expansion, which is assumed to be due to another exotic substance called dark energy. Can this be the one and the same with the substance behind inflation? In this talk I present a novel idea, in which inflation leaves behind a minute potential density, which can become the dark energy observed today. The field responsible for inflation (scalaron), is trapped in a local minimum of its scalar potential until the electroweak phase transition. The transition releases the field and allows it to vary slowly down a shallow potential tail, becoming dark energy. This behaviour is facilitated by a suitable coupling between the scalaron field and the electroweak Higgs field. The model is successful without fine-tuning, because it makes use of the curious fact that the electroweak energy scale is roughly the geometric mean of the Planck scale and the dark energy scale.
Nov 21	Wed	Igor Sikora (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		Eilenberg-Zilber map and Acyclic Models
		Hicks Seminar Room J11
	Abstract: When we are thinking about homology of a product of topological spaces, the first answer coming into mind is the Kunneth Theorem. Actually, it is only part of the truth. During the talk I will focus on the other part, which is chain level relation between singular complex of a product and a product of complexes - or more generally, between chain complexes associated to the simplicial abelian group and a product of complexes. This is done by very nice technique, called acyclic models. I assume basic knowledge of singular homology, i.e. definition of a chain complex and of a singular complex of a space.
Nov 22	Thu	David O' Sullivan (Sheffield Hallam University)	Teaching Lunch
13:00		A reflection on Higher Education across Sheffield.
		LT5
	Abstract: In this talk I will attempt to draws comparisons between my experience of mathematics education as both an undergraduate and a postgraduate student in SoMaS with my experience of mathematics education in my current role at Sheffield Hallam. I will talk about some of the high points from my time in SoMaS that helped me become a lecturer, and in doing so I hope to highlight some of the examples of good practice in what the department does/did. Then, in the spirit of collaboration, I will share some of the things I think we do well at Hallam that SoMaS could maybe learn from.
Nov 22	Thu	Istvan Ballai (Sheffield)	Plasma Dynamics Group
15:00		Introduction to multiple scaling methods to solve differential equations with applications to plasma physics. Part II: Nonlinear partial differential equations
		Lecture Theatre 2 (Hicks Building)
	Abstract: In the second part of my seminar I will focus on nonlinear partial differential equations that can be obtained from the MHD equations. Using the multiple scale technique I will present a method to obtain the Korteweg-de Vries-Burgers equation in a non-ideal plasma in the presence of Hall currents. Using simple methods, I will find solutions to the limiting cases of shock waves and solutions.
Nov 22	Thu	Robert Bruner (Wayne State)	Topology Seminar
16:00		The mod 2 Adams Spectral Sequence for Topological Modular Forms
		Hicks Seminar Room J11
	Abstract: In joint work with John Rognes, we have computed the 2-local homotopy of tmf, with full details. We first compute the cohomology of A(2) by a method of general interest. Grobner bases play a key role in allowing us to give a useful description it. I will briefly describe this. We then show that all the Adams spectral sequence differentials follow from general properties together with three key relations in the homotopy of spheres. We then compute the hidden extensions and the relations in homotopy using the cofibers of 2, eta and nu. This allows us to give a clear and memorable description of tmf_*. I will end with a brief description of the duality present in tmf_* coming from the Anderson duality for tmf.
Nov 26	Mon	Elaine Crooks (Swansea)	Mathematical Biology Seminar
14:00
		Hicks LT10
Nov 27	Tue	Jack Shotton (Durham)	Number Theory seminar
14:00		Shimura curves and Ihara's lemma
		Hicks Seminar Room J11
	Abstract: Ihara's lemma is a statement about the structure of the mod l cohomology of modular curves that was the key ingredient in Ribet's results on level raising. I will motivate and explain its statement, and then describe joint work with Jeffrey Manning on its extension to Shimura curves.
Nov 27	Tue	Caitlin McAuley (Sheffield)	Algebra / Algebraic Geometry seminar
16:00		Stability conditions of the Kronecker quiver
		Hicks Seminar Room J11
	Abstract: To a quiver $Q$, we can associate a sequence of Calabi--Yau-$n$ triangulated categories. The spaces of stability conditions of these categories can then be computed. I will give a description of these stability manifolds, and discuss the relationship between them and the Frobenius structure of the quantum cohomology of the projective line.
Nov 27	Tue	Colin Angus (ScHARR, Sheffield)	RSS Seminar
16:30		What is a 'safe' level of alcohol? Developing the UK low-risk drinking guidleines
		Hicks LT6
	Abstract: At the beginning of 2016, the UK Chief Medical Officers announced new 'low-risk' drinking guidelines. The development of these guidelines was informed by statistical modelling work to estimate the risks associated with drinking at different levels. In this presentation, Colin Angus, who led this work, will present how these risks were estimated and the ways in which they were used to define 'low-risk' drinking. He will also discuss the limitations of this approach and the challenges in communicating the risks associated with drinking to the public. Finally the presentation will address recent work from the Global Burden of Disease study which argues that there is 'no safe level' of alcohol consumption.
Nov 28	Wed	Paul McFadden (Newcastle)	Cosmology, Relativity and Gravitation
00:00		Conformal field theory in momentum space
		Hicks Seminar Room J11
	Abstract: Conformal symmetry places strong constraints on the properties of a quantum field theory, fixing the form of all 2- and 3-point functions up to constants. The resulting expressions are well-known in position space, yet surprisingly their counterparts in momentum space have only recently been identified. We review these developments, introducing an elementary method for solving the momentum-space conformal Ward identities. In special cases, divergences arise and we must renormalise giving rise to beta functions and anomalies. Our results have interesting new applications ranging from condensed matter physics to holographic cosmology.
Nov 28	Wed	Yanki Lekili (King's College London)	Pure Maths Colloquium
14:00		Homological mirror symmetry made concrete
		Hicks Seminar Room J11
	Abstract: Mirror symmetry is a broad correspondence between algebraic and symplectic geometry. It is a bit scary in the beginning as a true understanding of it requires some knowledge of both of these rather deep fields. In this talk, I will not give you a true understanding, rather I will provide examples of how fascinating this correspondence is. My intention is to get you "hooked" - it's up to you to decide whether you want to pursue this for a true understanding.
Nov 28	Wed	Daniel Graves (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		Homology theories for algebras
		Hicks Seminar Room J11
	Abstract: Since the 40s people have been developing homology and cohomology theories to try to encode information about algebras over commutative rings. In this talk I will discuss three such: Hochschild homology, Cyclic homology and Symmetric homology. The first two are classical theories that have found applications in many diverse areas. Symmetric homology is a related theory that is less well studied and slightly mysterious in comparison.
Nov 29	Thu	Hope Thackray (Sheffield)	Plasma Dynamics Group
15:00		Fast MHD modes of a two (and three) shell semi-cylindrical waveguide
		Lecture Theatre D (Hicks Building)
	Abstract: The modelling of coronal loop structures has long been pursued as a means of determining physical properties of the Sun's corona. Here, a 3D semi-cylindrical waveguide is proposed, representing a coronal loop arcade anchored in the photosphere. By considering the eigenfunctions formed at the interface of a sharp density discontinuity (represented by "two-shell" and subsequently "three-shell" density structures), we show that waves are elliptically polarised, and that small changes in density contrast between shells can drastically affect the presence of eigenmodes. Since observational information has restrictions on resolution, the implication is that two similarly determined density structures may produce vastly different estimations of potential eigenmodes.
Dec 4	Tue	Ciaran Schembri (Sheffield)	Number Theory seminar
14:00		Modularity of abelian surfaces over imaginary quadratic fields
		Hicks Seminar Room J11
	Abstract: In this talk I will discuss the modularity of abelian surfaces with quaternionic endomorphisms. This includes a discussion of how they correspond to Bianchi newforms and how to prove this for individual cases using the Faltings-Serre method. Furthermore, we give explicit examples which do not arise as the base-change of a GL(2)-type surface, which settles a question posed by J. Cremona in 1992.
Dec 4	Tue	Cristina Manolache (Imperial)	Algebra / Algebraic Geometry seminar
15:00		The enumerative content of Gromov-Witten theory
		Hicks Seminar Room J11
	Abstract: I will discuss old and new ways of answering questions in enumerative geometry. New methods have many advantages and one major drawback. In this talk I will discuss this drawback. I will introduce Gromov--Witten invariants and I will give evidence that they do not give correct curve counts. I will introduce new enumerative invariants from curves with cusps and I will argue that cuspidal invariants have a better enumerative meaning. In the end, I will highlight one application. This is based on work in collaboration with L Battistella, F Carocci and T Coates.
Dec 4	Tue	Andrea Brini (Birmingham)	Algebra / Algebraic Geometry seminar
16:00		Structures in Gromov-Witten theory
		Hicks Seminar Room J11
	Abstract: I will survey the existence of hidden recursive structures in the Gromov--Witten (GW) theory of a complex projective variety. I will discuss a characterisation of recursions for genus zero invariants in terms of associative deformations of the cup product in cohomology, and some alternative presentations of the deformed cup product motivated by singularity theory (the celebrated "mirror symmetry"). In some happy (and central) instances mirror symmetry is often a tool powerful enough to determine recursively all GW invariants starting from minimal input data. I will consider one application of these ideas to low-dimensional topology, which is partly joint work with Gaetan Borot, relating a class of smooth invariants of 3-manifolds to recursions for GW invariants.
Dec 5	Wed	Elisa Posthingel (Loughborough)	Pure Maths Colloquium
14:00		Newton polytopes: from the origin to their modern use
		Hicks Seminar Room J11
	Abstract: This talk aims to be a journey through the history of the Newton polygon. To any multivalued polynomial we can associate a convex polytope in Euclidean space by taking the convex hull of its exponent vectors. These polygons are named after Newton who, in the 17th century, made use of them in the setting of infinitesimal calculus. In the late 19th century they were employed by Baker to compute the genus of plane curves. An extensive study of the relation between hypersurfaces (zero loci of polynomial equations) and Newton polytopes took off in the 20th century with the advent of toric algebraic geometry. A further generalisation was introduced by Okounkov, in the last two decades, to study further properties of polarised algebraic varieties.
Dec 5	Wed	Jake Shipley (SoMaS)	Applied Mathematics Colloquium
14:00		Strong-field gravitational lensing by black holes
		Hicks, LT 11
	Abstract: A key prediction of Einstein's theory of general relativity (GR) is the bending of light due to gravity, a phenomenon known as gravitational lensing. In 1919, Eddington's observation of light deflection by the Sun – weak-field gravitational lensing – played a key role in the establishment of GR as our best theory of gravitation. Almost 100 years later, we are on the verge of a new era in the field of gravitational lensing. Using the Event Horizon Telescope (EHT), an Earth-scale virtual telescope which employs very-long-baseline interferometry, astronomers will soon directly observe the supermassive black hole at the galactic centre. The high-resolution images formed by the EHT will allow us to test GR in the strong-field regime. In this talk, I will review the subject of gravitational lensing, before presenting an overview of the EHT's main aims and objectives. I will conclude with a review of some recent theoretical work on the subject of strong-field gravitational lensing by black holes.
	Slides
Dec 5	Wed	Thomas Morley (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Renormalised vacuum polarisation on topological black holes
		Hicks Seminar Room J11
	Abstract: Anti-de Sitter spacetime is a solution of Einstein's equations with a negative cosmological constant. This fact allows for unusual black hole solutions with non-spherical horizon topology. We calculate the renormalised vacuum polarisation for black holes with spherical, flat and hyperbolic event horizons, following the “extended coordinates” method, which uses a mode-sum representation for the Hadamard parametrix. Renormalisation counter terms are subtracted from the Green’s function mode-by-mode, leaving each individual term manifestly finite.
Dec 5	Wed	Jake Percival (Sheffield)	Cosmology, Relativity and Gravitation
15:30		Semiclassical gravity for static spacetimes: Universality and structure dependence.
		Hicks Seminar Room J11
Dec 6	Thu	Dan Heller (King Edward's School)	Teaching Lunch
13:00		The New Maths A Level
		LT3
Dec 10	Mon	Rachel Norman (Stirling)	Mathematical Biology Seminar
14:00
		Hicks LT10
Dec 11	Tue	Dominic Joyce (Oxford)	Algebra / Algebraic Geometry seminar
16:00		A Ringel-Hall type construction of vertex algebras
		Hicks Seminar Room J11
	Abstract: Vertex algebras are complicated algebraic structures coming from Physics, which also play an important role in Mathematics in areas such as monstrous moonshine and geometric Langlands. I will explain a new geometric construction of vertex algebras, which seems to be unknown. The construction applies in many situations in algebraic geometry, differential geometry, and representation theory, and produces vast numbers of new examples. It is also easy to generalize the construction in several ways to produce different types of vertex algebra, quantum vertex algebras, representations of vertex algebras, … It seems to be related to work by Grojnowski, Nakajima and others, which produces representations of interesting infinite-dimensional Lie algebras on the homology of moduli schemes such as Hilbert schemes. Suppose A is a nice abelian category (such as coherent sheaves coh(X) on a smooth complex projective variety X, or representations mod-CQ of a quiver Q) or T is a nice triangulated category (such as D^bcoh(X) or D^bmod-CQ) over C. Let M be the moduli stack of objects in A or T, as an Artin stack or higher stack. Consider the homology H_*(M) over some ring R. Given a little extra data on M, for which there are natural choices in our examples, I will explain how to define the structure of a graded vertex algebra on H_*(M). By a standard construction, one can then define a graded Lie algebra from the vertex algebra; roughly speaking, this is a Lie algebra structure on the homology H_*(M^{pl}) of a “projective linear” version M^{pl} of the moduli stack M. For example, if we take T = D^bmod-CQ, the vertex algebra H_*(M) is the lattice vertex algebra attached to the dimension vector lattice Z^{Q_0} of Q with the symmetrized intersection form. The degree zero part of the graded Lie algebra contains the associated Kac-Moody algebra. There is also a differential-geometric version, involving putting a vertex algebra structure on homology of moduli stacks of connections on a compact manifold X equipped with an elliptic complex E.
Dec 12	Wed	Steffen Kionke (Karlsruhe Institute for Technology)	Pure Maths Colloquium
14:00		Profinite properties of arithmetic groups
		Hicks Seminar Room J11
	Abstract: Which properties of a group are determined by the set of its finite quotients? We give an introduction to this classical question and present examples and non-examples of such "profinite" properties. Afterwards we take a closer look at profinite properties of arithmetic groups. An arithmetic group is, roughly speaking, a group of matrices with integer entries. We present a property which is surprisingly determined by the finite quotients and we try to explain this phenomenon. In the end, we mention possible generalizations and open problems. This is based on joint work with H. Kammeyer, J. Raimbault and R. Sauer.
Dec 12	Wed	Sebastian Trojanowski (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Looking forward to new physics with FASER: ForwArd Search ExpeRiment at the LHC
		Hicks Seminar Room J11
	Abstract: One of the most rapidly developing areas of research in particle physics nowadays is to look for new, light, extremely weakly-interacting particles that could have avoided detection in previous years due to the lack of luminosity. These, so-called intensity frontier searches, have also broad cosmological connections to e.g. dark matter, as well as can help to unravel the mystery of neutrino masses. In this talk, we will summarize the current status of this field with a particular emphasis on a newly proposed experiment to search for such particles produced in the far-forward region of the LHC, namely FASER, the ForwArd Search ExpeRiment. FASER has been proposed as a relatively cheap detector to supplement traditional experimental programmes searching for heavy new physics particles in the high-pT region and, therefore, to increase the whole BSM physics potential of the LHC. On top of potentially far-reaching implications to BSM particle physics and cosmology, the newly proposed detector can also be used to measure high-energy SM neutrino cross sections.
Dec 12	Wed	Luca Pol	ShEAF: postgraduate pure maths seminar
16:00		The spectrum of a triangulated category
		Hicks Seminar Room J11
	Abstract: The spectrum of a commutative ring spec(R) is an interesting topological space that encodes lots of geometric and algebraic information. In 2004, Paul Balmer generalized this definition to any tensor triangulated category setting the scene for Tensor Triangular Geometry. One of the main achievement of the Balmer spectrum is to put in a unique framework three classification results: Devinats, Hopkins and Smith's theorem in Stable Homotopy Theory, Thomason's theorem in Algebraic Geometry and Benson, Carlson and Rickard's theorem in Modular Representation Theory. In this talk I will define the Balmer spectrum and show some concrete examples.
Dec 13	Thu	Konstantina Loumou (University of Glasgow)	SP2RC seminar
10:00		The association of RHESSI flares to the Hale Sector Boundary and Active Longitudes
		LT 10
	Abstract: Are some parts of the Interplanetary Magnetic Field’s (IMF) neutral line more flare energetic than others? What are Hale Sector Boundaries (HSBs) and are they connected with flares? Do they have anything to do with Active Longitudes? In this work, I will discuss how RHESSI flares are associated with structures in the solar magnetic field termed as HSBs. If you think of the large-scale domains of different polarity that the IMF is formed of, they the parts of the boundary between them, that have the same polarity change as the sunspots back at the Sun. As the polarity of sunspots follows Hale’s law, the HSB of a particular polarity change will only occur in one hemisphere per cycle, and then alternate in the next cycle. It has previously been shown that HSBs coincide with stronger magnetic fields and more frequent flare occurrence (Dittmer 1975, Svalgaard & Wilcox 1976, Svalgaard et al. 2011). I will explain how we extended this work through solar cycles 23 and 24 using RHESSI flare locations from 2002 to 2016. We compared these flares to the HSBs determined using two different methods. One uses the polarity change at the Earth to estimate when the HSB was at solar central meridian and the other uses Potential Field Source Surface (PFSS) extrapolations to identify the HSB for all times. We found that for both Cycle 23 and 24 more than 40% of non-limb flares were located near a HSB, a correlation that varies with cycle phase and hemisphere. I will describe how this evolves with time and the potential of these approaches for assisting flare forecasting. We then used the locations of HSBs calculated with the first method, using Earth-based data, to a Carrington rotation system and compared them with the migration paths of Active Longitudes as show in Gyenge et al. (2016). We found that there are times where they overlap, but that is not happening in a consistent manner. They often move at different rates relative to each other (and the Carrington solar rotation rate) and these vary over each Cycle.
Dec 13	Thu	Steffen Kionke (Karlsruhe Institute of Technology)	Number Theory seminar
11:00		The first Betti number of arithmetic hyperbolic 3-manifolds
		Hicks Seminar Room J11
	Abstract: An arithmetic hyperbolic 3-manifold is the quotient of the 3-dimensional hyperbolic space by an action of a discrete arithmetically defined subgroup of SL(2,C). The cohomology of these manifolds contains number theoretic information and it is of interest to understand the dimension of the cohomology. We discuss some known results about the first Betti numbers of arithmetic hyperbolic 3-manifolds. In particular, we review a method to obtain lower bounds which was developed by Harder, Rohlfs and others. Finally, we explain how the representation theory of compact p-adic Lie groups can be used to obtain significantly stronger results.
Dec 14	Fri	Marianna Korsos (Sheffield)	SP2RC seminar
13:00		Leap forward in Space Weather forecast: Novel prediction of flares
		K14
	Abstract: In this presentation, we address newly discovered pre-flare behavioural patterns in typical sunspot groups by focusing on their evolution as a function of height above the solar surface in a 3-dimensional solar AR. Here, we further probe and apply the concept of the pre-flare behavioural patterns using a magneto-hydrodynamic (MHD) simulation generating solar-like flares. We introduce and discuss the relevant properties and the capability of pre-flare tracking of ARs to improve Space Weather forecasting by focusing on the evolution from the photosphere towards the chromosphere, Transition Region and low corona. The basis of a proxy measure of our approach is the so-called weighted horizontal gradient of magnetic field (W_GM) defined between spots of opposite polarities closer to the polarity inversion line(s) of an AR. The value and the temporal variation of W_GM is found to possess novel and potentially important diagnostic information about (i) the intensity of expected flares and (ii) the accuracy of onset time prediction. Next, we will demonstrate how, by tracking the temporal evolution of W_GM, distance between opposite polarity spots and the associated net flux at various heights in the lower solar atmosphere evolves as function of height. We show that this latter temporal behaviour across the chromosphere-low corona has fundamentally new forecast capabilities. We found, that at a certain height the converging of opposite polarities begins much earlier than at the photosphere or at other heights. Therefore we present a tool to identify the optimum height in the solar atmosphere for flare prediction that may considerably increase the capability of the time prediction .
Dec 17	Mon	Alice Pozzi (UCL)	Number Theory seminar
14:00		The eigencurve at Eisenstein weight one points
		Hicks Seminar Room J11
	Abstract: In 1973, Serre observed that the Hecke eigenvalues of Eisenstein series can be $p$-adically interpolated. In other words, Eisenstein series can be viewed as specializations of a $p$-adic family parametrized by the weight. The notion of $p$-adic variations of modular forms was later generalized by Hida to include families of ordinary cuspforms. In 1998, Coleman and Mazur defined the eigencurve, a rigid analytic space classifying much more general $p$-adic families of Hecke eigenforms parametrized by the weight. The local nature of the eigencurve is well-understood at points corresponding to cuspforms of weight $k \geq 2$, while the weight one case is far more intricate. In this talk, we discuss the geometry of the eigencurve at weight one Eisenstein points. In particular, we focus on the unusual phenomenon in which cuspidal Hida families specialize to Eisenstein series at weight one. Our approach consists in studying the deformation rings of certain (deceptively simple!) Artin representations. We discuss how this Galois-theoretic method yields some new insight on Gross’s formula relating the leading term of the $p$-adic L-function to $p$-adic logarithms of units of certain number fields.
Dec 18	Tue	Alexis Virelizier (Lille)	Topology Seminar
16:00		Generalized Kuperberg invariants of 3-manifolds
		Hicks Seminar Room J11
	Abstract: In the 90s, Kuperberg defined a scalar invariant of 3-manifolds from each finite-dimensional involutory Hopf algebra over a field. The construction is based on the presentation of 3-manifolds by Heegaard diagrams and involves tensor products of the structure tensors of the Hopf algebra. These tensor products are then contracted using integrals of the Hopf algebra to obtain the scalar invariant. We generalize this construction by contracting the tensor products with other morphisms. Examples of such morphisms are derived from involutory Hopf algebras in symmetric monoidal categories. This is a joint work with R. Kashaev.
Jan 8	Tue	Josep Alvarez-Montaner (Universitat Politecnica de Catalunya)	Algebra / Algebraic Geometry seminar
14:00		Local cohomology of binomial edge ideals and their generic initial ideals
		Hicks Seminar Room J11
	Abstract: The aim of this talk is to give a detailed study of local cohomology modules of binomial edge ideals. Our main result is a Hochster type decomposition formula for these modules. As a consequence, we obtain a simple criterion for the Cohen-Macaulayness of these ideals and we describe their Castelnuovo-Mumford regularity and their Hilbert series. We also prove a conjecture of Conca, De Negri and Gorla relating the graded components of the local cohomology modules of binomial edge ideals and their generic initial ideals.
Jan 16	Wed	Atsushi Takahashi (Osaka)	Algebra / Algebraic Geometry seminar
16:00		On a full exceptional collection in the category of maximally graded matrix factorizations of an invertible polynomial of chain type
		Hicks Seminar Room J11
	Abstract: In ’77 Orlik-Randell asked about the existence of a certain distinguished basis of vanishing cycles in the Milnor fiber associated to an invertible polynomial of chain type. With my student, Daisuke Aramaki we transport their conjecture to the category of matrix factorizations by the (conjectural) homological mirror symmetry equivalence and then prove the resulting statement.
Jan 17	Thu	Ricardo Gaferia (Instituto de Astrofísica de Andalucía - CSIC )	SP2RC seminar
10:00		Machine learning assisted parallel inversions
		LT 10
	Abstract: With the increase of data volume and the need of more complex inversion codes to interpret and analyze solar observations, it is necessary to develop new tools to boost inversions and reduce computation times and costs. In this presentation, I discuss the possibilities and limitations of using machine learning as a tool to estimate optimum initial physical atmospheric models necessary for initializing spectral line inversions. Tests have been carried out for the SIR and DeSIRer inversion codes. This approach allows firstly to reduce the number of cycles in the inversion and increase the number of nodes and secondly to automatically cluster pixels which is an important step to invert maps where completely different regimes are present. Finally, I also present a warp for SIR and DeSIRer inversion codes that allows the user to easily set up parallel inversions.
Jan 18	Fri	Norbert Gyenge (Sheffield)	SP2RC seminar
13:00		The Nonaxisymmetric Behaviour Of Solar Eruptive Events
		LT 10
	Abstract: This thesis investigates new approaches for predicting the occurrence of solar eruptive events based on coronal mass ejection (CME), solar flare and sunspot group observations. The scope of the present work is to study the spatio-temporal properties of the above-mentioned solar features. The analysis may also provide a deeper understanding of the subject of solar magnetic field reorganisation. Furthermore, the applied approaches may open opportunities for connecting these local phenomena with the global physical processes that generate the magnetic field of the Sun, called the solar dynamo. The investigation utilises large solar flare statistical populations and advanced computational tools, such as clustering techniques, wavelet analysis, autoregressive moving average (ARIMA) forecast, kernel density estimations (KDEs) and so on. This work does not attempt to make actual predictions because it is out of the scope of the recent investigation. However, the thesis introduces new possible approaches in the subject of flare and CME forecasting. The future aim is to construct a real-time database with the ability to forecast eruptive events based on the findings of this thesis. This potential forecasting model may be crucial for protecting a wide range of satellite systems around the Earth or predicting space weather based on the obtained results may also assist to plan safe space exploration in the future.
Jan 23	Wed	Richard Webb (Cambridge)	Pure Maths Colloquium
14:00		An interplay between topology, geometry, and the algebra of the mapping class group
		Hicks Seminar Room J11
	Abstract: The braid groups were defined by Artin in 1925, and are usually defined in terms of strings in 3-dimensional space. However there is a fruitful 2-dimensional perspective of the braid groups as homeomorphisms (up to some natural equivalence) of a disc with holes, in other words, the braid groups are special cases of mapping class groups of surfaces. Mapping class groups can be viewed in a number of ways, and are of interest in several different fields, such as dynamics, algebraic geometry, surface bundles, hyperbolic geometry, to name a few. A key theorem that demonstrates this intradisciplinary feature is the Nielsen--Thurston classification. I will explain what the Nielsen--Thurston classification is, describe some basic examples and analogies, and highlight its importance. I will then explain how to view this from the geometric group theory perspective, and discuss my work with Mark Bell that uses this point of view to solve the conjugacy problem for mapping class groups in polynomial time. At the end of the talk I will discuss some new ideas that may lead to applications in knot theory via the braid groups.
Jan 25	Fri	Kalevi Mursula (University of Oulu)	SP2RC seminar
10:30		Centennial evolution and terrestrial effects of the global solar magnetic field
		LT E
Jan 31	Thu	Prof. Valery Nakariakov (Centre for Fusion, Space and Astrophysics, University of Warwick)	Plasma Dynamics Group
15:00		The effect of thermal misbalance on compressive oscillations in solar coronal loops
		Lecture theatre 1 (Hicks Building)
	Abstract: Fast and slow magnetoacoustic waves are a promising tool for the seismological diagnostics of physical parameters of various plasma structures in the corona of the Sun. In particular, compressive waves can provide us with information about the thermodynamic equilibrium in the coronal plasma, and hence the heating function. Compressive perturbations of the thermodynamic equilibrium by magnetoacoustic waves can cause the misbalance of the radiative cooling and unspecified heating. The effect of the misbalance is determined by the derivatives of the combined heating/cooling function with respect to the plasma density and temperature, and can lead to either enhanced damping of the compressive oscillations or their magnification. Moreover, in the regime of strong misbalance, compressive MHD waves are subject to wave dispersion that can slow down the formation of shocks and can cause the formation of quasi-periodic wave trains.
Feb 6	Wed	Viveka Erlandsson (Bristol)	Pure Maths Colloquium
14:00		Determining the shape of a billiard table from its bounces
		Hicks Seminar Room J11
	Abstract: Consider a billiard table shaped as a Euclidean polygon with labeled sides. A ball moving around on the table determines a bi-infinite “bounce sequence” by recording the labels of the sides it bounces off. We call the set of all possible bounce sequences the “bounce spectrum” of the table. In this talk I will explain why the bounce spectrum essentially determines the shape of the table: with the exception of a very small family (right-angled tables), if two tables have the same bounce spectrum, then they have to be related by a Euclidean similarity. The main ingredient in proving this fact is a technical result about non-singular geodesics on surfaces equipped with flat cone metrics. This is joint work with Moon Duchin, Chris Leininger, and Chandrika Sadanand.
Feb 7	Thu	Jeremy Colman (Sheffield)	Statistics Seminar
14:00		Accounting for Uncertainty in Estimates of Extremes
		LT E
	Abstract: Devastating consequences can flow from the failure of certain structures, such as coastal flood defences, nuclear installations, and oil rigs. Their design needs to be robust under rare (p < 0.0001) extreme conditions, but how can the designers use data typically from only a few decades to predict the size of an event that might occur once in 10,000 years? Extreme Value Theory claims to provide a sound basis for such far-out-of-sample prediction, and using Bayesian methods a full posterior distribution can be obtained. If the past data are supplemented by priors that take into account expert opinion, seemingly tight estimates result. Are such claims justified? Has all uncertainty been taken into account? My research is addressing these questions.
Feb 7	Thu	Masahiro Nakahara (Manchester)	Number Theory seminar
14:00		Index of Fibrations and Brauer classes that never obstruct the Hasse principle
		Hicks Seminar Room J11
	Abstract: Let X be a smooth projective variety over a number field with a fibration into varieties that satisfy a certain condition. We study the classes in the Brauer group of X that never obstruct the Hasse principle for X. We prove that if the generic fiber has a zero-cycle of degree d over the generic point, then the Brauer classes whose orders are prime to d do not play a role in the Brauer-Manin obstruction. As a result we show that the odd torsion Brauer classes never obstruct the Hasse principle for del Pezzo surfaces of degree 2, certain K3 surfaces, and Kummer varieties.
Feb 13	Wed	Ana Caraiani (Imperial)	Pure Maths Colloquium
14:00		On the Ramanujan conjecture and its generalisations
		Hicks Seminar Room J11
	Abstract: In 1916, Ramanujan made a conjecture that can be stated in completely elementary terms: he predicted an upper bound on the coefficients of a power series obtained by expanding a certain infinite product. In this talk, I will discuss a more sophisticated interpretation of this conjecture, via the Fourier coefficients of a highly symmetric function known as a modular form. I will give a hint of the idea in Deligne’s proof of the conjecture in the 1970’s, who related it to the arithmetic geometry of smooth projective varieties over finite fields. Finally, I will discuss generalisations of this conjecture and some recent progress on these using the machinery of the Langlands program. The last part is based on joint work with Allen, Calegari, Gee, Helm, Le Hung, Newton, Scholze, Taylor, and Thorne.
Feb 14	Thu	Carolina Robustini (Stockholm University)
10:00		Chromospheric observations and magnetic configuration of a supergranular structure
	Abstract: We present high spatial resolution narrow-band images in three different chromospheric spectral lines, including Ca II K with the new CHROMospheric Imaging Spectrometer installed at the Swedish 1-m Solar Telescope. These observations feature a unipolar region enclosed in a supergranular cell, and located 68º off the disk-centre. The observed cell exhibits a radial arrangement of the fibrils which recalls of a chromospheric rosette. However, in this case, the convergence point of the fibrils is located at the very centre of the supergranular cell. Our study aims to show how the chromosphere appears in this peculiar region and retrieve its magnetic field and velocity distribution. In the centre of the cell, we measured a significant blue-shift in the Ca II K nominal line core associated to an intensity enhancement. We interpreted it as the product of a strong velocity gradient along the line of sight. In this talk, we will discuss the techniques employed to obtain magnetic field maps so close to the limb and suggest a possible configuration that takes into account also the measured velocity within the unipolar region.
Feb 14	Thu	Eleanor Stillman (Sheffield)
12:00		An overview of the HEA direct application process.
		Hicks LT5
	Abstract: This talk will outline the process of directly applying to become a (associate-principal) fellow of the HEA. The talk will help Ph.D. students to Professors understand what is required in the application and how to be successful. We may also discuss the value and implications of receiving professional recognition from the HEA.
Feb 14	Thu	Andrey Lazarev (Lancaster)	Topology Seminar
16:00		Homotopy theory of monoids
		Hicks Seminar Room J11
	Abstract: I will explain how the category of discrete monoids models the homotopy category of connected spaces. This correspondence is based on derived localization of associative algebras and could be viewed as an algebraization result, somewhat similar to rational homotopy theory (although not as structured). Closely related to this circle of ideas is a generalization of Adams’s cobar construction to general nonsimply connected spaces due to recent works of Rivera-Zeinalian and Hess-Tonks. (joint with J. Chuang and J. Holstein)
Feb 14	Thu	Will Hulme / Nick Monk / Rhoda Hawkins (Manchester / Sheffield / Sheffield)	RSS Seminar
16:30		Experiences of AIMS
		Hicks Room F38
	Abstract: AIMS is an academic network that enables Africa’s talented students to become innovators who propel scientific, educational and economic self-sufficiency. The RSS Local Group are delighted to welcome Will Hulme (University of Manchester, taught at AIMS Cameroon), Prof Nick Monk (University of Sheffield, SOMAS, taught at AIMS Ghana) and Dr Rhoda Hawkins (University of Sheffield, Department of Physics and Astronomy, taught at AIMS South Africa, Senegal and Ghana) to present on their experiences on the AIMS project. Tutor/lecturer opportunities that may be of interest will be highlighted.
Feb 15	Fri	Dan Graves	THH reading group
14:00		Hochschild Homology and Cyclic Homology of rings
		Hicks Seminar Room J11
Feb 20	Wed	Farrell Brumley (Paris 13)
11:00		Concentration properties of theta lifts
		Hicks Seminar Room J11
	Abstract: I will present some results on the concentration properties of automorphic forms obtained through the theta correspondence. Among other things, the method relies on a distinction principle for these lifts, which detect their functorial origin via the non vanishing of orthogonal periods. The examples we treat are in higher rank, and shed light on a purity conjecture of Sarnak. This is joint work with Simon Marshall.
Feb 20	Wed	Heather Harrington (Oxford)	Applied Mathematics Colloquium
14:00		Comparing models and biological data using computational algebra and topology
		Hicks, LT 9
	Abstract: Many biological problems, such as tumor-induced angiogenesis (the growth of blood vessels to provide nutrients to a tumor), or signaling pathways involved in the dysfunction of cancer (sets of molecules that interact that turn genes on/off and ultimately determine whether a cell lives or dies), can be modeled using differential equations. There are many challenges with analyzing these types of mathematical models, for example, rate constants, often referred to as parameter values, are difficult to measure or estimate from available data. I will present mathematical methods we have developed to enable us to compare mathematical models with experimental data. Depending on the type of data available, and the type of model constructed, we have combined techniques from computational algebraic geometry and topology, with statistics, networks and optimization to compare and classify models without necessarily estimating parameters. Specifically, I will introduce our methods that use computational algebraic geometry (e.g., Gröbner bases) and computational algebraic topology (e.g., persistent homology). I will present applications of our methodology on datasets involving cancer. Time permitting, I will conclude with our current work for analyzing spatio-temporal datasets with multiple parameters using computational algebraic topology. Mathematically, this is studying a module over a multivariate polynomial ring, and finding discriminating and computable invariants.
Feb 20	Wed	Andreea Mocanu (University of Nottingham)
14:00		Newform theory for Jacobi forms of lattice index
		Hicks Seminar Room J11
	Abstract: I will give a brief introduction to Jacobi forms, including some examples and their relation to other types of modular forms. After that, I will discuss some of the ingredients that go into developing a theory of newforms for Jacobi forms of lattice index, namely Hecke operators, level raising operators and orthogonal groups of discriminant modules.
Feb 20	Wed	Clark Barwick (Edinburgh)	Topology Seminar
16:00		Primes, knots, and exodromy
		LT11
	Abstract: Half a century ago, Barry Mazur and David Mumford suggested a remarkable dictionary between prime numbers and knots. I will explain how the story of exodromy permits one to make this dictionary precise, and I will describe some applications.
Feb 21	Thu	Farrell Brumley (Paris 13)	Pure Maths Colloquium
14:00		Automorphic forms and rational points
		Hicks Seminar Room J11
	Abstract: In what sense can automorphic forms or Galois representations be viewed as rational points on an algebraic variety? One way to explore this question is by counting arguments. The first result in this direction dates back to an early theorem of Drinfeld, which computes the number of 2-dimensional Galois representations of a function field in positive characteristic; the resulting expression is reminiscent of a Lefschetz fixed point theorem on a smooth algebraic variety over a finite field. More recently it was observed that in the number field setting there are formal similarities between the asymptotic counting problems for rational points on Fano varieties and for automorphic representations on reductive algebraic groups. Very little is known in the latter context. I’ll discuss joint work on this topic with Djordje Milicevic, in which we (mostly) solve the automorphic counting problem on the general linear group. Our results can be viewed as being analogous to the well-known result of Schanuel on the number of rational points of bounded height on projective spaces. If time permits, I may also present a short argument, using sphere packings in large dimensions, to give upper bounds on such automorphic counts.
Feb 21	Thu	Sophia Wright (Warwick)	Statistics Seminar
14:00		Bayesian Networks, Total Variation and Robustness
		LT E
	Abstract: This talk explores the robustness of large Bayesian Networks when applied in decision support systems which have a pre-specified subset of target variables. We develop new methodology, underpinned by the total variation distance, to determine whether simplifications which are currently employed in the practical implementation of such graphical systems are theoretically valid. This same process can identify areas of the system which should be prioritised if elicitation is required. This versatile framework enables us to study the effects of misspecification within a Bayesian network (BN), and also extend the methodology to quantify temporal effects within Dynamic BNs. Unlike current robustness analyses, our new technology can be applied throughout the construction of the BN model; enabling us to create tailored, bespoke models. For illustrative purposes we shall explore the field of Food Security within the UK.
Feb 22	Fri	James Cranch	THH reading group
14:00		Topological Hochschild Homology
		Hicks Seminar Room J11
Feb 27	Wed	Raven Waller (Nottingham)	ShEAF: postgraduate pure maths seminar
16:00		Level structures - a crossroads between topology, representation theory, and number theory
		Hicks Seminar Room J11
	Abstract: The arithmetic, algebraic, and topological properties of local fields are intimately related. For higher dimensional local objects these relationships begin to break down, and this may cause considerable difficulty when studying them. The notion of a level structure allows us to work around some of these issues. We will discuss various applications of level structures, including the explicit study of representations of reductive groups over higher dimensional local fields, which is also related to the geometric Langlands program.
Feb 28	Thu	Björn Löptien (Max Planck Institute for Solar System Research )
10:00		A new method for measuring the Wilson depression of sunspots
		F41
	Abstract: The Wilson depression is the difference in geometric height of the layer of unit continuum optical depth between the sunspot umbra and the quiet Sun. Measuring the Wilson depression is important for understanding the geometry of sunspots. Current methods suffer from systematic effects or need to make assumptions on the geometry of the magnetic field. This leads to large systematic uncertainties of the derived Wilson depressions. Here we present a method for deriving the Wilson depression that only requires the information about the magnetic field that are accessible by spectropolarimetry and that does not rely on assumptions on the geometry of sunspots or on its magnetic field. Our method is based on minimizing the divergence of the magnetic field vector derived from spectropolarimetric observations. We focus on large spatial scales only in order to reduce the number of free parameters. We test the performance of our method using synthetic Hinode data derived from two sunspot simulations. We find that the maximum and the umbral averaged Wilson depression for both spots determined with our method typically lies within 100 km of the true value obtained from the simulations. In addition, we apply the method to spots from the Hinode sunspot database at MPS. The derived Wilson depressions (500-700 km) are consistent with results typically obtained from the Wilson effect. In our sample, larger spots with a stronger magnetic field exhibit a higher Wilson depression than smaller spots.
Feb 28	Thu	Dan Graves and Sarah Whitehouse	Teaching Lunch
13:00		Analysis and AiM
		Hicks LT6
	Abstract: Sarah will start by talking about various changes that have been made to MAS221 Analysis to address issues of poor student engagement and poor exam performance. This includes use of the AiM online test system for mid-term assessment. Dan will present examples of the type of AiM questions that have been used in MAS221 and in MAS220 Algebra, including proofs and multiple choice questions.
Feb 28	Thu	Wil Ward (Sheffield)	Statistics Seminar
14:00		A Variational Approach to Approximating State Space Gaussian Processes
		LT E
	Abstract: The state space representation of a Gaussian process (GP) models the dynamics of an unknown (non-linear) function as a white-noise driven Itô differential equation. Representation in this form allows for the construction of joint models that mix known dynamics (e.g. population) with latent unknown input. Where these interactions are non-linear, or observed through non-Gaussian likelihoods, there is no exact solution and approximation techniques are required. This talk introduces an approach using black box variational inference to model surrogate samples and estimate the underlying parameters. The approximations are compared with full batch solutions and demonstrated to be indistinguishable in two-sample tests. Software and implementation challenges will also be addressed.
Feb 28	Thu	Scott Balchin (Warwick)	Topology Seminar
16:00		Adelic reconstruction in prismatic chromatic homotopy theory
		Hicks Seminar Room J11
	Abstract: Prismatic homotopy theory is the study of stable monoidal homotopy theories through their Balmer spectrum. In this talk, I will discuss how one can use localised p-complete data at each Balmer prime in an adelic fashion to reconstruct the homotopy theory in question. There are two such models, one is done by moving to categories of modules, which, for example, recovers the algebraic models for G-equivariant cohomology theories. The other, newer model, works purely at the categorical level and requires the theory of weighted homotopy limits. This is joint work with J.P.C Greenlees.
Feb 28	Thu	Mark Wrigley (Chair IOP Yorkshire)	Plasma Dynamics Group
16:00		1201 Alarm Project
		Room K14 (Hicks Building)
	Abstract: The 1201 Alarm Project is the restoration, exhibition and sharing of materials recorded in 1969 of the Apollo moon landings from a domestic television. The talk will review the Apollo flight plan, the recording technologies of the day and the impact that it had on the speaker. The materials will form the basis for an exhibition celebrating the 50th anniversary of moon landings to be held at the National Science and Media Museum in Bradford, Yorkshire.
Mar 1	Fri	Luca Pol	THH reading group
14:00		Computations of THH
		Hicks Seminar Room J11
Mar 6	Wed	Matt Aldridge / Sarah Penington / Helena Stage / Henning Sulzbach (Leeds / Bath / Manchester / Birmingham)	Probability in the North East
12:30
		LT C
Mar 6	Wed	Gwyneth Stallard (Open University)	Pure Maths Colloquium
14:00		Complex dynamics: the intriguing case of wandering domains
		Hicks Seminar Room J11
	Abstract: Complex dynamics concerns the iteration of analytic functions of the complex plane. For each function, the plane is split into two sets: the Fatou set (where the behaviour of the iterates is stable under local variation) and the Julia set (where the behaviour is chaotic). The dynamical behaviour of the iterates inside the periodic components of the Fatou set was classified into four different types by the founders of the subject and this classification has played a key role in the development of the subject. One of the most dramatic breakthroughs was given by Sullivan in the 1980s when he proved that, for rational functions, all components of the Fatou set are eventually periodic and there are no so-called wandering domains. For transcendental functions, however, wandering domains can exist and the rich variety of possible behaviours that can occur is only just becoming apparent.
Mar 6	Wed	Rachael Hardman (SoMaS)	Applied Mathematics Colloquium
14:00		Measuring the Ocean Spectrum using HF Radar Data and a Neural Network
		Hicks, K14
	Abstract: High frequency, or HF, coastal radars can provide continuous high resolution measurements of ocean surface currents, winds and waves. First derived in 1972, the expected radar signal when electromagnetic waves are scattered by the ocean surface can be modelled by the radar cross section, a nonlinear integral equation which enables us to predict the radar output for any ocean state. Methods for inverting the radar cross section - which ultimately permit us to measure ocean parameters from HF radar data - have been developed over the last few decades; however there are times when the measured data cannot be modelled by the mathematical equations and are therefore not suitable for inversion using the existing methods. Using a neural network, trained on simulated radar data, we have successfully inverted HF radar data not modelled by the radar cross section. In this talk, I will give an overview of how HF radar is used in ocean sensing before introducing neural networks. I will finish by presenting the results of a validation experiment, showing how a neural network can learn the complex inverse relationship between HF radar and the ocean surface.
Mar 6	Wed	Paolo Dolce (Nottingham)	ShEAF: postgraduate pure maths seminar
16:00		Two dimensional adelic geometry
		Hicks Seminar Room J11
	Abstract: I will give an overview of a novel approach to the study of two dimensional algebraic and arithmetic geometry by means of adelic and idelic structures. Particular emphasis will be given to the case of arithmetic surfaces since the aim of the theory is to give a two dimensional version of Tate's thesis.
Mar 7	Thu	Christian Fonseca Mora (Costa Rica)	Statistics Seminar
14:00		Stochastic PDEs in Infinite Dimensional Spaces
		LT E
	Abstract: In this talk we will give an introduction to SPDEs in spaces of distributions. In the first part of the talk we consider a model of environmental pollution with Poisson deposits that will help to introduce the basic concepts for the study of SPDEs on infinite dimensional spaces. In the second part of the talk, we introduce a generalized form of SPDEs in spaces of distributions and explain conditions for the existence and uniqueness of its solutions. For this talk we will not assume any previous knowledge on SPDEs.
Mar 7	Thu	Jean-Stefan Koskivirta (Tokyo)	Number Theory seminar
14:00		Ampleness and vanishing results
		Hicks Seminar Room J11
	Abstract: We explain an application of the existence of generalized Hasse invariants to show ampleness of certain line bundles on flag spaces of Shimura varieties of Hodge type in positive characteristic. These methods generalize to other types of schemes which carry a universal G-zip. We deduce vanishing results for the cohomology of automorphic vector bundles. We compare them with similar results of Lan-Suh.
Mar 7	Thu	Irakli Patchkoria (Aberdeen)	Topology Seminar
16:00		Computations in real topological Hochschild and cyclic homology
		Hicks Seminar Room J11
	Abstract: The real topological Hochschild and cyclic homology (THR, TCR) are invariants for rings with anti-involution which approximate the real algebraic K-theory. In this talk we will introduce these objects and report about recent computations. In particular we will dicuss components of THR and TCR and some recent and ongoing computations for finite fields. This is all joint with E. Dotto and K. Moi.
Mar 7	Thu	Patrick Antolin (University of St Andrews)	Plasma Dynamics Group
16:00		Transverse MHD Waves and associated dynamic instabilities in the solar atmosphere
		Room K14 (Hicks Building)
	Abstract: A large amount of recent simulations and analytical work indicate that standing transverse MHD waves in loops should easily lead to the generation of dynamic instabilities at their edges, and in particular of the Kelvin-Helmholtz kind. While a direct observation of these transverse wave-induced Kelvin-Helmholtz rolls (or TWIH rolls) is still lacking, the forward modelling of these simulations give us an indication of what to look for in next generation instrumentation, and which currently observed features could actually be the result of TWIKH rolls. In this talk I will go through some of these results, comparing observations with various instruments with simulations of coronal loops, prominences and spicules.
Mar 7	Thu	David Robinson (Capital One)	RSS Seminar
16:30		Data Science & Machine Learning
		F38
	Abstract: David will start his talk with a brief history of Statistics and Data Science at Capital One: how we got here, what's changed, and what the current expectations and challenges are in the era of "Big Data" and "Machine Learning". The main technical focus will then be on the use of "Gradient Boosting Machines", which over the last few years have emerged as the modelling method of choice for most classification problems within Financial Services. David will cover what they are, why they have become popular and how many of the practical considerations and pitfalls of traditional statistical techniques still very much apply. Example uses will focus on credit risk and affordability, looking at how we can ensure we make fair lending decisions when faced with unfair and biased data.
Mar 8	Fri	Hope Thackray, Jake Percival, Bryony Moody (Sheffield)	Postgraduate seminars
16:00		PGR Student Seminar
		Hicks Seminar Room J11
	Abstract: Hope Thackray - How do we see inside the Sun? Much like the waves known to exist above the solar surface, the Sun itself exhibits a widespread pulsation, mimicking the beating of a heart. Sound waves resonate inside the Sun, buffeting the surface, and causing light emitted to experience Doppler-shifting. The structures of these resonant cavities may then be deduced from observations of these shifts, allowing us to "see'' the Sun's interior. Here, one such method of deriving the Sun's sub-surface flows is described, in a technique known as Ring Diagram Analysis. Jake Percival - RNG's: How computers handle randomness When we want a “random” number in everyday life, such as when playing a board game, we rely on processes that aren't truly random, such as rolling a die. Perhaps more reliable would be to ask a computer to produce a random number for us. The code used to give these numbers is called a Random Number Generator (RNG) and like rolling a die, they aren't truly random! But if they aren't random, what is actually happening “under the hood”? In this talk we'll look at how RNG's work and how they can go wrong, including a fun example from the world of video games! Bryony Moody - The hidden layer of statistics in archaeology This talk will give a brief overview of Bayesian inference and the concepts of prior and posterior knowledge. Then I will discuss the various forms of prior knowledge available in archaeology, as well as the data that are used in conjunction with the prior knowledge to form a posterior. Finally I will conclude by discussing the priors I am focusing on for my PhD and what my plans are for modelling them.
Mar 12	Tue	Giovanni Marchetti
13:00		Motivic Homotopy Reading Seminar
		Hicks Seminar Room J11
	Abstract: Talk 1: Ouverture.
Mar 13	Wed	Fatemeh Mohammadi (Bristol)	Pure Maths Colloquium
14:00		Chip-firing game and Riemann-Roch theory for graphs
		Hicks Seminar Room J11
	Abstract: Theory of divisors on graphs is analogous to the classical theory for algebraic curves. The combinatorial language in this setting is "chip-firing game” which has been independently introduced in other fields. A divisor on a graph is simply a configuration of dollars (integer numbers) on its vertices. In each step of the chip-firing game we are allowed to select a vertex and then lend one dollar to each of its neighbors, or borrow one dollar from each of its neighbors. The goal of the chip-firing game is to get all the vertices out of debt. In this setting, there is a combinatorial analogue of the classical Riemann-Roch theorem. I will explain the mathematical structure arising from this process and how it sits in a more general framework of (graphical) hyperplane arrangements.
Mar 13	Wed	Tobias Grafke (Warwick)	Applied Mathematics Colloquium
14:00		Hydrodynamic instantons and the universal route to rogue waves
		Hicks, LT 9
	Abstract: In stochastic systems, extreme events are known to be described by "instantons", saddle point configurations of the action of the associated stochastic field theory. In this talk, I will present experimental evidence of a hydrodynamic instanton in a real world fluid system: A 270m wave channel experiment in Norway. The experiment attempts to model conditions on the ocean in order to observe so-called rogue waves, realisations of extreme ocean surface elevation out of relatively calm surroundings. These rogue waves are also observed in the ocean, where they are rare and hard to predict but pose significant danger to naval vessels. We show that the instanton approach, which is rigorously grounded in large deviation theory, offers a unified description of rogue waves in the water tank, covering the entire range of parameters for deep water waves in the ocean. In particular, this approach allows for a unified description of both the predominantly linear and the highly nonlinear regimes, and is able to explain the experimental data in the tank regardless of the strength of the nonlinearity.
Mar 13	Wed	Karoline Van Gemst (Birmingham)	ShEAF: postgraduate pure maths seminar
16:00		Enumerative geometry in projective space and Kontsevich's formula
		Hicks Seminar Room J11
	Abstract: Enumerative geometers are interested in counting certain geometric objects given a set of conditions. One example of such a counting problem is how many degree d rational curves pass through 3d-1 generically placed given points in the projective plane. This particular problem proved extremely difficult using classical methods, even for low d. In the 1990s however, a revolution within this area took place, originating in the world of physics. This led to Kontsevich solving the counting problem by proving a recursive formula for calculating this number for any d. Kontsevich’s formula requires a single initial datum, the case of d=1, which translates to the fact that a single line passes through two given points in the plane. In this talk, I will present some of the crucial ingredients in setting up for and proving Kontsevich’s formula, and illustrate how it makes sense through a few examples. If time permits, I will also motivate how the formula can be viewed as expressing the associativity of the quantum product.
Mar 14	Thu	Luca Giovannelli (University of Rome Tor Vergata)	SP2RC seminar
10:00		Emerging bipolar magnetic pairs in the solar photosphere: diffusion properties and contribution to the coronal heating
		F28
	Abstract: The ubiquitous presence of small magnetic elements in the Quiet Sun represents a prominent coupling between the photosphere and the upper layers of the Sun’s atmosphere. Small magnetic element tracking has been widely used to study the transport and diffusion of the magnetic field on the solar photosphere. From the analysis of the displacement spectrum of these tracers, it has been recently agreed that a regime of super-diffusivity dominates the solar surface. In this talk we will focus on the analysis of the bipolar magnetic pairs in the solar photosphere and their diffusion properties, using a 25-h dataset from the HINODE satellite. Interestingly, the displacement spectrum for bipolar couples behaves similarly to the case where all magnetic pairs are considered. We also measure, from the same dataset, the magnetic emergence rate of the bipolar magnetic pairs and we interpret them as the magnetic footpoints of emerging magnetic loops. The measured magnetic emergence rate is used to constrain a simplified model that mimics the advection on the solar surface and evolves the position of a great number of loops, taking into account emergence, reconnection and cancellation events. In particular we compute the energy released by the reconnection between different magnetic loops in the nano-flares energy range. Our model gives a quantitative estimate of the energy released by the reconfiguration of the magnetic loops in a quiet Sun area as a function of height in the solar atmosphere, from hundreds of Km above the photosphere up to the corona, suggesting that an efficiency of ~10% in the energy deposition might sustain the million degree corona.
Mar 14	Thu	Jeremy Oakley (Sheffield)	Statistics Seminar
14:00		Variational inference reading group
		LT E
	Abstract: We will be spending two seminar slots on the following: Variational Inference: A Review for Statisticians https://arxiv.org/abs/1601.00670 David M. Blei, Alp Kucukelbir, Jon D. McAuliffe
Mar 14	Thu	Neil Strickland (Sheffield)	Topology Seminar
16:00		Dilation of formal groups, and potential applications
		Hicks Seminar Room J11
	Abstract: I will describe an extremely easy construction with formal group laws, and a slightly more subtle argument to show that it can be done in a coordinate-free way with formal groups. I will then describe connections with a range of other phenomena in stable homotopy theory, although I still have many more questions than answers about these. In particular, this should illuminate the relationship between the Lambda algebra and the Dyer-Lashof algebra at the prime 2, and possibly suggest better ways to think about related things at odd primes. The Morava K-theory of symmetric groups is well-understood if we quotient out by transfers, but somewhat mysterious if we do not pass to that quotient; there are some suggestions that dilation will again be a key ingredient in resolving this. The ring $MU_*(\Omega^2S^3)$ is another object for which we have quite a lot of information but it seems likely that important ideas are missing; dilation may also be relevant here.
	Slides
Mar 15	Fri	Jonathan Potts (Sheffield)	Teaching Lunch
13:00		MOLE exams are great
		Hicks LT10
	Abstract: We explain our use of MOLE exams in MAS222 and why it is a win-win tool for students and staff alike. The "win" for staff is particularly wonderful as it removes that most onerous task: exam marking. We'll start with a very brief presentation of how to set a MOLE exam up and how we've used them in MAS222. Then we'll open the floor to discussion about how they might be used more widely in SoMaS.
Mar 15	Fri	Luca Pol	THH reading group
14:00		$E_n$ algebras
		Hicks Seminar Room J11
Mar 20	Wed	Sven Meinhardt (Sheffield)	Pure Maths Colloquium
14:00		New developments in modern moduli theory
		Hicks Seminar Room J11
	Abstract: The idea of moduli spaces classifying structures in various fields of mathematics dates back to Riemann who tried to classify complex structures on a compact surface. It took another hundred years and many ingenious ideas of Grothendieck, Mumford and other mathematicians to write down a proper definition of moduli spaces and to construct nontrivial examples including Riemann‘s vague idea of a moduli space of complex structures on a surface. However, it became quite obvious that the concept of moduli spaces/stacks developed in the 60‘s and 70‘s is not sufficient to describe all moduli problems. Another 50 years and a fair amount of homotopy theory was needed to provide a definition of moduli spaces having all required properties. A large class of examples comes from (higher) representation theory. The aim of my talk is to provide a gentle introduction into these new concepts and thereby to show how nicely algebraic geometry, topology and representation theory interact with each other. If time permits, I will also sketch applications in Donaldson-Thomas theory.
Mar 20	Wed	Gianmarco Brocchi (Birmingham)	ShEAF: postgraduate pure maths seminar
16:00		What does extremise a Strichartz estimate?
		Hicks Seminar Room J11
	Abstract: This will be a blunt talk on sharp inequalities. Roughly speaking, these are inequalities which cannot be improved. In particular, I will introduce inequalities for the restriction of the Fourier transform, explaining why I got interested in them and how they are related to other inequalities in PDE, such as Strichartz estimates. These are a key tool in understanding the evolution of waves in dispersive PDE. If time allows, I will discuss a sharp Strichartz estimate for the fourth order Schrödinger equation from a joint work with Diogo Oliveira e Silva and René Quilodrán.
Mar 21	Thu	Theo Kypraios (Nottingham)	Statistics Seminar
14:00		Recent Advances in Identifying Transmission Routes of Healthcare Associated Infections using Whole Genome Sequence Data
		LT E
	Abstract: Healthcare-associated infections (HCAIs) remain a problem worldwide, and can cause severe illness and death. It is estimated that 5-10% of acute-care patients are affected by nosocomial infections in developed countries, with higher levels in developing countries. Statistical modelling has played a significant role in increasing understanding of HCAI transmission dynamics. For instance, many studies have investigated the dynamics of MRSA transmission in hospitals, estimating transmission rates and the effectiveness of various infection control measures. However, uncertainty about the true routes of transmission remains and that is reflected on the uncertainty of parameters governing transmission. Until recently, the collection of whole genome sequence (WGS) data for bacterial organisms has been prohibitively complex and expensive. However, technological advances and falling costs mean that DNA sequencing is becoming feasible on a larger scale. In this talk we first describe how to construct statistical models which incorporate WGS data with regular HCAIs surveillance data (admission/discharge dates etc) to describe the pathogen's transmission dynamics in a hospital ward. Then, we show how one can fit such models to data within a Bayesian framework accounting for unobserved colonisation times and imperfect screening sensitivity using efficient Markov Chain Monte Carlo algorithms. Finally, we illustrate the proposed methodology using MRSA surveillance data collected from a hospital in North-East Thailand.
Mar 21	Thu	Tom Fisher (Cambridge)	Number Theory seminar
14:00		The proportion of genus one curves that are everywhere locally soluble
		Hicks Seminar Room J11
	Abstract: I will describe joint work with Bhargava and Cremona, and with Ho and Park, on the probability that a randomly chosen genus one curve is soluble over the p-adics. A striking feature of this work is that we obtain exact answers in the form of explicit rational functions of p. I will also discuss what is expected to happen globally.
Mar 21	Thu	Mike Prest (Manchester)	Topology Seminar
16:00		Categories of imaginaries for additive categories
		Hicks Seminar Room J11
	Abstract: There is a construction of Freyd which associates, to any ring R, the free abelian category on R. That abelian category may be realised as the category of finitely presented functors on finitely presented R-modules. It has an alternative interpretation as the category of (model-theoretic) imaginaries for the category of R-modules. In fact, this extends to additive categories much more general than module categories, in particular to finitely accessible categories with products and to compactly generated triangulated categories. I will describe this and give some examples of its applications.
Mar 21	Thu	Peter Keys (Queen's University (Belfast))	Plasma Dynamics Group
16:00		Small-scale magnetic field evolution with high resolution observations.
		Room K14 (Hicks Building)
	Abstract: Small-scale magnetic fields, ubiquitous across the solar surface, manifest as intensity enhancements in intergranular lanes and, thus, often receive the moniker of magnetic bright point (MBP). MBPs are frequently studied as they are considered as a fundamental building block of magnetism in the solar atmosphere. The theory of convective collapse developed in the late 70’s and early 80’s is often used to explain how kilogauss fields form in MBPs. The dynamic nature of MBPs coupled with these kilogauss fields means that they are frequently posited as a source of wave phenomena in the solar atmosphere. Here, with high resolution observations of the quiet Sun with full Stokes spectropolarimetry, we investigate the magnetic properties of MBPs. By analysing the temporal evolution of various physical properties obtained from inversions, we show that kilogauss fields in MBPs can appear due to a variety of reasons, and is not limited to the process of convective collapse. Analysis of MURaM simulations confirms the processes we observe in our data. Also, magnetic field amplification happens on rapid timescales, which has significant implications for many wave studies.
Mar 22	Fri	Steffen Gielen (Nottingham)	Applied Mathematics Colloquium
14:00		The universe as a condensate of spacetime atoms
		TBA
	Abstract: In the standard picture of cosmology, the Universe began at the Big Bang; the Big Bang itself is a singularity where the laws of physics break down. A quantum theory of gravity should resolve this singularity and help in understanding the initial state of the Universe needed to account for present observations. I will present some progress towards this goal in the group field theory approach to quantum gravity, using the idea of a universe formed as a "condensate", i.e. a very homogeneous quantum configuration, from a large number of discrete building blocks of geometry. I will show how this setting produces new cosmological models without an initial singularity; demanding that such models be both theoretically self-consistent and potentially compatible with observation then gives new ways for constraining theories of quantum gravity.
Mar 22	Fri	Nicola Bellumat	THH reading group
14:00		Periodic Theories
		Hicks Seminar Room J11
Mar 27	Wed	Daniele Avitabile (Nottingham)	Applied Mathematics Colloquium
14:00		Interfacial dynamics for neurobiological networks: from excitability thresholds to localised spatiotemporal chaos
		Hicks, LT 9
	Abstract: We will discuss level-set based approaches to study the existence and bifurcation structure of spatio-temporal patterns in biological neural networks. Using this framework, which extends previous ideas in the study of neural field models, we study the first example of canards in an infinite-dimensional dynamical system, and we give a novel characterisation of localised structures, informally called “bumps”, supported by spiking neural networks. We will initially consider a spatially-extended network with heterogeneous synaptic kernel. Interfacial methods allow for the explicit construction of a bifurcation equation for localised steady states. When the model is subject to slow variations in the control parameters, a new type of coherent structure emerges: the structure displays a spatially-localised pattern, undergoing a slow-fast modulation at the core. Using interfacial dynamics and geometric singular perturbation theory, we show that these patterns follow an invariant repelling slow manifold, hence we name them "spatio-temporal canards". We classify spatio-temporal canards and give conditions for the existence of folded-saddle and folded-node canards. We also find that these structures are robust to changes in the synaptic connectivity and firing rate. The theory correctly predicts the existence of spatio-temporal canards with octahedral symmetries in a neural field model posed on a spherical domain. We will then discuss how the insight gained with interfacial dynamics may be used to perform coarse-grained bifurcation analysis on neural networks, even in models where the network does not evolve according to an integro-differential equation. As an example I will consider a well-known event-driven network of spiking neurons, proposed by Laing and Chow. In this setting, we construct numerically travelling waves whose profiles possess an arbitrary number of spikes. An open question is the origin of the travelling waves, which have been conjectured to form via a destabilisation of a bump solution. We provide numerical evidence that this mechanism is not in place, by showing that disconnected branches of travelling waves with countably many spikes exist, and terminate at grazing points; the grazing points correspond to travelling waves with an increasing number of spikes, a well-defined width, and decreasing propagation speed. We interpret the so called “bumps” and “meandering bumps”, supported by this model as localised states of spatiotemporal chaos, whereby the dynamics visits a large number of unstable localised travelling wave solutions.
Mar 27	Wed	Andreea Mocanu (Nottingham)	ShEAF: postgraduate pure maths seminar
16:00		On the connection between Jacobi forms and elliptic modular forms
		Hicks Seminar Room J11
	Abstract: Jacobi forms arise naturally in number theory, for example as functions of lattices or as Fourier-Jacobi coefficients of other types of modular forms. They have applications in algebraic geometry, string theory and the theory of vertex operator algebras, among other areas. We are interested in establishing a precise connection between Jacobi forms of lattice index and elliptic modular forms, in other to transfer information from one side to the other. In this talk, we illustrate this connection via an example, namely that of Jacobi forms whose indices are the root lattices of type $D_n$.
Mar 28	Thu	Stanislav Gunár (Astronomical Institute of the Czech Academy of Sciences)	SP2RC seminar
10:00		3D Whole-Prominence Fine Structure models: the current state of the affairs
		F28
	Abstract: To understand the links between the distribution of the prominence plasma, the configuration of its magnetic field and the observations of prominence/filament fine structures obtained in UV/EUV, optical and radio domains from various vantage points, we need complex 3D prominence models. We have developed two such models which combine 3D magnetic field configurations of an entire prominence with a detailed description of the prominence plasma distributed along hundreds of fine structures. The first 3D Whole-Prominence Fine Structure (WPFS) model, developed by Gunár & Mackay (2015), uses a magnetic field configuration obtained from non-linear force-free field simulations of Mackay & van Ballegooijen (2009). The second WPFS model was developed by Gunár, Dudík, Aulanier, Schmieder & Heinzel (2018). The model employs a magnetic field configuration of a polar crown prominence based on the linear force-free field modelling approach designed by Aulanier & Démoulin (1998) which allows us to calculate linear magneto-hydrostatic extrapolations from photospheric flux distributions. The prominence plasma in both models is located in magnetic dips that occur naturally in the predominantly horizontal prominence magnetic field. This plasma has a realistic distribution of the density and temperature, including the prominence-corona transition region. The models thus provide comprehensive information about the 3D distribution of the prominence plasma and magnetic field which can be consistently studied both as a prominence on the limb and as a filament on the disk. These models can be visualized for example in the H-alpha spectral line. Together with the models, we will present some of their capabilities which allow us to study the evolution of prominences/filaments or to analyze the true and apparent shapes and motions of the prominence fine structures.
Mar 28	Thu	Mark Quinn (Sheffield)	Teaching Lunch
13:00		Colcalc and Sagemath
		Hicks LT6
Mar 28	Thu	Jeremy Oakley (Sheffield)	Statistics Seminar
14:00		Variational inference reading group
		LT E
	Abstract: We will be spending two seminar slots on the following: Variational Inference: A Review for Statisticians https://arxiv.org/abs/1601.00670 David M. Blei, Alp Kucukelbir, Jon D. McAuliffe
Mar 28	Thu	Jordan Williamson (Sheffield)	Topology Seminar
16:00		A Left Localization Principle and Cofree G-Spectra
		Hicks Seminar Room J11
	Abstract: Greenlees-Shipley developed a Cellularization Principle for Quillen adjunctions in order to attack the problem of constructing algebraic models for rational G-spectra. One example of this was the classification of free rational G-spectra as torsion modules over the cohomology ring H*(BG) (for G connected). This has some disadvantages; namely that it is not monoidal and that torsion modules supports only an injective model structure. I will explain a related method called the Left Localization Principle, and how this can be used to construct a monoidal algebraic model for cofree G-spectra. This will require a tour through the different kinds of completions available in homotopy theory. This is joint work with Luca Pol.
Mar 29	Fri	Jordan Williamson	THH reading group
14:00		Tate Diagonal
		Hicks Seminar Room J11
Apr 2	Tue	Matthew Allcock, Farhad Allian, Callum Reader (Sheffield)	Postgraduate seminars
13:00		Postgraduate Student Seminar
		Hicks Seminar Room J11
	Abstract: Matthew Allcock - The mathematics of making the right decisions In philosophy, there are two types of uncertainty: empirical uncertainty - uncertainty about what “is” - and normative uncertainty - uncertainty about what “should be”. We know how to deal with empirical uncertainty - we use expected value theory. But how should we deal with normative uncertainty? It turns out that we can define a mathematical framework analogous to expected value theory that deals with normative uncertainty. This framework works… sometimes… until it breaks. Let’s try to fix those breaks using mathematics. Farhad Allian - Observations of solar coronal loop oscillations Imagine you're hiking up the highest hill in the Peak District. But to your disbelief, you notice that your surrounding air becomes hotter as you approach the summit. This is exactly what happens on our Sun: The solar atmosphere is around 200 times hotter than its surface, and this seemingly paradoxical statement has left solar physicists puzzled for decades. In this talk, I will present my research on how I'm combining high-resolution images with mathematics to understand how the Sun's atmosphere can be heated to 2,000,000 Kelvin. Callum Reader - Biodiversity metrics from category theory In 1973 philosopher and mathematician Lawvere published his paper “Metric Spaces, Generalised Logic, and Closed Categories”, outlining the theory of enriched categories: a generalisation common of both regular categories and metric spaces. Around forty years later, Leinster introduced the concept of magnitude (a generalisation of Euler characteristic) for an enriched category, distilling all its information to a single value in some ring. Interestingly, when specifically applied to a metric space this seems to give some information about the “effective number of points” of the space, providing a better means of measuring biodiversity and answering the age old question: “yeah but what are the applications?”
Apr 2	Tue	Arne Grauer, Lukas Lüchtrath (Cologne)	Statistics Seminar
16:00		The age-dependent random connection model
		F28
	Abstract: We consider a class of growing graphs embedded into the $d$-dimensional torus where new vertices arrive according to a Poisson process in time, are randomly placed in space and connect to existing vertices with a probability depending on time, their spatial distance and their relative ages. This simple model for a scale-free network is called the age-based spatial preferential attachment network and is based on the idea of preferential attachment with spatially induced clustering. The graphs converge weakly locally to a variant of the random connection model, which we call the age-dependent random connection model. This is a natural infinite graph on a Poisson point process where points are marked by a uniformly distributed age and connected with a probability depending on their spatial distance and both ages. We use the limiting structure to investigate asymptotic degree distribution, clustering coefficients and typical edge lengths in the age-based spatial preferential attachment network.
Apr 3	Wed	Mahesh Kakde (King's College London)	Pure Maths Colloquium
14:00		Explicit formulae for Gross-Stark units and Hilbert’s 12 problem
		Hicks Seminar Room J11
	Abstract: I will introduce the Gross-Stark units and present their application to Hilbert’s 12th problem. Following an earlier work in special case with Darmon, Dasgupta gave precise conjectural p-adic analytic formula for these units. After giving a formulation of this conjecture, I will sketch a proof of this conjecture. This is a joint work in progress with Samit Dasgupta.
Apr 3	Wed	Matt Turner (Surrey)	Applied Mathematics Colloquium
14:00		Dynamic sloshing via time-dependent conformal mappings
		Hicks, LT 9
	Abstract: In this talk we examine two-dimensional, inviscid, irrotational fluid sloshing in both fixed and moving vessels. In particular we focus on a numerical scheme which utilizes time-dependent conformal mappings of doubly-connected domains to produce a scheme which is fast and efficient. Results are presented for flows in a fixed vessel, a moving vessel with bottom topography, a coupled pendulum slosh problem and a fixed vessel with multiple horizontal baffles. The application of this work is to the modelling of offshore wave energy converters.
Apr 4	Thu	Chris Birkbeck (UCL)	Number Theory seminar
14:00		Overconvergent Hilbert modular forms via perfectoid methods
		Hicks Seminar Room J11
	Abstract: Following a construction of Chojecki-Hansen-Johansson, we use Scholze's infinite level modular varieties and the Hodge-Tate period map to give a new definition of overconvergent elliptic and Hilbert modular forms which is analogous to the standard construction of modular forms as functions on the upper half plane. This has applications to constructing overconvergent Eichler-Shimura maps in these settings. This is all work in progress joint with Ben Heuer and Chris Williams.
Apr 4	Thu	Richard Hepworth (Aberdeen)	Topology Seminar
16:00		CANCELLED
		Hicks Seminar Room J11
Apr 5	Fri	Luca Pol	THH reading group
14:00		Topological Cyclic Homology
		Hicks Seminar Room J11
Apr 18	Thu	Philippa Browning (University of Manchester)	Plasma Dynamics Group
16:00		Plasma heating and particle acceleration by magnetic reconnection in solar and stellar flares
		Room K14 (Hicks Building)
	Abstract: In this talk, I will describe recent models of plasma heating and non-thermal particle acceleration in flares, focussing on the role of twisted magnetic flux ropes as reservoirs of free magnetic energy. First, using 2D magnetohydrodynamic simulations coupled with a guiding-centre test-particle code, I will describe magnetic reconnection and particle acceleration in a large-scale flaring current sheet, triggered by an external perturbation – the “forced reconnection” scenario. I will show how reconnection is involved both in creating twisted flux ropes, and in their merger, how this depends on the nature of the driving disturbance, and how particles are accelerated by the different modes of reconnection. Moving to 3D models, showing how fragmented current structures in kink-unstable twisted loops can both heat plasma and accelerate charged particles. Forward modelling of the observational signatures of this process in EUV, hard X-rays and microwaves will be described, and the potential for observational identification of twisted magnetic fields in the solar corona discussed. Then, coronal structure with multiple twisted threads will be considered, showing how instability in a single unstable twisted thread may trigger reconnection with stable neighbours, releasing their stored energy and causing an "avalanche" of heating events, with important implications for solar coronal heating. This avalanche can also accelerate electrons and ions throughout the structure. Many other stars exhibit flares, and I will briefly discuss recent work on modelling radio emission in flares in young stars (T Tauri stars). In particular, the enhanced radio luminosity of these stars relative to scaling laws for the Sun and other Main Sequence stars will be discussed.
May 1	Wed	Sam Falle (Leeds)	Applied Mathematics Colloquium
14:00		Shock structures described by hyperbolic balance laws
		Hicks, LT 9
	Abstract: In this talk I will consider shock structures that arise in systems of hyperbolic balance laws, i.e. hyperbolic systems of conservation laws with source terms. I show how the Whitham criterion for the existence of such shock structures can be extended to systems with more than one relaxation variable. In addition, I descibe a method based on the Hermite-Biehler theorem that is useful for determining the stability of the equilibrium states of such systems. The utility of this method is illustrated by a number of examples: ideal gas with two internal degrees of freedom, two fluid magnetohydrodynamics and magnetohydrodynamics with tensor resistivity.
May 1	Wed	Esmee te Winkel (Warwick)	ShEAF: postgraduate pure maths seminar
16:00		A combinatorial approach to surface homeomorphisms
		Hicks Seminar Room J11
	Abstract: In geometric group theory, it is common to try to study a group by finding a meaningful action on a metric space. This talk is about the mapping class group of a compact surface and its action on various graphs. The mapping class group is the group of homeomorphisms up to isotopy. I will define this group and state some of its properties and open questions. After this motivation, I will introduce the curve graph and the pants graph associated to a surface and explain how the mapping class group acts on them.
May 2	Thu	Celeste Damiani (Leeds)	Topology Seminar
16:00		TBA
		Hicks Seminar Room J11
May 2	Thu	Youra Taroyan (Aberystwyth University)	Plasma Dynamics Group
16:00		Amplification of magnetic twists during prominence formation
		Room K14 (Hicks Building)
	Abstract: Solar prominences are dense magnetic structures that are anchored to the visible surface known as the photosphere. They extend outwards into the Sun’s upper atmosphere known as the corona. Twists in prominence field lines are believed to play an important role in supporting the dense plasma against gravity as well as in prominence eruptions and coronal mass ejections (CMEs), which may have severe impact on the Earth and its near environment. We will use a simple model to mimic the formation of a prominence thread by plasma condensation. The process of coupling between the inflows and the twists will be discussed. We show that arbitrarily small magnetic twists should be amplified in time during the mass accumulation process. The growth rate of the twists is proportional to the mass condensation rate.
May 3	Fri	James Brotherston	THH reading group
14:00		Loop Spaces
		Hicks Seminar Room J11
May 8	Wed	Aditi Kar (Royal Holloway)	Pure Maths Colloquium
14:00		2D Problems in Groups
		Hicks Seminar Room J11
	Abstract: I will discuss a conjecture about stabilisation of deficiency in finite index subgroups of a finitely presented group and relate it to the D2 Problem of C.T.C. Wall and the Relation Gap problem. I will explain a pro-p version of the conjecture, as well as its higher dimensional abstract analogues and why we can verify the conjecture in these cases.
May 8	Wed	Kasia Rejzner (York)	Applied Mathematics Colloquium
14:00		Perturbative algebraic QFT - Example of the sine-Gordon model
		Hicks, LT 9
	Abstract: In this talk I will present recent results on the construction of the net of local algebras for the sine-Gordon model. The approach I will present is that of perturbative algebraic QFT, in which the interacting fields are constructed using formal S-matrices. It has been shown that in sine-Gordon model these formal S-matrices can be realized as unitary operators in certain Hilbert space representation, appropriate for massless scalar field in 2 dimensions.
May 9	Thu	Rebecca Killick (Lancaster)	Statistics Seminar
14:00		Computationally Efficient Multivariate Changepoint Detection with Subsets
		LT E
	Abstract: Historically much of the research on changepoint analysis has focused on the univariate setting. Due to the growing number of high dimensional datasets there is an increasing need for methods that can detect changepoints in multivariate time series. In this talk we focus on the problem of detecting changepoints where only a subset of the variables under observation undergo a change, so called subset multivariate changepoints. One approach to locating changepoints is to choose the segmentation that minimises a penalised cost function via a dynamic program. The work in this presentation is the first to create a dynamic program specifically for detecting changes in subset-multivariate time series. The computational complexity of the dynamic program means it is infeasible even for medium datasets. Thus we propose a computationally efficient approximate dynamic program, SPOT. We demonstrate that SPOT always recovers a better segmentation, in terms of penalised cost, then other approaches which assume every variable changes. Furthermore under mild assumptions the computational cost of SPOT is linear in the number of data points. In small simulation studies we demonstrate that SPOT provides a good approximation to exact methods but is feasible for datasets that contain thousands of variables observed at millions of time points. Furthermore we demonstrate that our method compares favourably with other commonly used multivariate changepoint methods and achieves a substantial improvement in performance when compared with fully multivariate methods.
May 13	Mon	Natasha Ellison, Sara Hilditch, Elena Marensi, Alison Parton, Lizzie Sheppeck, Sarah Whitehouse, Sadiah Zahoor (University of Sheffield)	International Women in Mathematics Day
10:00
		LT-5
May 13	Mon	Suzana de Souza e Almeida Silva (Technological Institute of Aeronautics, Sao Paulo)	Plasma Dynamics Group
13:00		Lagrangian Coherent Structures: Overview and applications in solar physics
		LT9 (Hicks Building)
	Abstract: Lagrangian coherent structures (LCS) is a newly developed theory which describes the skeleton of turbulent flows. LCS act as barriers in the flow, separating regions with different dynamics and organizing the flow into coherent patterns. This talk will introduce some concepts of LCT techniques as well as recent application to solar physics problems.
May 13	Mon	Yuri M. Pismak (St. Petersburg State University)	Applied Mathematics Colloquium
14:00		Modelling the interaction of the quantum electrodynamics fields with extended material bodies
		Hicks, LT 9
	Abstract: The method proposed by K. Symanzik for constructing quantum field models in an inhomogeneous space-time is used to describe the interaction of the quantum electrodynamics (QED) fields with material objects. It is carried out within the framework of quantum field models in which the QED Lagrangian is modified according to the QED basic principles (locality, gauge invariance, renormalizability) and taking into account the properties of the material medium interacting with QED fields. Models with interactions of electromagnetic and Dirac fields with two-dimensional materials of flat, spherical and cylindrical shape are considered. The results obtained in such models for the Casimir effect, scattering processes and bound states are discussed.
May 13	Mon	Nuria Folguera Blasco (Crick Institute)	Mathematical Biology Seminar
14:00
		Hicks F20
May 14	Tue	Anna Krystalli / Alison Parton / Lyn Taylor (Sheffield / Sheffield / Phastar)	RSS Seminar
16:00		Putting the R in Reproducible Research / Cloud Computing with R / R Validation Hub Project
		LT 5
	Abstract: R and its ecosystem of packages offers a wide variety of statistical and graphical techniques and is increasing in popularity as the tool of choice for data analysis in academia. In addition to its powerful analytical features, the R ecosystem provides a large number of tools and conventions to help support more open, robust and reproducible research. This includes tools for managing research projects, building robust analysis workflows, documenting data and code, testing code and disseminating and sharing analyses. In this talk we’ll take a whistle-stop tour of the breadth of available tools, demonstrating the ways R and the Rstudio integrated development environment can be used to underpin more open reproducible research and facilitate best practice. R has cemented itself as the language of choice for many a statistician and data scientist, but is often heckled as a sluggish competitor to the likes of python. This talk will discuss one avenue for maintaining the comfort and power of R (see Anna’s talk!) without having to wait days for your desktop analysis to complete. The foreach package is a set of functions that allow virtually anything that can be expressed as a for-loop as a set of parallel tasks. By registering a parallel backend through the doParallel package, you can speed up the run-time of your work by utilising the full capacity of your machine. I’ll introduce how to rewrite workflows to utilise the foreach approach and show how you can implement a parallel workflow on your own machine with doParallel. For a low-range machine, this will reduce your run-time by 4-fold and for those lucky few with high-range budgets you’ll receive something around 16-fold. So how about going one step further, and increasing to hundreds-fold? We can achieve this by using cloud computing services, taking the load away from your own machine. Cloud computing services have been seen to have a steep learning curve and this has led to many shying away from using such a useful resource. I’ll introduce you to the doAzureParallel package for R, create by Microsoft to bypass this learning curve and allow you to implement the foreach package in parallel in the cloud with only minor amendments to the R code that has been blighting you for months. To date, the use of R Software in the pharmaceutical industry has been relatively limited to exploratory work and not routinely used in regulatory submissions where SAS® Software is still favored. One of the difficulties in using R for submissions is being able to provide the regulators with appropriate documentation of testing and validation for the packages used. In June 2018 the R consortium granted funding for a PSI AIMS SIG initiative to create an online ‘R package validation repository’. With representatives from Abbvie, Amgen, Biogen, Eli Lilly, FDA, GSK, J&J, Merck, Merck KGaA, Novartis, PPD, PRA, Pfizer, Roche / Genentech, Syne qua non and the Transcelerate project, the ‘R Validation Hub’ team launched a free to access web site to host validation documentation and metrics for R packages (https://www.pharmar.org/). Although, the project is still in its early stages, we are looking to expand on the website content and encourage contribution of R metrics and tests for packages from all R-users. The talk will discuss what is meant by validation, how R differs to SAS, justify our approach to the validation issue and present the future capabilities of the website and how all R-users are set to benefit from the work.
May 15	Wed	Martina Balagovic (Newcastle)	Pure Maths Colloquium
14:00		Quantum Yang Baxter equation, the reflection equation, and their universal solutions
		Hicks Seminar Room J11
	Abstract: The quantum Yang Baxter equation arose in statistical mechanics around 1970 as the consistency condition for an interaction of two particles on a line. In the 1980s, Drinfled and Jimbo introduced quantum groups (deformations of universal enveloping algebras of Lie algebras), and showed that they allow a universal R matrix - an element constructed from the algebra, which systematically produces a solution of the quantum Yang Baxter equation in every representation of this algebra. In turn, this imposes a structure of a braided tensor category on representations of the quantum group (i.e. gives an action of the braid group of type A) and leads to the Reshetikhin-Turaev construction of invariants of knots, braids, and ribbons. Considering the same problem with a boundary (on a half line instead of a line) leads to the consistency condition called the (quantum) reflection equation, introduced by Cherednik and Sklyanin in the 1980s. I will explain how, in the joint work with S. Kolb, we use quantum symmetric pairs (Noumi, Sugitani, and Dijkhuizen; Letzter 1990s) to construct a universal K-matrix - an element which systematically produces solutions of the reflection equation. This gives an action of the braid group of type B, endowing the corresponding category of representations with a structure of a braided tensor category with a cylinder twist (as defined by T. tom Dieck, R. Haring-Oldenburg 1990s).
May 16	Thu	Christopher Fallaize (Nottingham)	Statistics Seminar
14:00		Unlabelled Shape Analysis with Applications in Bioinformatics
		LT E
	Abstract: In shape analysis, objects are often represented as configurations of points, known as landmarks. The case where the correspondence between landmarks on different objects is unknown is called unlabelled shape analysis. The alignment task is then to simultaneously identify the correspondence between landmarks and the transformation aligning the objects. In this talk, I will discuss the alignment of unlabelled shapes, and discuss two applications to problems in structural bioinformatics. The first is a problem in drug discovery, where the main objective is to find the shape information common to all, or subsets of, a set of active compounds. The approach taken resembles a form of clustering, which also gives estimates of the mean shapes of each cluster. The second application is the alignment of protein structures, which will also serve to illustrate how the modelling framework can incorporate very general information regarding the properties we would like alignments to have; in this case, expressed through the sequence order of the points (amino acids) of the proteins.
May 16	Thu	Peter Wyper (University of Durham)	Plasma Dynamics Group
16:00		Reconnection, Topology and Solar Eruptions
		Room K14 (Hicks Building)
	Abstract: The majority of free energy in the solar corona is stored within sheared magnetic field structures known as filament channels. Filament channels spend most of their life in force balance before violently erupting. The largest produce powerful solar flares and coronal mass ejections (CMEs), whereby the filament channel is bodily ejected from the Sun. However, a whole range of smaller eruptions and flares also occur throughout the corona. Some are ejective, whilst others are confined. Recently it has been established that coronal jets are also typically the result of a filament channel eruption. The filament channels involved in jets are orders of magnitude smaller than the ones which produce CMEs. In this talk I will start by considering these tiny, jet producing eruptions. I will introduce our MHD simulation model that well describes them and then discuss what jets can tell us about solar eruptions in general. Specifically, I will argue that many different types of eruption can be understood by considering two defining features: the scale of the filament channel and its interaction via reconnection with its surrounding magnetic topology.
May 17	Fri	Gong Show	Topology Seminar
16:00
		Hicks Seminar Room J11
May 30	Thu	David Jess (Queen's University (Belfast))	Plasma Dynamics Group
14:00		Resonance Cavities: A wave amplification mechanism above highly magnetic sunspots
		Room LT10 (Hicks Building)
	Abstract: The solar atmosphere provides a unique astrophysical laboratory to study the formation, propagation, and subsequent dissipation of magnetohydrodynamic (MHD) waves across a diverse range of spatial scales. The concentrated magnetic fields synonymous with sunspots allow the examination of guided magnetoacoustic modes as they propagate upwards into the solar corona, where they exist as ubiquitous 3-minute waves readily observed along loops, plumes and fan structures. While cutting-edge observations and simulations are providing insights into the underlying wave generation and damping mechanisms, the in-situ amplification of magnetoacoustic waves as they propagate through the solar chromosphere has proved difficult to explain. Here we provide observational evidence of a resonance cavity existing above a magnetic sunspot, where the intrinsic temperature stratification provides the necessary atmospheric boundaries responsible for the resonant amplification of these waves. Through comparisons with high-resolution numerical MHD simulations, the geometry of the resonance cavity is mapped across the diameter of the underlying sunspot, with the upper boundaries of the chromosphere ranging between 1300–2300 km. This brings forth important implications for next-generation ground-based observing facilities, and provides an unprecedented insight into the MHD wave modelling requirements for laboratory and astrophysical plasmas.
May 31	Fri	Prof Yuanyong Deng (Director of Huairoi Observatory) (NAOC, CAS, China)	SP2RC seminar
13:00		The observational research and projects of solar physics in China
		LT09
	Abstract: In this presentation I will briefly introduce recent solar observation and related research in China. Up to now all these observations come from ground-based telescopes. In the near future, Chinese will have our first space solar observatory by the Advanced Space solar telescope (ASO-S). In addition to ASO-S, some other projects under development or proposed will also be introduced and discussed.
Jun 11	Tue	Andreas Krug (Magburg)	Algebra / Algebraic Geometry seminar
14:00		Stability of Tautological Bundles on Symmetric Products of Curves
		Hicks Seminar Room J11
	Abstract: Given a vector bundle E over smooth variety X, there is a natural way to associate a vector bundle, called tautological bundle, on the Hilbert scheme of points on X. In this talk, we will discuss stability of tautological bundles in the case that X is a curve.
Jun 18	Tue	Tong Liu (Purdue)	Number Theory seminar
14:00		p-divisible groups and crystalline representations over relative base
		Hicks Seminar Room J11
	Abstract: Let K be a p-adic field, it is known that p-adic Tate module of p-divisible group over O_K is crystalline representation with Hodge-Tate weights in [0, 1]. And conversely any such crystalline representation arise from a p-divisible group over O_K. In this talk, we discuss how to generalize this result to relative bases when O_K is replaced by more general rings, like, Z_p[[t]]. This is a joint work with Yong Suk Moon.
Jun 20	Thu	Ioannis Kontogiannis (Leibniz-Institut für Astrophysik Potsdam, AIP)
10:00		Emergence of small-scale magnetic flux in the quiet Sun, observed from the photosphere to the corona
		LT11
	Abstract: We study the emergence and evolution of new magnetic flux in the vicinity of a quiet Sun network. We employ high-resolution spectropolarimetric, spectroscopic and spectral imaging observations from ground-based (Dutch Open Telescope) and space-born instruments (TRACE, Hinode, SoHO), which provided a multi-wavelength, tomographic view of the region from the photosphere up to the corona. Throughout its evolution, the region exhibited many of the phenomena revealed by recent simulations. The event starts with a series of granular-scale events, which follow the photospheric flow field and merge to form a small-scale magnetic flux system of the order of 1018 Mx. Spectropolarimetric inversions reveal an evolving, complicated pattern of horizontal and vertical magnetic field patches at the region between the main polarities. As the magnetic flux accumulates and the region expands, Doppler-shifted H-alpha absorption features appear above and at the crests of the structure, indicating an immediate interaction with the pre-existing, overlying magnetic field. Roughly 60 min after the region first emerged at the photosphere, a jet-like feature appeared in the chromosphere and a small soft X-ray bright point formed in the corona. The coronal brightening exhibited intense spatial and temporal variations and had a lifetime that exceeded one hour. EUV spectroscopy and DEM analysis revealed temperatures up to 106 K and densities up to 1010 cm-3. Even in the absence of a strong ambient magnetic field, small-scale magnetic flux emergence affects dramatically the dynamics and shape of the quiet Sun.
Jun 20	Thu	Ioannis Kontogiannis (Leibniz-Institut für Astrophysik Potsdam, AIP)	SP2RC seminar
10:00		Emergence of small-scale magnetic flux in the quiet Sun, observed from the photosphere to the corona
		LT11
	Abstract: We study the emergence and evolution of new magnetic flux in the vicinity of a quiet Sun network. We employ high-resolution spectropolarimetric, spectroscopic and spectral imaging observations from ground-based (Dutch Open Telescope) and space-born instruments (TRACE, Hinode, SoHO), which provided a multi-wavelength, tomographic view of the region from the photosphere up to the corona. Throughout its evolution, the region exhibited many of the phenomena revealed by recent simulations. The event starts with a series of granular-scale events, which follow the photospheric flow field and merge to form a small-scale magnetic flux system of the order of 1018 Mx. Spectropolarimetric inversions reveal an evolving, complicated pattern of horizontal and vertical magnetic field patches at the region between the main polarities. As the magnetic flux accumulates and the region expands, Doppler-shifted H-alpha absorption features appear above and at the crests of the structure, indicating an immediate interaction with the pre-existing, overlying magnetic field. Roughly 60 min after the region first emerged at the photosphere, a jet-like feature appeared in the chromosphere and a small soft X-ray bright point formed in the corona. The coronal brightening exhibited intense spatial and temporal variations and had a lifetime that exceeded one hour. EUV spectroscopy and DEM analysis revealed temperatures up to 106 K and densities up to 1010 cm-3. Even in the absence of a strong ambient magnetic field, small-scale magnetic flux emergence affects dramatically the dynamics and shape of the quiet Sun.
Jul 2	Tue	Evgeny Shinder (Sheffield)
15:00		Geometry of Singularities
		Hicks LT 2
Jul 2	Tue	Caitlin Buck (Sheffield)
15:30		Maintaining Impact in Interdisciplinary Research
		Hicks, LT2
Jul 2	Tue	Neil Dummigan (Sheffield)
16:30		Lattices and theta series
		Hicks LT2
Aug 14	Wed	Ben Evans (Bristol)	Mathematical Biology Seminar
16:00		Building biological constraints into convolutional neural networks for classification overcomes biases within datasets
		Alfred Denny Conference Room
	Abstract: Part of the appeal of deep convolutional networks is their ability to learn on raw data, obviating the need to hand-code the feature space. It has been demonstrated that when networks perform "end- to-end" learning, they develop features in early layers that not only lead to a good classification performance but also resemble the representations found in biological vision systems. These results have been used to draw various parallels between deep learning systems and human visual perception. In this study, we show that end-to-end learning in standard convolutional neural networks (CNNs) trained on a modified CIFAR-10 dataset are found to rely upon idiosyncratic features within the dataset. Instead of relying on abstract features such as object shape, end-to-end learning can pick up on low-level and spatially high-frequency features, such as noise-like masks. Such features are extremely unlikely to play any role in human object recognition, where instead a strong preference for shape is observed. Through a series of empirical studies, we show that these CNNs cannot overcome such problems merely through regularisation methods or more ecologically plausible training regimes. However, we show that these problems can be ameliorated by forgoing end-to-end learning and processing images with Gabor filters in a manner that more closely resembles biological vision systems. These results raise doubts over the assumption that simply learning end-to-end in "vanilla" CNNs leads to the emergence of similar representations to those observed in biological vision systems. By adding more biological input constraints, we show that deep learning models can not only capture more aspects of human visual perception, but also become more robust to idiosyncratic biases within training sets.
Aug 22	Thu	Jason Green (Massachusetts Boston)	Applied Mathematics Colloquium
11:00		The struggle between order and chaos in atomistic fluids
		Hicks, K14
	Abstract: Molecular motion in fluids is a consequence of well-known physical laws, but in diverse soft matter contexts, it is challenging to construct predictions of bulk properties directly from the nonlinear intermolecular forces. The difficulty is that molecules in liquids are constantly moving, in a perpetual state of collision and chaos. As a result, their dynamics sit balanced at the knife-edge between the sharp, well-defined collisions in gases and the ordered oscillations in crystalline solids. That is, the disordered liquid state reflects a tension between order and chaos. This tension is especially heightened at the liquid-vapor critical point where strong statistical correlations imply structural organization that is intrinsically opposed by the chaotic dynamics. The goal of this talk will be to explain some recent developments coupling nonlinear dynamics and statistical physics and how these advances are beginning to offer a mechanistic view of longstanding paradigms in liquid state theory and critical phenomena. Critical fluctuations and slowing down of chaos Moupriya Das, Jason R. Green Nat. Commun. 2019 10(1) p. 2155 Self-averaging fluctuations in the chaoticity of simple fluids Moupriya Das, Jason R. Green Phys. Rev. Lett. 2017 119(11), p. 115502 Extensivity and additivity of the Kolmogorov-Sinai entropy for simple fluids Moupriya Das, Anthony B. Costa, Jason R. Green Phys. Rev. E 2017 95(2), p. 022102
Sep 11	Wed	Baofang Song (Center for Applied Mathematics, Tianjin University)	Applied Mathematics Colloquium
14:00		The transition to turbulence and turbulence control in pipe flow
		Hicks, K14
	Abstract: The transition to turbulence in wall-bounded shear flows, such as pipe, channel, and Couette flows, is a fundamental problem of fluid dynamics. The questions of when and how turbulence rises in these flows, as Reynolds number increases, have challenged scientists and engineers for over a century and have not been fully understood till today. The complexity lies in the subcritical nature of the transition in these flows and the coexistence of various turbulent states and the quiescent laminar state during the transition process. Nevertheless, in recent years, significant advancements in this research area have been made. In this talk, I will present some results of our team on the transition to turbulence as well as turbulence control in pipe flow.
Sep 17	Tue	Francesco Sala (IPMU Tokyo)	Algebra / Algebraic Geometry seminar
14:00		Categorification of 2d cohomological Hall algebras
		Hicks Seminar Room J11
	Abstract: Let $\mathcal{M}$ denote the moduli stack of either coherent sheaves on a smooth projective surface or Higgs sheaves on a smooth projective curve $X$. The convolution algebra structure on the Borel-Moore homology of $\mathcal{M}$ is an instance of two-dimensional cohomological Hall algebras. These examples were defined by Kapranov-Vasserot and by Schiffmann and me, respectively. In the present talk, I will describe a full categorification of the cohomological Hall algebra of $\mathcal{M}$. This is achieved by exhibiting a derived enhancement of $\mathcal{M}$. Furthermore, this method applies also to several other moduli stacks, such as the moduli stack of vector bundles with flat connections on $X$ and the moduli stack of finite-dimensional representations of the fundamental group of $X$. In the curve case, we call the corresponding categorified algebras the Betti, de Rham, and Dolbeaut categorified Hall algebras of the curve $X$, respectively. In the second part of the talk, I will discuss some relations between these categorified Hall algebras. This is based on a joint work with Mauro Porta.
Sep 30	Mon	Evgeny Shinder (Sheffield)
15:00		K3 surfaces, 1. Introduction to K3 surfaces and distribution of the talks
		Hicks Seminar Room J11
Oct 1	Tue	Paul Johnson (Sheffield)	Algebra / Algebraic Geometry seminar
12:00		Partitions and Hilbert Schemes of Points
		Hicks Seminar Room J11
	Abstract: This will be a gentle, expository talk explaining some connections between the two objects in the title. I will begin with partitions: using the cores-and-quotients formula to motivate the statement of an enriched version of Euler's product formula for partitions, that was conjectured by Gusein-Zade, Luengo, and Melle-Hernández in 2009, and that I proved this summer with Jørgen Rennemo. Most of the talk will be giving the geometric context for this combinatorial formula, namely how Gusein-Zade, Luengo and Melle-Hernández came to discover it by studying Hilbert schemes of points on orbifolds, and how to use Chen-Ruan cohomology to generalise it and connect it to existing results on Hilbert schemes. I will vaguely gesture toward the proof in the last five minutes for the experts, but most of the talk should be accessible to the whole audience.
Oct 2	Wed	Bartek Protas (McMaster/INI Cambridge)	Applied Mathematics Colloquium
14:00		Maximum Amplification of Enstrophy in Navier-Stokes Flows and the Hydrodynamic Blow-Up Problem
		Hicks, LT 9
	Abstract: In the presentation we will discuss our research program focused on a systematic search for extreme, potentially singular, behaviors in the Navier-Stokes system and in other models of fluid flow. Enstrophy and enstrophy-like quantities serve as convenient indicators of the regularity of solutions to such system -- as long as these quantities remains finite, the solutions are guaranteed to be smooth and satisfy the equations in the classical (pointwise) sense. However, there are no available estimates with finite a priori bounds on the growth of enstrophy in 3D Navier-Stokes flows and hence the regularity problem for this system remains open. While the 1D Burgers and the 2D Navier-Stokes system are known to be globally well posed, the question whether the corresponding estimates on the instantaneous and finite-time growth of various enstrophy-like quantities is quite relevant. We demonstrate how new insights concerning such questions can be obtained by formulating them as variational PDE optimization problems which can be solved computationally using suitable discrete gradient flows. More specifically, such an optimization formulation allows one to identify "extreme" initial data which, subject to certain constraints, leads to the most singular flow evolution which can then be compared with upper bounds obtained using rigorous methods of mathematical analysis. In order to quantify the maximum possible growth of enstrophy in 3D Navier-Stokes flows, we consider a family of such optimization problems in which initial conditions with prescribed enstrophy E_0 are sought such that the enstrophy in the resulting Navier-Stokes flow is maximized at some time T. By solving these problems for a broad range of values of E_0 and T, we demonstrate that the maximum growth of enstrophy is in fact finite and scales in proportion to E_0^{3/2} as E_0 becomes large. Thus, in such worst-case scenario the enstrophy still remains bounded for all times and there is no evidence for formation of singularity in finite time. We also analyze properties of the Navier-Stokes flows leading to the extreme enstrophy values and show that this behavior is realized by a series of vortex reconnection events.
Oct 2	Wed	Peter Millington (University of Nottingham)	Cosmology, Relativity and Gravitation
15:00		Quasi-normal modes and fermionic vacuum decay around a Kerr black hole
		Hicks Seminar Room J11
	Abstract: The non-rotating fermion vacuum in Kerr spacetimes is unstable to a spontaneous vacuum decay, which leads to the formation of a co-rotating Dirac sea. This decay, which amounts to the fermionic pendant of the black hole bomb instability, has an analogue in the electrodynamics of supercritical fields, and we show that the decay process is encoded by the set of quasi-normal fermion modes.
	Slides
Oct 3	Thu	Ulrich Pennig (Cardiff)	Topology Seminar
16:00		Equivariant higher twisted K-theory of SU(n) via exponential functors
		Hicks Seminar Room J11
	Abstract: Twisted K-theory is a variant of topological K-theory that allows local coefficient systems called twists. For spaces and twists equipped with an action by a group, equivariant twisted K-theory provides an even finer invariant. Equivariant twists over Lie groups gained increasing importance in the subject due to a result by Freed, Hopkins and Teleman that relates the corresponding K-groups to the Verlinde ring of the associated loop group. From the point of view of homotopy theory only a small subgroup of all possible twists is considered in classical treatments of twisted K-theory. In this talk I will discuss an operator-algebraic model for equivariant higher (i.e. non-classical) twists over SU(n) induced by exponential functors on the category of vector spaces and isomorphisms. These twists are represented by Fell bundles and the C*-algebraic picture allows a full computation of the associated K-groups at least in low dimensions. I will also draw some parallels of our results with the FHT theorem. This is joint work with D. Evans.
Oct 7	Mon	Adel Betina, Evgeny Shinder
15:00		K3 surfaces, 2 (Hodge structures)
		Hicks Seminar Room J11
Oct 8	Tue	Dhruv Ranganathan (Cambridge)	Algebra / Algebraic Geometry seminar
12:00		A Mayer-Vietoris theorem for Gromov-Witten theory
		Hicks Seminar Room J11
	Abstract: The Gromov-Witten theory of a smooth variety X is a collection of invariants, extracted from the topology of the space of curves in X. I will explain how the Gromov-Witten theory of X can be computed algorithmically from the components of a simple normal crossings degeneration of X. The combinatorics of the geometry and complexity of the algorithm are both controlled by tropical geometry. The formula bears a strong resemblance to the Mayer-Vietoris sequence in elementary topology, and I will try to give some indication of how deep this analogy runs. Part of this story is still work in progress, joint with Davesh Maulik.
Oct 9	Wed	Xenia de la Ossa (University of Oxford)	Pure Maths Colloquium
14:00		Finding new geometric structures in string theory
		Hicks Seminar Room J11
	Abstract: The mathematical structure of quantum moduli spaces in string theory contains a wealth of information about the physical behaviour of the effective field theories. However, research in this area has also lead to very interesting new mathematical structures. In this seminar I will describe new geometrical structures appearing in the context of “heterotic strings” associated to gauge bundles on manifolds with certain special structures. We will see how to recast these geometric systems in terms of the existence of a nilpotent operator and describe the tangent space to the moduli space. I will talk about a number of open problems, in particular, the efforts to understand higher order deformations, the global structure of the full moduli space, and the expectation of new dualities similar to mirror symmetry.
Oct 9	Wed	Adam Moss (University of Nottingham)	Cosmology, Relativity and Gravitation
15:00		Accelerated Bayesian inference using deep learning
		Hicks Seminar Room J11
	Abstract: I introduce a novel Bayesian inference tool that uses a neural network to parameterise efficient Markov Chain Monte-Carlo (MCMC) proposals. The target distribution is first transformed into a diagonal, unit variance Gaussian by a series of non-linear, invertible, and non-volume preserving flows. Neural networks are extremely expressive, and can transform complex targets to a simple latent representation from which one can efficiently sample. Using this method, I develop a nested MCMC sampler, finding excellent performance on highly curved and multi-modal analytic likelihoods. I also demonstrate it on Planck 2015 data, showing accurate parameter constraints, and calculate the evidence for simple one-parameter extensions to LCDM in $\sim20$ dimensional parameter space.
Oct 10	Thu	Daniel Nóbrega-Siverio (Rosseland Centre for Solar Physics, University of Oslo)	SP2RC seminar
10:00		European Solar Physics Seminars: Nonequilibrium ionization and ambipolar diffusion in magnetic flux emergence processes
		Hicks Building E39
	Abstract: Magnetic flux emergence from the solar interior has been shown to be a key mechanism for unleashing a wide variety of ejective and eruptive phenomena. However, there are still open questions concerning the role of different physical processes, like nonequilibrium (NEQ) ionization/recombination and the electrodynamics of partially ionized gases, in the rise of the magnetized plasma. Our aim is to investigate, for the first time, the impact of the NEQ formation of atomic and molecular hydrogen as well as the ambipolar diffusion term of the generalized Ohm’s law on the flux emergence process. This is possible through 2.5D flux emergence numerical experiments using the Bifrost code. In this presentation, we will report the first results of this research, emphasizing on the importance of having NEQ ionization to properly compute the effects of the ambipolar diffusion.
Oct 10	Thu	Richard Glennie (St Andrews)	Statistics Seminar
14:00		Modelling latent processes in population abundance surveys using hidden Markov models
		K14
	Abstract: Distance sampling and spatial capture-recapture are statistical methods to estimate the number of animals in a wild population based on encounters between these animals and scientific detectors. Both methods estimate the probability an animal is detected during a survey, but do not explicitly model animal movement and behaviour. The primary challenge is that animal movement in these surveys is unobserved; one must average over all possible histories of each individual. In this talk, a general statistical model, with distance sampling and spatial capture-recapture as special cases, is presented that explicitly incorporates animal movement. An algorithm to integrate over all possible movement paths, based on quadrature and hidden Markov modelling, is given to overcome common computational obstacles. For distance sampling, simulation studies and case studies show that incorporating animal movement can reduce the bias in estimated abundance found in conventional models and expand application of distance sampling to surveys that violate the assumption of no animal movement. For spatial capture-recapture, continuous-time encounter records are used to make detailed inference on where animals spend their time during the survey. In surveys conducted in discrete occasions, maximum likelihood models that allow for mobile activity centres are presented to account for transience, dispersal, and heterogeneous space use. These methods provide an alternative when animal movement causes bias in standard methods and the opportunity to gain richer inference on how animals move, where they spend their time, and how they interact.
Oct 10	Thu	Daniel Graves (Sheffield)	Topology Seminar
16:00		Now that's what I call...homology theories for algebras
		Hicks Seminar Room J11
	Abstract: Homology theory for algebras was first introduced by Hochschild in the 40s to classify extensions of associative algebras. Since then a great many homology theories have been introduced to encode and detect desirable properties of algebras. I will describe a selection of these homology theories, discuss how they relate to one another and introduce some chain complexes for computing them.
Oct 10	Thu	Anwar Aldhafeeri (Sheffield)	Plasma Dynamics Group
16:00		Solar atmospheric magnetohydrodynamic wave modes in magnetic flux tubes of elliptical cross-sectional shape
		Room F28 (Hicks Building)
	Abstract: The approach to understanding and analysing the behaviour of MHD we observed in the solar atmosphere is to find a relevant wave solution for the MHD equations. Therefore many previous studies focused on deriving a dispersion relation equation and solving this equation for a cylindrical tube. We know perfectly well that sunspots and pores do not have an ideal circular cross-section. Therefore, any imbalance in waveguide’s diameters, even if very small, will move the study of the problem from the cylindrical coordinates to elliptical coordinates. Thus the emphasis on knowing the properties and what type of wave modes exist in elliptical waveguides are much more critical than studying them in cylindrical coordinates. In this talk, I will start by deriving the dispersion relation in a compressible flux tube with elliptical cross-sectional shape. I will then solve the dispersion equation and discuss the solution of dispersion equation and how the ellipticity of tube effects the solutions with applications to coronal and photospheric conditions. However, the information we get from the dispersion diagram does not give the full picture of how we can observe a wave, and how much the wave mode changes when the cross-sectional shape of waveguide changes. Therefore I will present some visualisations of eigenfunctions of MHD wave modes and explain how the eccentricity effects each MHD wave mode.
Oct 14	Mon	Jeremy Oakley (Sheffield)	Statistics Seminar
13:00		Deep Learning reading group: Chapter 6 from Goodfellow et al. (2016)
		LT 6
	Abstract: Discussion of Chapter 6 from "Deep Learning", by Goodfellow, Bengio and Courville https://www.deeplearningbook.org/
Oct 14	Mon	George Moulantzikos, Evgeny Shinder
15:00		K3 surfaces, 3 (more on Hodge structures and basic geometry of K3 surfaces)
		Hicks Seminar Room J11
Oct 15	Tue	Jenny August (Max Planck Institute for Mathematics in Bonn)	Algebra / Algebraic Geometry seminar
12:00		The Stability Manifold of a Contraction Algebra
		Hicks Seminar Room J11
	Abstract: For a finite dimensional algebra, Bridgeland stability conditions can be viewed as a continuous generalisation of tilting theory, providing a geometric way to study the derived category. Describing this stability manifold is often very challenging but in this talk, I’ll look at a special class of symmetric algebras whose tilting theory is determined by a related hyperplane arrangement. This simple picture will then allow us to describe the stability manifold of such an algebra.
Oct 15	Tue	Emma Gordon (Director of Administrative Data Research UK)	Statistics Seminar
16:00		Royal Statistical Society (RSS) Sheffield Local group seminar. The potential and pitfalls of linked administrative data
		LT B
	Abstract: Administrative databases that are linked with each other or with survey data can allow deeper insights into the population’s life trajectories and needs and signal opportunities for improved and ultimately more personalised service delivery. Yet government agencies have to meet several prerequisites to realise these benefits. First among them is a stable legal basis. Appropriate laws and regulations have to exist to allow data merging within the limits of existing privacy protection. When different institutions are involved, these regulations have to clearly define each agencies’ responsibilities in collecting, safeguarding and analysing data. Second are technical requirements. This includes creating a safe infrastructure for data storage and analysis and developing algorithms to match individuals when databases do not share common unique personal identifiers. Third is the buy-in of the population. Public communication can highlight the value-added of linked databases and outline the steps taken to ensure data security and privacy. Involving citizens in dialogues about what data uses they are and are not comfortable with can help build public trust that appropriate limits are set and respected.
Oct 16	Wed	Haluk Sengun (Sheffield)	Pure Maths Colloquium
14:00		A K-theoretic Selberg trace formula
		Hicks Seminar Room J11
	Abstract: The close relationship between index theory and representation theory is a classical theme. In particular, the trace formula has been studied through the lens of index theory by several researchers already. In joint work with Bram Mesland (Leiden) and Hang Wang (Shanghai), we take this connection further and obtain a formulation of the trace formula in K-theoretic terms. The central object here is the K-theory group of the C*-algebra associated to a locally compact group. This work is part of a program which explores the potential role that operator K-theory could play in the theory of automorphic forms.
Oct 16	Wed	Nathan Johnson-McDaniel (Cambridge)	Applied Mathematics Colloquium
14:00		Testing general relativity with gravitational wave observations: From numerical analysis to Bayesian statistics
		Hicks, LT 9
	Abstract: Gravitational waves carry information directly to us from some of the most violent events in the universe, such as the mergers of binaries of black holes or neutron stars. Observations of such gravitational wave signals allow us to extract considerable information about the binaries that generate them. In particular, we can test whether general relativity (GR) is still a good description of gravity in such extreme situations. I will give an overview of the mathematics and statistics used in the analysis of gravitational wave data, from the analytical and numerical methods used to solve the field equations of GR and obtain model waveforms, to the Bayesian methods used to compare the data to these models. As an illustration, I will describe the tests of general relativity carried out on the compact binary signals detected by Advanced LIGO and Advanced Virgo during their first two observing runs. These tests did not reveal any deviation from the predictions of GR and have allowed us to put the most stringent constraints to date on possible deviations from these predictions in the strong field, highly dynamical regime.
Oct 17	Thu	Pierrick Bousseau (ETH Zurich)	Algebra / Algebraic Geometry seminar
15:00		Quasimodular forms from Betti numbers
		Hicks Seminar Room J11
	Abstract: I will explain how to construct quasimodular forms starting from Betti numbers of moduli spaces of dimension 1 coherent sheaves on P2. This gives a proof of some stringy predictions about the refined topological string theory of local P2 in the Nekrasov-Shatashvili limit. Partly based on work in progress with Honglu Fan, Shuai Guo, and Longting Wu.
Oct 17	Thu	Alexander Schenkel (Nottingham)	Topology Seminar
16:00		Higher categorical structures in algebraic quantum field theory
		Hicks Seminar Room J11
	Abstract: Algebraic quantum field theory (AQFT) is a well-established framework to axiomatize and study quantum field theories on Lorentzian manifolds, i.e. spacetimes in the sense of Einstein’s theory of general relativity. In the first part of the talk, I will try to explain both the physical context and the mathematical formalism of AQFT in a way that is hopefully of interest to topologists. In the second part of the talk, I will give an overview of our recent works towards establishing a higher categorical framework for AQFT. This will include the construction of examples of such higher categorical theories from (linear approximations of) derived stacks and a discussion of their descent properties.
Oct 21	Mon	Raluca Eftimie (Dundee)	Mathematical Biology Seminar
14:00
		Hicks LT9
Oct 21	Mon
15:00		K3 surfaces, 4
		Hicks Seminar Room J11
Oct 22	Tue	Nick Sheridan (Edinburgh)	Algebra / Algebraic Geometry seminar
12:00		The Gamma and SYZ conjectures: a tropical approach to periods
		Hicks Seminar Room J11
	Abstract: I'll start by explaining a new method of computing asymptotics of period integrals using tropical geometry, via some concrete examples. Then I'll use this method to give a geometric explanation for a strange phenomenon in mirror symmetry, called the Gamma Conjecture, which says that mirror symmetry does not respect integral cycles: rather, the integral cycles on a complex manifold correspond to integral cycles on the mirror multiplied by a certain transcendental characteristic class called the Gamma class. We find that the appearance of zeta(k) in the asymptotics of period integrals arises from the codimension-k singular locus of the SYZ fibration.
Oct 22	Tue	Fionnlagh Mackenzie-Dover (SP2RC/Sheffield)
14:00		SWAT/SP2RC Paper Club - Selected topical paper
		I12
Oct 22	Tue	Thanasis Bouganis (Durham)	Number Theory seminar
14:00		Quaternionic modular forms and the Rankin-Selberg method
		Hicks Seminar Room J11
	Abstract: The properties (analytic, algebraic or p-adic) of special values of the standard L-function attached to Siegel and Hermitian modular forms are of central interest and have been extensively studied. In this talk, we will discuss another family of modular forms, which are associated to the isometry group of a quaternionic skew hermitian form. There are many similarities to the Siegel and Hermitian case but also important differences. We will present some results on the study of their standard L-function using the Rankin-Selberg method. This will lead us to discuss the existence of some theta series, a problem of which, in turn, is related to Howe duality and invariant theory.
Oct 23	Wed	Takashi Sakajo (Kyoto/INI Cambridge)	Applied Mathematics Colloquium
14:00		Topological Flow Data Analysis - Theory and Applications
		Hicks, LT 9
	Abstract: We have investigated a mathematical theory classifying the topological structures of streamline patterns for 2D incompressible (Hamiltonian) vector fields on surfaces such as a plane and a spherical surface, in which a unique combinatorial structure, called partially Cyclically Ordered rooted Tree (COT), associated with a symbolic expression (COT representation) is assigned to every streamline topology. With the COT representations, one can identify the topological streamline structures without ambiguity and predict the possible transition of streamline patterns with a mathematical rigor. In addition, we have recently developed a software converting the values of stream function on structured/non-structured grid points in the plane into the COT representation automatically. It enables us to conduct the classification of streamline topologies for a large amount of flow datasets and the snapshots of time-series of flow evolutions obtained by measurements and numerical simulations, which we call Topological Flow Data Analysis (TFDA). The combinatorial classification theory of flow topologies is now extended to the flow of finite type, which contains Morse-Smale vector fields, compressible flows and 2D slices of 3D vector fields. I will present an overview of basic theory and its applications to atmospheric data and engineering problem.
Oct 23	Wed	Joseph Martin (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		An Introduction to the Periodic Table of n-Categories
		Hicks Seminar Room J11
	Abstract: The aim is to provide much of what is needed to understand the relationship between low-dimensional degenerate n-categories and their counterparts in the Periodic Table of n-categories. We first seek to establish a good understanding of equivalences between categories via a thorough study of adjunctions. Then we give an overview of the structures that can be found in the Periodic Table along with a useful result in each case. Finally, this is followed by an inspection of degenerate categories and bicategories, in particular we compare their totalities to that of monoids.
Oct 24	Thu	Petros Syntelis (Solar and Magnetospheric Theory Group, University of St Andrews)	SP2RC seminar
10:00		ESPOS: Eruptions and flaring activity in emerging quadrupolar regions
		E39
	Abstract: Some of the most dynamic solar phenomena occur in complex magnetic configurations such as quadrupolar regions. To study eruptivity in quadrupolar regions, we perform 3D magnetohydrodynamic simulations of the partial emergence of two segments of a flux tube from the solar interior into a non-magnetized, stratified atmosphere. The emergence leads to the formation of two initially separated bipoles, which later come in contact, forming a strong polarity inversion line. Above the two bipoles, two magnetic lobes expand and interact through a series of current sheets at the interface between them. Two recurrent confined eruptions are produced. In both cases, the reconnection between sheared, low-lying field lines forms a flux rope. The confined eruptions result from the interaction between the two magnetic lobes at different heights in the solar atmosphere. These interactions create field lines that assist the eruption of the flux ropes, and also create other field lines that inhibit the eruptions. The flux rope of the first, weaker, eruption almost fully reconnects with the overlying field. The flux rope of the second, more energetic, eruption is confined by the overlying strapping field. During the second eruption, the flux rope is enhanced in size, flux, and twist, similar to confined-flare-to-flux-rope observations. Proxies of the emission reveal the two erupting filaments channels. A flare arcade is only formed in the second eruption owing to the longer lasting and more efficient reconnection at the current sheet below the flux rope.
Oct 24	Thu	Frazer Jarvis (Sheffield)	Teaching Lunch
13:00		Bloom's Taxonomy, or How to Get New Modules Approved by APSE
		K14
	Abstract: New module approval forms have a strong recommendation that proposers should refer to 'Bloom's Taxonomy' when preparing their submissions. In this talk, we will discuss what this is, its history, and what it means in practice.
Oct 24	Thu	Lyudmila Mihaylova (Sheffield)	Statistics Seminar
14:00		Nonparametric Methods and Models with Uncertainty Propagation
		LT E
	Abstract: We are experiencing an enormous growth and expansion of data provided by multiple sensors. The current monitoring and control systems face challenges both in processing big data and making decisions on the phenomena of interest at the same time. Urban systems are hugely affected. Hence, intelligent transport and surveillance systems need efficient methods for data fusion, tracking and prediction of individual vehicular traffic and aggregated flows. This talk will focus on two main methods able to solve such monitoring problems, by fusing multiple types of data while dealing with nonlinear phenomena – sequential Markov Chain Monte Carlo (SMCMC) methods with adaptive subsampling and Gaussian Process regression methods. The first part of this talk will present a SMCMC approach able to deal with massive data based on adaptively subsampling the sensor measurements. The main idea of the method to approximate the logarithm of the likelihood ratio by performing a trade-off between complexity and accuracy. The approach efficiency will be demonstrated on object tracking tasks. Next, Gaussian Process methods will be presented – for point and extended object tracking, i.e. both in space and in time. Using the derivatives of the Gaussian Process leads to an efficient replacement of multiple models that usually are necessary to represent the whole range of behaviour of a dynamic system. These methods give the opportunity to assess the impact of uncertainties, e.g. from the sensor data on the developed solutions.
Oct 24	Thu	Richard Hepworth (Aberdeen)	Topology Seminar
16:00		Homological Stability: Coxeter, Artin, Iawahori-Hecke
		Hicks Seminar Room J11
	Abstract: Homological stability is a topological property that is satisfied by many families of groups, including the symmetric groups, braid groups, general linear groups, mapping class groups and more; it has been studied since the 1950's, with a lot of current activity and new techniques. In this talk I will explain a set of homological stability results from the past few years, on Coxeter groups, Artin groups, and Iwahori-Hecke algebras (some due to myself and others due to Rachael Boyd). I won't assume any knowledge of these things in advance, and I will try to introduce and motivate it all gently!
Oct 24	Thu	Yuyang Yuan (Sheffield)	Plasma Dynamics Group
16:00		The Solar Spicule Tracking Code (SSTC)
		Room F28 (Hicks Building)
	Abstract: In this talk I will explain and demonstrate the Solar Spicule Tracking Code (SSTC) that I have developed. This code has the ability to automatically detect and track the motion spicules in imaging data. I will specifically demonstrate the code working with images obtained using the H alpha line from the CRisp Imaging SpectroPolarimeter (CRISP) based at the Swedish Solar Telescope.
Oct 28	Mon	Jeremy Oakley (Sheffield)	Statistics Seminar
13:00		Deep Learning reading group: 6.5-7.2 from Goodfellow et al. (2016)
		LT 6
Oct 28	Mon
15:00		K3 surfaces, 5
		Hicks Seminar Room J11
Oct 29	Tue	Noah Arbesfeld (Imperial College London)	Algebra / Algebraic Geometry seminar
12:00		K-theoretic Donaldson-Thomas theory and the Hilbert scheme of points on a surface
		Hicks Seminar Room J11
	Abstract: Tautological bundles on Hilbert schemes of points often enter into enumerative and physical computations. I'll explain how to use the Donaldson-Thomas theory of threefolds to produce certain combinatorial identities involving Young diagrams. The resulting identities can be expressed geometrically in terms of tautological bundles over the Hilbert scheme of points on the plane. I'll also explain how these identities can be used to study Euler characteristics of tautological bundles over Hilbert schemes of points on general surfaces.
Oct 29	Tue	Robertus (Sheffield)
13:00		SWAT/SP2RC Paper Club: Solar jets
		Hicks, G07
Oct 30	Wed	Natasha Morrison (University of Cambridge)	Pure Maths Colloquium
14:00		The typical structure of sets with small sumset
		Hicks Seminar Room J11
	Abstract: One of the central objects of interest in additive combinatorics is the sumset $A + B := \{ a+b : a \in A, \, b \in B \}$ of two sets $A,B \subset \mathbb{Z}$. Our main theorem, which improves results of Green and Morris, and of Mazur, implies that the following holds for every fixed $\lambda > 2$ and every $k \ge (\log n)^4$: if $\omega \to \infty$ as $n \to \infty$ (arbitrarily slowly), then almost all sets $A \subset [n]$ with $|A| = k$ and $|A + A| \le \lambda k$ are contained in an arithmetic progression of length $\lambda k/2 + \omega$. This is joint work with Marcelo Campos, Mauricio Collares, Rob Morris and Victor Souza.
Oct 30	Wed	Xin Huang (NAOC Beijing)	Applied Mathematics Colloquium
14:00		Solar flare forecasting models from the perspective of machine learning: past, present and future
		Hicks, LT 9
	Abstract: Solar flares are intense flashes of radiation emanating from the Sun. A strong solar flare and it’s related eruptive events can interfere with high frequency radio communication, satellite operation, navigation equipment and so on. Furthermore, effects of solar flares could reach the earth within approximately 8 minutes. Therefore, solar flare forecast has caused long-term concern in the field of space weather. Solar flares originate from the release of the energy stored in the magnetic field of solar active regions, the triggering mechanism for these flares, however, remains unknown. Hence the statistical and machine learning methods are used to build the solar flare forecasting model. From the perspective of machine learning, we review the solar flare forecasting models and try to discuss the possible directions to build more powerful solar flare forecasting models.
Oct 30	Wed	Thomas Stratton (University of Sheffield)	Cosmology, Relativity and Gravitation
15:00		Scattering of gravitational waves by a neutron star
		Hicks Seminar Room J11
	Abstract: Since the direct detection of gravitational waves in 2015, a new window on the physical Universe has begun to open. A region of spacetime with large enough curvature, such as a black hole or neutron star, may scatter a freely propagating gravitational wave. I will consider scattering of gravitational waves by a compact star modelled with a polytropic equation of state. Within the framework of perturbation theory, I calculate the differential scattering cross section and discuss the interference effects present, namely rainbow and glory scattering. I will show how the star’s properties, such as the equation of state, imprint themselves on the cross section, and compare our results with black hole scattering.
	Slides
Oct 30	Wed	Maram Alossaimi, Lewis Combes, & Yirui Xiong (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		Poisson Algebra (Maram Alossaimi) An Introduction to the Theory of Elliptic Curve Cryptography (Lewis Combes) Calabi-Yau algebras and superpotentials (Yirui Xiong)
		Hicks Seminar Room J11
	Abstract: Poisson Algebra The concept of a Poisson algebra comes from defining a bilinear product {·, ·} on a commuta- tive algebra over a field K to bring a new non-commutative algebra structure. I will give some definitions, examples and the main Lemma in our research. In the end, if there is enough time I will introduce our new Poisson algebra structure. An Introduction to the Theory of Elliptic Curve Cryptography An elliptic curve over a finite field can be endowed with the structure of an abelian group. Within this group there are computations that are easy to perform, but hard to reverse. These computations form the basis of elliptic curve cryptography, an encryption standard with advantages and disadvantages when compared to traditional RSA methods. The downsides are such that an intimate understanding of certain mathematical properties of the chosen elliptic curve is needed to keep the protocol secure. In this talk I will go through the theory behind using elliptic curves for encryption, as well as some of the mathematical considerations that should be made when designing such a system. Calabi-Yau algebras and superpotentials Calabi-Yau algebras arise from transporting the conception of Calabi-Yau manifolds to noncommutative geometry, and now have profound applications in algebraic geometry and representation theory. One of the central problems in the study of Calabi-Yau algebras is their structural problem: can Calabi-Yau algebras be derived from superpotentials? We will review the answers to the problem based on work in the past years. And if time is permitted, I will introduce some applications based on structural theorems of Calabi-Yau algebras.
Oct 31	Thu	Tom Hutchcroft (Cambridge)	Statistics Seminar
14:00		Phase transitions in hyperbolic spaces
		LT E
	Abstract: Many questions in probability theory concern the way the geometry of a space influences the behaviour of random processes on that space, and in particular how the geometry of a space is affected by random perturbations. One of the simplest models of such a random perturbation is percolation, in which the edges of a graph are either deleted or retained independently at random with retention probability p. We are particularly interested in phase transitions, in which the geometry of the percolated subgraph undergoes a qualitative change as p is varied through some special value. Although percolation has traditionally been studied primarily in the context of Euclidean lattices, the behaviour of percolation in more exotic settings has recently attracted a great deal of attention. In this talk, I will discuss conjectures and results concerning percolation on the Cayley graphs of nonamenable groups and hyperbolic spaces, and give the main ideas behind our recent result that percolation in any transitive hyperbolic graph has a non-trivial phase in which there are infinitely many infinite clusters. The talk is intended to be accessible to a broad audience.
Oct 31	Thu	Ai Guan (Lancaster)	Topology Seminar
16:00		A model structure of second kind on differential graded modules
		Hicks Seminar Room J11
	Abstract: Koszul duality is a phenomenon appearing in many areas of mathematics, such as rational homotopy theory and deformation theory. For differential graded (dg) algebras, the modern formulation of Koszul duality says there is a Quillen equivalence between model categories of augmented dg algebras and conilpotent dg coalgebras, and also Quillen equivalences between corresponding dg modules/comodules. I will give an overview of this circle of ideas, and then consider what happens when the conilpotence condition is removed. The answer to this question leads to an exotic model structure on dg modules that is "of second kind", i.e. weak equivalences are finer than quasi-isomorphisms. This is based on joint work with Andrey Lazarev from the recent preprint https://arxiv.org/abs/1909.11399.
Nov 4	Mon	Adriana Dawes (Ohio State)	Mathematical Biology Seminar
14:00
		Hicks LT9
Nov 4	Mon
15:00		K3 surfaces, 6
		Hicks Seminar Room J11
Nov 5	Tue	Ben Davison (Edinburgh)	Algebra / Algebraic Geometry seminar
12:00		Strong positivity for quantum cluster algebras
		Hicks Seminar Room J11
	Abstract: I will discuss the positivity for quantum theta functions, a result of joint work with Travis Mandel: For a given skew-symmetric quantum cluster algebra, these functions provide a basis of a larger algebra, for which the structure constants are Laurent polynomials with positive coefficients. I will explain how the proof of this result follows from scattering diagram techniques and a very special case of the cohomological integrality theorem, joint work with Sven Meinhardt.
Nov 5	Tue	Chris Nelson (QUB)
14:00		SWAT/SP2RC Paper Club - Selected topical paper
		I12
Nov 5	Tue	Robert Kurinczuk (Imperial)	Number Theory seminar
14:00		Local Langlands in families
		Hicks Seminar Room J11
	Abstract: For general linear groups over a p-adic field, local Langlands in families (established recently by Helm-Moss) provides a description of the integral Bernstein centre in terms of rings of functions on moduli spaces of Galois representations. I will describe a conjectural generalization of this picture to all split reductive p-adic groups and, time permitting, I will discuss recent progress towards proving this conjecture. This is joint work with Jean-François Dat, David Helm, and Gil Moss.
Nov 6	Wed	Ana Khukhro (University of Cambridge)	Pure Maths Colloquium
14:00		Expander graphs and where to find them
		Hicks Seminar Room J11
	Abstract: Expander graphs are somewhat contradictory geometric objects that have many applications, even outside of pure mathematics. We will see how they can be constructed with the help of geometric group theory, and how one can use some coarse-geometric variants of notions from topology to explore the world of resulting constructions.
Nov 6	Wed	Nobert Magyar (Warwick)	Applied Mathematics Colloquium
14:00		Waves and turbulence in the solar corona and solar wind
		Hicks, LT 9
	Abstract: The solar corona and solar wind are still enigmatic from a physical standpoint. The coronal heating problem and the solar wind acceleration are one of the most important unsolved probems in astrophysics. Waves, which are omnipresent in the inner heliosphere, are strong candidates that might solve these conundrums. Just to make it even more difficult, the presence of waves might lead to the generation of turbulence, which is an unsolved problem on its own right. In this talk, we will explore what we know (and what we don't), first observationally and then by theory, about waves and turbulence in the extended solar corona. We will present the current magnetohydrodynamical (MHD) understading of turbulence generation in a plasma, which will be supplemented by my recent findings in the field.
Nov 6	Wed	Lasse Schmieding (University of York)	Cosmology, Relativity and Gravitation
15:00		Scalar Fields in two dimensional de Sitter Space
		Hicks Seminar Room J11
	Abstract: Unlike higher dimensional de Sitter spaces, two dimensional de Sitter space is not simply connected. The behaviour of the fields on making a full rotation of the spatial direction must therefore be specified. Previously, Epstein and Moschella have shown that anti-periodic real scalar fields have no analogue of a Bunch-Davies vacuum state. For complex scalar fields, more general behaviour is possible. I will discuss complex scalar field theories in two dimensional de Sitter space and then comment on the existence of de Sitter invariant and Hadamard states for these theories. Along the way, I will review aspects of the representation theory of SL(2,R), the symmetry group relevant for two dimensional (anti-)de Sitter space.
Nov 6	Wed	Eve Pound (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		The Structure of Chevalley Groups over Local Fields.
		Hicks Seminar Room J11
	Abstract: The Chevalley group is a subgroup of the automorphism group of a Lie algebra. In 1965, Iwahori and Matsumoto showed that, when the underlying field admits a nonarchimedean discrete valuation (for example, over Qp), these groups admit a double coset decomposition, or Bruhat decomposition. This decomposition allows lots of information about the group to be read off, and is intricately linked with the associated Bruhat-Tits building. In this talk, I'll start with the definition of a Lie algebra and try to motivate why we care about the Chevalley group, and give an overview of the geometric and combinatorial ideas in Iwahori and Matsumoto's work. If there is time, I will give some examples of how this links to buildings.
Nov 7	Thu	Anwar Ali Aldhafeeri (Plasma Dynamics Group, University of Sheffield)	SP2RC seminar
10:00		ESPOS: MHD wave modes in the solar magnetic flux tubes with elliptical cross-section
		E39
	Abstract: Many previous studies of MHD modes in the magnetic flux tubes were focussed on deriving a dispersion relation for cylindrical waveguides. However, from observations it is well known that, for example, the cross-sectional shape of sunspots and pores are not perfect circles and can often be much better approximated by ellipses. From a theoretical point of view, any imbalance in a waveguide’s diameters, even if very small, will move the study of the problem from cylindrical to elliptical coordinates. In this talk, I will therefore describe a model that predicts the MHD wave modes that can be trapped and propagate in a compressible magnetic flux tube with an elliptical cross-section embedded in a magnetic environment. I will discuss the resultant dispersion relations for body and surface modes, then then I will show how the ellipticity of a magnetic flux tube effects these solutions (with specific applications to the coronal and photospheric conditions). From a practical point of view the information from these dispersion diagrams does not show how these MHD modes will manifest themselves in observational data. Therefore, I will also present several visualisations of the eigenfunctions of these MHD wave modes and explain how the eccentricity effects each wave mode.
Nov 7	Thu	Deborah Ashby (Imperial College London, President Royal Statistical Society)	Statistics Seminar
14:15		Royal Statistical Society (RSS) Sheffield Local group seminar. Pigeon-holes and mustard seeds: Growing capacity to use data for society
		Hicks Seminar Room J11
	Abstract: The Royal Statistical Society was founded to address social problems ‘through the collection and classification of facts’, leading to many developments in the collection of data, the development of methods for analysing them, and the development of statistics as a profession. Nearly 200 years later an explosion in computational power has led, in turn, to an explosion in data. We outline the challenges and the actions needed to exploit that data for the public good, and to address the step change in statistical skills and capacity development necessary to enable our vision of a world where data are at the heart of understanding and decision-making.
Nov 7	Thu	Emanuele Dotto (Warwick)	Topology Seminar
16:00		The Witt vectors with coefficients
		Hicks Seminar Room J11
	Abstract: We will introduce the Witt vectors of a ring with coefficients in a bimodule and use them to calculate the components of the Hill-Hopkins-Ravenel norm for cyclic p-groups. This algebraic construction generalizes Hesselholt's Witt vectors for non-commutative rings and Kaledin's polynomial Witt vectors over perfect fields. We will discuss applications to the characteristic polynomial over non-commutative rings and to the Dieudonné determinant. This is all joint work with Krause, Nikolaus and Patchkoria.
Nov 7	Thu	Norbert Magyar (University of Warwick)	Plasma Dynamics Group
16:00		Simulations of MHD waves in structured plasmas
		Room F28 (Hicks Building)
	Abstract: It is well known that in an infinite and homogeneous plasma, there are three types of waves: fast, slow, and Alfvén. However, richer dynamics appear in MHD once inhomogeneities are considered. The solar corona and solar wind is often seen to be highly structured, most probably even way below the current resolving capabilities of imaging instruments. The structuring of the plasma gives rise to some well-known phenomena such as surface and body modes, reflection/refraction of waves, phase mixing, resonant absorption and so on. The nonlinear implications of structuring are less well-known, though. In a series of numerical simulations, we will review the basic dynamics of waves supported by structures, and will connect these findings to the generation of turbulence in a structured plasma.
Nov 11	Mon	CANCELLED	Statistics Seminar
13:00		Deep Learning reading group
		LT 6
Nov 11	Mon	Nebojsa Pavic (Sheffield)
15:00		K3 surfaces, 7
		Hicks Seminar Room J11
Nov 13	Wed	Tom Morley (SoMaS)	Applied Mathematics Colloquium
14:00		A quantum tour of anti-de Sitter spacetime
		Hicks, LT 9
	Abstract: In General Relativity, the rate of expansion of the universe is governed by the cosmological constant. We know, from observations, that our universe is expanding at an accelerated rate, so the cosmological constant is usually taken to be positive. What happens if we choose the cosmological constant to be negative instead? Then we find ourselves in the weird and wonderful anti-de Sitter universe, a universe with a timelike boundary and closed timelike curves. And if we try to define a quantum field theory in this spacetime, we find some very surprising results indeed. In this talk, I will show how the vacuum polarisation, a divergent quantity associated with the local temperature of a quantum field, is affected by varying conditions imposed on the adS boundary.
Nov 14	Thu	Greg Stevenson (Glasgow)	Topology Seminar
16:00		An introduction to derived singularities
		LT7
	Abstract: The aim of this talk is to give an introduction to what it might mean for a differential graded algebra (or ring spectrum) to be singular, in a sense analogous to the situation in algebraic geometry. As in geometry one can distinguish between smoothness and regularity, and I'll discuss both concepts and their relationship. The failure of the latter, i.e. the presence of singularities, can in good situations be described by a corresponding singularity category and time permitting I'll sketch how this category can be defined as in joint work with John Greenlees.
Nov 18	Mon	Rastko Skepnek (Dundee)	Mathematical Biology Seminar
14:00
		Hicks LT9
Nov 18	Mon	Anna Barbieri
15:00		K3 surfaces, 8
		Hicks Seminar Room J11
Nov 19	Tue	Cathy Hsu (Bristol)	Number Theory seminar
14:00		Eisenstein congruences and an explicit non-Gorenstein R=T
		Hicks Seminar Room J11
	Abstract: In his seminal work on modular curves and the Eisenstein ideal, Mazur studied the existence of congruences between certain Eisenstein series and newforms, proving that Eisenstein ideals associated to weight 2 cusp forms of prime level are locally principal. In this talk, we begin by discussing several generalizations of Mazur's results to squarefree levels, focusing primarily on the non-principality of the Eisenstein ideal in the anemic Hecke algebra associated to elliptic modular forms of weight 2 and trivial Nebentypus. We then discuss some work in progress, joint with Preston Wake and Carl Wang-Erickson, that establishes an algebraic criterion for having R=T in a certain non-Gorenstein setting.
Nov 19	Tue	Jiawen Zhang (Southampton)	Noncommutative Geometry Seminar
14:00		Quasi-locality and asymptotic expanders
		I12
	Abstract: Roe algebras are C*-algebras associated to metric spaces, which encode their large scale structure. These algebras play a key role in higher index theory, bridging geometry, topology and analysis together. Recently we provide a new quasi-local perspective on Roe algebras, provided the underlying spaces have Yu’s Property A. In the special case of a sequence of finite graphs, we study the quasi-locality of the averaging projection and introduce the notion of asymptotic expanders. Furthermore, we provide a structure theorem showing that asymptotic expanders can be ‘exhausted’ by classic expanders. Consequently, we show that asymptotic expanders cannot be coarsely embedded into any Hilbert space, and being asymptotic expanders can be detected via the Roe algebras. This is a joint project with Ana Khukhro, Kang Li, Piotr Nowak, Jan Spakula and Federico Vigolo.
Nov 20	Wed	Jan Spakula (University of Southampton)	Pure Maths Colloquium
14:00		Quasi-locality and Property A
		Hicks Seminar Room J11
	Abstract: Let X be a countable discrete metric space, and think of operators on $\ell^2(X)$ in terms of their X-by-X matrix. Band operators are ones whose matrix is supported on a "band" along the main diagonal; all norm-limits of these form a C*-algebra, called uniform Roe algebra of X. This algebra "encodes" the large-scale (a.k.a. coarse) structure of X. Quasi-locality, coined by John Roe in '88, is a property of an operator on $\ell^2(X)$, designed as a condition to check whether the operator belongs to the uniform Roe algebra (without producing band operators nearby). The talk is about our attempt to make this work. (Joint with A Tikuisis and J Zhang.) In the talk, I will introduce basics of coarse geometry, Property A and Roe algebras. Then I will move on to quasi-locality and (hopefully) the main ingredients of our argument: If X has Property A, then any quasi-local operator actually belongs to the Roe algebra.
Nov 20	Wed	Dongho Chae (Chun-Ang)	Applied Mathematics Colloquium
14:00		Liouville type theorems in the stationary Navier-Stokes and related equations
		Hicks, LT 9
	Abstract: We consider the stationary Navier-Stokes equations in $ \Bbb R^{3}$ \begin{align} -\Delta u + (u \cdot \nabla) u = - \nabla p ,\quad \qquad\qquad \nabla \cdot u=0. \hspace{1cm}(1) \end{align} The standard boundary condition to impose at the spatial infinity is \begin{equation} u(x)\to 0 \quad \text{as} \quad |x|\to 0 . \hspace{4.5cm} (2) \end{equation} We also assume finiteness of the Dirichlet integral, \begin{equation} \int_{\Bbb R^3} |\nabla u|^2 dx <+\infty. \hspace{5cm} (3) \end{equation} Obviously $(u,p)$ with $u=0$ and $p=$constant is a trivial solution to (1)-(3). A very challenging open question is if there is another nontrivial solution. This Liouville type problem is wide open, and has been actively studied recently in the community of mathematical fluid mechanics. The explicit statement of the problem is written in Galdi's book [1][Remark X. 9.4, pp. 729], where under the stronger assumption $u\in L^{\frac{9}{2}} (\Bbb R^3)$ he concludes $u=0$. After that many authors deduce sufficient conditions stronger than (2) and/or (3) to obtain the Liouville type result. In this talk we review various previous results and present recent progresses in getting sufficient condition in terms of the potential functions of the velocity. We also show that similar method can applied to prove Liouville type theorems for the other related equations such as the magnetohydrodynamic equations(MHD), Hall-MHD and the non-Newtonian fluid equations. G. P. Galdi,: An introduction to the mathematical theory of the Navier- Stokes equations: Steady-State Problems, Springer, 2011. G. Seregin, Liouville type theorem for stationary Navier-Stokes equations, Nonlinearity, 29, (2016), pp. 2191-2195. D. Chae, Note on the Liouville type problem for the stationary Navier-Stokes equations in $\Bbb R^3$, J. Diff. Eqns, (in press) D. Chae and J. Wolf, On Liouville type theorem for the stationary Navier-Stokes equations, Calculus of Variations and PDEs, 58, (2019), no.3, 58:111. D. Chae and J. Wolf, On Liouville type theorems for the steady Navier-Stokes equations in $\Bbb R^3$, J. Diff. Eqns., 261, (2016), 5541-5560 D. Chae, Liouville-type theorems for the forced Euler equations and the Navier-Stokes equations, Comm. Math. Phys., 326, (2014), pp. 37-48.
Nov 20	Wed	Cesare Giulio Ardito (Manchester)	ShEAF: postgraduate pure maths seminar
16:00		Classifying 2-blocks with an elementary abelian defect group
		Hicks Seminar Room J11
	Abstract: Donovan’s conjecture predicts that given a $p$-group $D$ there are only finitely many Morita equivalence classes of blocks of group algebras with defect group $D$. While the conjecture is still open for a generic $p$-group $D$, it has been proven in 2014 by Eaton, Kessar, Külshammer and Sambale when $D$ is an elementary abelian 2-group, and in 2018 by Eaton and Livesey when $D$ is any abelian 2-group. The proof, however, does not describe these equivalence classes explicitly. A classification up to Morita equivalence over a complete discrete valuation ring $\mathcal{O}$ has been achieved for $D$ with rank 3 or less, and for $D = (C_2)^4$. I have done $(C_2)^5$, and I have partial results on $(C_2)^6$. I will introduce the topic, give the relevant definitions and then describe the process of classifying this blocks, with a particular focus on the methodology and the individual tools needed to achieve a complete classification.
Nov 21	Thu	Dr Julius Koza (Astronomical Institute, Slovak Academy of Sciences)	SP2RC seminar
10:00		ESPOS: Spectral diagnostics of cool flare loops observed by SST
		LT 9
	Abstract: Flare loops form an integral part of eruptive events, being detected in the range of temperatures from X-rays down to cool chromospheric-like plasmas. While the hot loops are routinely observed by the Solar Dynamics Observatory’s Atmospheric Imaging Assembly, cool loops seen off-limb are rare. In this paper we employ unique observations of the SOL2017-09-10T16:06 X8.2-class flare which produced an extended arcade of loops. The Swedish 1 m Solar Telescope made a series of spectral images of the cool off-limb loops in the Ca II 8542 Å and the hydrogen H-beta lines. Our focus is on the loop apices. Non-LTE spectral inversion (non-LTE; i.e., departures from LTE) is achieved through the construction of extended grids of models covering a realistic range of plasma parameters. The Multilevel Accelerated Lambda Iterations (MALI) code solves the non-LTE radiative-transfer problem in a 1D externally illuminated slab, approximating the studied loop segment. Inversion of the Ca II 8542 Å and H-beta lines yields two similar solutions, both indicating high electron densities around 2x10^12 cm^(-3) and relatively large microturbulence around 25 km/s. These are in reasonable agreement with other independent studies of the same or similar events. In particular, the high electron densities in the range 10^12 - 10^13 cm^(-3) are consistent with those derived from the Solar Dynamics Observatory’s Helioseismic and Magnetic Imager white-light observations and they are also required to explain SST/CHROMIS continuum observations in the wide-band channel centered at 4845.5 Å.
Nov 21	Thu	Soheyla Feyzbakhsh (Imperial College London)	Algebra / Algebraic Geometry seminar
12:00		Stability conditions on the derived category of coherent systems and Brill-Noether theory
		Hicks Seminar Room J11
	Abstract: A classical method to study Brill-Noether locus of higher rank semistable vector bundles on curves is to examine the stability of coherent systems. To have an abelian category we enlarge the category of coherent systems by the category $A(C)$ which consists of triples $(E_1, E_2, f)$ where $E_1$ is a direct sum of the structure sheaf of $C, E_2$ is a coherent sheaf on $C$, and $f$ is a sheaf morphism from $E_1$ to $E_2$. In this talk after a short description of the derived category of $A(C)$, I will describe a 2-dimensional slice of the space of Bridgeland stability conditions on this category and sketch some of the possible applications of wall-crossing in Brill-Noether theory.
Nov 21	Thu	Leo Bastos (LSHTM)	Statistics Seminar
14:00		Modelling reporting delays for disease surveillance data
		LT E
	Abstract: One difficulty for real-time tracking of epidemics is related to reporting delay. The reporting delay may be due to laboratory confirmation, logistic problems, infrastructure difficulties and so on. The ability to correct the available information as quickly as possible is crucial, in terms of decision making such as issuing warnings to the public and local authorities. A Bayesian hierarchical modelling approach is proposed as a flexible way of correcting the reporting delays and to quantify the associated uncertainty. Implementation of the model is fast, due to the use of the integrated nested Laplace approximation (INLA). The approach is illustrated on dengue fever incidence data in Rio de Janeiro, and Severe Acute Respiratory Illness (SARI) data in Paraná state, Brazil.
Nov 21	Thu	Abigail Linton (Southampton)	Topology Seminar
16:00		Non-trivial Massey products in moment-angle complexes
		Hicks Seminar Room J11
	Abstract: A moment-angle complex $\mathcal{Z}_\mathcal{K}$ is obtained by associating a product of discs and circles to each simplex in a simplicial complex $\mathcal{K}$ and gluing these products according to how the corresponding simplices intersect. These spaces can have a complicated topological structure. For example, Baskakov (2003) found examples of non-trivial Massey products in the cohomology of moment-angle complexes. I will give a complete combinatorial classification of lowest-degree non-trivial triple Massey products in the cohomology of moment-angle complexes and describe constructions of simplicial complexes that give non-trivial higher Massey products on classes of any degree.
Nov 21	Thu	Farhad Allian (Plasma Dynamics Group, University of Sheffield)	Plasma Dynamics Group
16:00		A New Analysis Procedure for Detecting Periodicities within Complex Solar Coronal Arcades
		Room F28 (Hicks Building)
	Abstract: Coronal loop arcades form the building blocks of the hot and dynamic solar atmosphere. In particular, their oscillations serve as an indispensable tool in estimating the physical properties of the local environment by means of seismology. However, due to the nature of the arcade's complexity, these oscillations can be difficult to analyze. In this talk, I will present a novel image-analysis procedure based on the spatio-temporal autocorrelation function that can be utilized to reveal 'hidden' periodicities within EUV imagery of complex coronal loop systems.
Nov 22	Fri	Barbara Bolognese (Sheffield)
13:30		K3 surfaces, 9
		Hicks Seminar Room J11
Nov 22	Fri	Eleonora Di Valentino (University of Manchester)	Cosmology, Relativity and Gravitation
14:00		Cosmology in tension
		LT9, Hicks
	Abstract: The Cosmic Microwave Background (CMB) temperature and polarization anisotropy measurements from the Planck mission have provided a strong confirmation of the LCDM model of structure formation. However, there are a few interesting tensions with other cosmological probes and anomalies in the data that leave the door open to possible extensions to LCDM. The most famous ones are the Hubble constant and the S8 parameter tensions, the Alens anomaly and a curvature of the Universe. I will review all of them, showing some interesting extended cosmological scenarios, in order to find a new concordance model that could explain the current cosmological data.
Nov 28	Thu	Fionnlagh Mackenzie-Dover (SP2RC/Sheffield)
14:00		SWAT/SP2RC Paper Club - Selected topical paper
		LT10
Nov 28	Thu	POSTPONED: Marcel Ortgiese (Bath)	Statistics Seminar
14:00
		LT E
Dec 2	Mon	Katrina Lythgoe (Oxford)	Mathematical Biology Seminar
14:00
		Hicks LT9
Dec 3	Tue	Dimitri Wyss (École Polytechnique Fédérale de Lausanne)	Algebra / Algebraic Geometry seminar
12:00		Non-archimedean and motivic integrals on the Hitchin fibration
		Hicks Seminar Room J11
	Abstract: Based on mirror symmetry considerations, Hausel and Thaddeus conjectured an equality between 'stringy' Hodge numbers for moduli spaces of $SL_n$/$PGL_n$ Higgs bundles. With Michael Groechenig and Paul Ziegler we prove this conjecture using non-archimedean integrals on these moduli spaces, building on work of Denef-Loeser and Batyrev. This approach reduces their conjecture essentially to the duality between generic Hitchin fibers. Similar ideas also lead to a new proof of the geometric stabilization theorem for anisotropic Hitchin fibers, a key ingredient in the proof of the fundamental lemma by Ngô. In my talk I will outline the main arguments of the proofs and discuss the adjustments needed, in order to replace non-archimedean integrals by motivic ones. The latter is joint work with François Loeser.
Dec 4	Wed	1. Farhad Allian / 2. Hope Thackray (SoMaS)	Applied Mathematics Colloquium
14:00		1. A New Analysis Procedure for Detecting Periodicities within Complex Solar Coronal Arcades 2. Fast Magnetohydrodynamic Modes of a Semi-cylindrical Waveguide
		Hicks, LT 9
	Abstract: 1. Coronal loop arcades form the building blocks of the hot and dynamic solar atmosphere. In particular, their oscillations serve as an indispensable tool in estimating the physical properties of the local environment by means of seismology. However, due to the nature of the arcade's complexity, these oscillations can be difficult to analyze. In this talk, I will present a novel image-analysis procedure based on the spatio-temporal autocorrelation function that can be utilized to reveal 'hidden' periodicities within EUV imagery of complex coronal loop systems. 2. Coronal loop models have often been used as a diagnostic tool for plasma properties in the Sun's corona. In particular, the oscillations triggered by nearby eruptive events may be modelled with a 3D semi-cylindrical waveguide. We investigate the resulting eigenfunctions for a “two-shell” (and later “three-shell”) density profile model that introduces sharp density contrast. We find that waves are elliptically polarised, but the eigenmodes can differ significantly when considering small changes to density profile. Such behaviour necessitates careful choice of density structure for understanding observational data.
Dec 4	Wed	Natalie Hogg (University of Portsmouth)	Cosmology, Relativity and Gravitation
15:00		Constraining the interacting vacuum model of dark energy
		Hicks Seminar Room J11
	Abstract: There are well-known problems within the LambdaCDM model of cosmology, such as the H0 tension, that motivate the search for alternative dark energy models. In this talk, I will present one such alternative, known as the interacting vacuum scenario. In this scenario, the vacuum is free to exchange energy with the cold dark matter. Models of this type have the potential to resolve the H0 tension. I will start by discussing LCDM and its problems, then introduce the theory of the interacting vacuum model. I will present the results of a recent work (1902.10694) in which we constrained this model with observational data and conclude with a model comparison between the interacting model and LCDM.
Dec 5	Thu	Jeroen Sijsling (Ulm)	Number Theory seminar
10:00		Curves and their Jacobians in computer algebra
		Hicks Seminar Room J11
	Abstract: Algebraic curves over number fields play an important role in arithmetic geometry, for example in the proof by Andrew Wiles of the modularity Theorem, which uses elliptic curves. A very useful object for the study of more general algebraic curves is its Jacobian, because this abelian variety has a more linear structure than the curve itself. This talk describes how one can calculate with Jacobians in computer algebra systems. Many of these techniques use analytic approximations, in which case it is important to certify the correctness of such results. We discuss current algorithms for: Calculating endomorphism rings of Jacobians; Decomposing Jacobians into simple factors; and Reconstructing curves from period matrices.
Dec 5	Thu	Maria Carmen Reguera (University of Birmingham)	Pure Maths Colloquium
13:00		Sparse bounds for Bochner-Riesz operators
		LT-9
	Abstract: Sparse operators are positive dyadic operators that have very nice boundedness properties. The L^p bounds and weighted L^p bounds with sharp constant are easy to obtain for these operators. In the recent years, it has been proven that singular integrals (cancellative operators) can be pointwise controlled by sparse operators. This has made the sharp weighted theory of singular integrals quite straightforward. The current efforts focus in understanding the use of sparse operators to bound rougher operators, such as oscillatory integrals. Following this direction, our goal in this talk is to describe the control of Bochner-Riesz operators by sparse operators.
Dec 5	Thu	POSTPONED: Heather Battey (Imperial)	Statistics Seminar
14:00		Aspects of high-dimensional inference
		LT 10
Dec 5	Thu	Ieke Moerdijk (Utrecht/Sheffield)	Topology Seminar
16:00		Labelled configuration spaces and a theorem of Segal
		Hicks Seminar Room J11
	Abstract: As a digression from (and sufficiently independently of) the course on configuration spaces, I will explain Graeme Segal's proof that configuration spaces with labels in a pointed space $X$ model $\Omega^n \Sigma^n X$.
Dec 5	Thu	Tom Van Doorsselaere (Centre for Mathematical Plasma-Astrophysics, KU Leuven )	Plasma Dynamics Group
16:00		Waves and seismology of pores
		Room F28 (Hicks Building)
	Abstract: In this seminar, I will discuss several aspects of waves in pores. These concentrations of magnetic field similar to miniature sunspots are wave guides for MHD waves. In contrast to waves in coronal loops, they are resolved across the wave guide, but it is harder to know what happens further along the magnetic field. I will discuss mode identification by using wave amplitude ratios, calculation of their energy fluxes as could be used for coronal heating, and resonant absorption of slow waves. An outlook to future work is also included.
Dec 6	Fri	Yirui Xiong (Sheffield)
14:00		K3 surfaces, 10
		Hicks Seminar Room J11
Dec 9	Mon	Yirui Xiong
15:00		K3 surfaces, 11
		Hicks Seminar Room J11
Dec 10	Tue	Sira Gratz (Glasgow)	Algebra / Algebraic Geometry seminar
12:00		Higher SL(k)-friezes
		Hicks Seminar Room J11
	Abstract: Classical frieze patterns are combinatorial structures which relate back to Gauss' Pentagramma Mirificum, and have been extensively studied by Conway and Coxeter in the 1970's. A classical frieze pattern is an array of numbers satisfying a local (2 x 2)-determinant rule. Conway and Coxeter gave a beautiful and natural classification of SL(2)-friezes via triangulations of polygons. This same combinatorics occurs in the study of cluster algebras, and has revived interest in the subject. From this point of view, a natural way to generalise the notion of a classical frieze pattern is to ask of such an array to satisfy a (k x k)-determinant rule instead, for k bigger than 2, leading to the notion of higher SL(k)-friezes. While the task of classifying classical friezes yields a very satisfying answer, higher SL(k)-friezes are not that well understood to date. In this talk, we'll discuss how one might start to fathom higher SL(k)-frieze patterns. The links between SL(2)-friezes and triangulations of polygons suggests a link to Grassmannian varieties under the Plücker embedding. We find a way to exploit this relation for higher SL(k)-friezes, and provide an easy way to generate a number of SL(k)-friezes via Grassmannian combinatorics, and suggest some ideas towards a complete classification using the theory of cluster algebras. This talk is based on joint work with Baur, Faber, Serhiyenko and Todorov.
Dec 10	Tue	Jessica Fintzen (Cambridge)	Number Theory seminar
14:00		Representations of p-adic groups
		Hicks Seminar Room J11
	Abstract: The Langlands program is a far-reaching collection of conjectures that relate different areas of mathematics including number theory and representation theory. A fundamental problem on the representation theory side of the Langlands program is the construction of all (irreducible, smooth, complex) representations of p-adic groups. I will provide an overview of our understanding of the representations of p-adic groups, with an emphasis on recent progress. I will also briefly discuss applications to other areas, e.g. to automorphic forms and the global Langlands program.
Dec 11	Wed	Anitha Thillaisundaram (University of Lincoln)	Pure Maths Colloquium
14:00		Ramification structures for quotients of generalised Grigorchuk-Gupta-Sidki groups
		Hicks Seminar Room J11
	Abstract: Groups of surfaces isogenous to a higher product of curves can be characterised by a purely group-theoretic condition, which is the existence of a so-called ramification structure. Gul and Uria-Albizuri showed that quotients of the periodic Grigorchuk-Gupta-Sidki groups, GGS-groups for short, admit ramification structures. We extend their result by showing that quotients of generalisations of the GGS-groups also admit ramification structures, with some deviations for the case p=2. This is joint work with Elena Di Domenico and Sukran Gul.
Dec 11	Wed	Adeel Khan (University of Regensburg)	Algebra / Algebraic Geometry seminar
15:00		Intersection theory of derived stacks
		LT-B
	Abstract: I will discuss how various formalisms of intersection theory (Chow groups, K-theory, cobordism) can be extended to the setting of derived schemes and stacks. This gives a new approach to virtual phenomena such as the virtual fundamental class and virtual Riemann-Roch formulas.
Dec 11	Wed	Theo Torres (University of Sheffield)	Cosmology, Relativity and Gravitation
15:00		Hydrodynamic simulations of rotating black holes
		Hicks Seminar Room J11
	Abstract: Wave scattering phenomena are ubiquitous in almost all Sciences, from Biology to Physics. Interestingly, it has been shown many times that different physical systems are the stage to the same processes. One stunning example is the observation that waves propagating on a flowing fluid effectively experience the presence of a curved space-time. In this talk we will use this analogy to investigate, both theoretically and experimentally, fundamental effects occurring around vortex flows and rotating black holes. In particular, we will focus on light-bending, superradiance scattering, and quasi-normal modes emission
Dec 11	Wed	Callum Reader	ShEAF: postgraduate pure maths seminar
16:00		TBA
		Hicks Seminar Room J11
	Abstract: TBA
Dec 12	Thu	James Cranch (Sheffield)	Teaching Lunch
13:00		Maths competitions, and the journey from school to university
		LT6
	Abstract: This summer, when I wasn't working in SoMaS as normal, I helped run the 60th International Mathematical Olympiad in Bath, and handed in a dissertation for a Masters degree in education. I'd like to talk about what these activities might have to do with one another: I'll speculate a bit about what universities can and should be doing to help school-aged students with their maths.
Dec 12	Thu	Jeremy Colman (Sheffield)	Statistics Seminar
14:00		Simulation-Based Calibration (SBC)
		LT E
	Abstract: SBC is a relatively new method for checking Bayesian inference algorithms. Its advocates (Talts et al. (2017)) argue that it identifies inaccurate computation and inconsistencies in model implementation and also provides graphical summaries to indicate the nature of the underlying problems. An example of such a summary is given. Although SBC has emerged from the Stan development team it is applicable to any Bayesian model that is capable of generating posterior samples. It does not require the use of any particular modelling language. I shall explain why there might indeed be a gap that SBC could fill, demonstrate how SBC works in practice, and discuss the balance between its costs and benefits.
Dec 12	Thu	Gong Show	Topology Seminar
16:00
		Hicks Seminar Room J11
Dec 16	Mon	Thomas Clay (Liverpool)	Mathematical Biology Seminar
14:00
		Hicks LT9
Dec 16	Mon
15:00		K3 surfaces, 12
		Hicks Seminar Room J11
Dec 18	Wed	Alexandr Buryak (Leeds)	Algebra / Algebraic Geometry seminar
14:00		Generalization of the Givental theory for the open WDVV equations
		Hicks Seminar Room J11
	Abstract: The WDVV equations, also called the associativity equations, is a system of non-linear partial differential equations for one function that describes the local structure of a Frobenius manifold. In enumerative geometry the WDVV equations control the Gromov-Witten invariants in genus zero. In his fundamental works, A. Givental interpreted solutions of the WDVV equations as cones in a certain infinite-dimensional vector space. This allowed him to introduce a group action on solutions of the WDVV equations which proved to be a powerful tool in Gromov-Witten theory. I will talk about a generalization of the Givental theory for the open WDVV equations that appeared in a work of A. Horev and J. Solomon in the context of open Gromov-Witten theory.
Dec 19	Thu	Kok Leng Yeo (Max Planck Institute for Solar System Research, MPS)	SP2RC seminar
10:00		ESPOS: Solar irradiance variability and surface magnetism
		E39, Hicks Building
	Abstract: The variation in solar irradiance is commonly assumed to be driven by its surface magnetism. Until recently, this assumption could not be verified conclusively as models of solar irradiance variability based on solar surface magnetism have to be calibrated to solar irradiance measurements. Making use of realistic three-dimensional magnetohydrodynamic simulations of the solar atmosphere and state-of-the-art full-disk magnetograms from SDO, we developed a model of total solar irradiance (TSI) that does not require any such calibration. The modelled TSI variability is therefore, unlike preceding models, independent of TSI measurements. The model replicates over 95% of the observed variability over the lifetime of SDO, confirming the relationship to solar surface magnetism and leaving limited scope for alternative drivers of solar irradiance variability (at least over the time scales examined, that is, days to years).
Jan 15	Wed	Igor Sikora (Warwick)	ShEAF: postgraduate pure maths seminar
16:00		Elmendorf's theorem
		Hicks Seminar Room J11
	Abstract: Elmendorf's theorem is an absolutely key result in the equivariant homotopy theory. It relates homotopy type of G-spaces with homotopy of its fixed points diagrams. During the talk I will state the theorem, discuss what actually a homotopy theory in some category is, discuss a little bit of model categories and eventually I may approach proving the theorem, but I cannot promise the latter right now.
Jan 23	Thu	Sudheer K. Mishra (Department of Physics, Indian Institute of Technology (BHU), Varanasi, India)	SP2RC/ESPOS seminar
10:00		ESPOS: Magnetic Rayleigh–Taylor Unstable Plumes and Hybrid KH-RT Instability into a Loop-like Eruptive Prominence
		LT10, Hicks Building
	Abstract: The magnetic Rayleigh–Taylor instability is a fundamental MHD instability and recent observations show that this instability develops in the solar prominences. We analyze the observations from Solar Dynamic Observatory/Atmospheric Imaging Assembly of a MRT unstable loop-like prominence. Initially, some small-scale perturbations are developed horizontally and vertically at the prominence-cavity interface. These perturbations are associated with the hot and low dense coronal plasma as compared to the surrounding prominence. The interface supports magneto-thermal convection process, which acts as a buoyancy to launch the hot and low denser plumes (P1 and P2) propagating with the speed of 35–46 km s-1 in the overlying prominence. The self-similar plume formation initially shows the growth of a linear MRT-unstable plume (P1), and thereafter the evolution of a nonlinear single-mode MRT-unstable second plume (P2). A differential emission measure analysis shows that plumes are less denser and hotter than the prominence. We have estimated the observational growth rate for both the plumes as 1.32±0.29×10−3 s−1 and 1.48±0.29×10^−3 s^−1, respectively, which are comparable to the estimated theoretical growth rate (1.95×10^−3 s^−1). Later, these MRT unstable plumes get stabilize via formation of rolled (vortex-like) plasma structures at the prominence-cavity interface in the downfalling plasma. These rolled-plasma structures depict Kelvin-Helmholtz instability, which corresponds to the nonlinear phase of MRT instability. However, even after the full development of MRT instability, the overlying prominence is not erupted. Later, a Rayleigh-Taylor unstable tangled plasma thread is evident in the rising segment of this prominence. This tangled thread is subjected to the compression between eruption site and overlying dense prominence at the interface. This compression initiates strong shear at the prominence-cavity interface and causes Kelvin-Helmholtz vortex-like structures. Due to this shear motion, the plasma downfall is occurred at the right part of the prominence–cavity boundary. It triggers the characteristic KH unstable vortices and MRT-unstable plasma bubbles propagating at different speeds and merging with each other. The shear motion and lateral plasma downfall may initiate hybrid KH-RT instability there.
Jan 24	Fri	Fiona Turner & Maram Alossaimi (Sheffield)	Postgraduate seminars
16:00		What can Bayesian methodology tell us about past ice sheet changes? (Fiona Turner) Poisson algebra (Maram Alossaimi)
		Hicks Seminar Room J11
	Abstract: What can Bayesian methodology tell us about past ice sheet changes? Ice sheet modellers and palaeo-climatologists have been reconstructing past global ice sheets for several decades. However, despite increasingly detailed models and more proxy data, there is still a large amount of uncertainty around what the planet looked like in previous ice ages. This is especially relevant for the Last Glacial Maximum (LGM, 21Ka); as the most recent cold period in the glacial cycle, understanding how much the ice sheets have changed since then helps us to understand how they adapt to changing climates. In my talk I will present the work I have been doing on using Bayesian methods to reduce uncertainty around the Antarctic ice sheets at the LGM. Using previous reconstructions, the climate model HadCM3 and proxy data collected form ice cores, I have built a probability distribution of the ice sheet and compared it to our prior estimates. Poisson algebra The concept of Poisson algebra comes from defining a bilinear product $\{\cdot,\cdot\}$ on $\mathbb{K}$-algebra in which $\mathbb{K}$ is a field, to bring a new noncommutative structure. I will give some definitions, examples and the main Lemma (Oh, 2006) in our research. In the end, if there is time I will introduce the new Poisson algebra class A.
Jan 28	Tue	Helge Ruddat (Johannes Gutenberg University Mainz)	Algebra / Algebraic Geometry seminar
12:00		Smoothing toroidal crossing varieties
		Hicks Seminar Room J11
	Abstract: Friedman and Kawamata-Namikawa studied smoothability of normal crossing varieties. I present the proof of a significantly more general smoothing result that also works for toroidal crossing spaces and relates to work on mirror symmetry by Gross-Siebert and Chan-Leung-Ma. The key technologies are the construction of log structures, a proof of a degeneration of the log Hodge to de Rham spectral sequence as well as deformation theory governed by Gerstenhaber algebras. This project is joint with Simon Felten and Matej Filip.
Jan 30	Thu	Kento Osuga (University of Sheffield)	Cosmology, Relativity and Gravitation
15:00		Topological Recursion and Supersymmetry
		Hicks Seminar Room J11
	Abstract: Topological recursion is an abstract recursive formalism which was originally introduced to solve matrix models to all order in the large N expansion. Somewhat surprisingly, however, topological recursion has its own life beyond matrix models and its applications appear in both physics and mathematics such as 2d quantum gravity and Gromov-Witten invariants. Then an interesting question arises: does a similar story hold with supersymmetry? In this talk, I will first review the notion of topological recursion and briefly explain how it can be used to solve matrix models. I will then introduce a supersymmetric analogue of matrix models called supereigenvalue models and discuss their recursive structure. This is a joint work with Vincent Bouchard.
Feb 5	Wed	Axel Polaczek (University of Sheffield)	Cosmology, Relativity and Gravitation
15:00		Quantum Gravity and Cosmology
		Hicks Seminar Room J11
	Abstract: In this talk I will give an overview of quantum gravity with an emphasis on approaches that involve discretisations of spacetime. I will then focus on group field theory (GFT) which is an approach aiming to describe the dynamics of the microscopic degrees of freedom. In particular, I will discuss cosmology in the context of GFT, where one of the main results is the resolution of the big bang singularity.
Feb 6	Thu	Andrés Adrover González (University of the Balearic Islands, Spain)	SP2RC/ESPOS seminar
10:00		ESPOS: Three-dimensional simulations of oscillations in solar prominences
		LT 11
	Abstract: We numerically investigate the periodicity and damping of transverse and longitudinal oscillations in a 3D model of a curtain-shaped prominence. We carried out a set of numerical simulations of vertical, transverse and longitudinal oscillations with the high-order finite-difference Pencil Code. We solved the ideal magnetohydrodynamic (MHD) equations for a wide range of parameters, including the width and density of the prominence, and the magnetic field strength (B) of the solar corona. We studied the periodicity and attenuation of the induced oscillations. We found that longitudinal oscillations can be fit with the pendulum model, whose restoring force is the field aligned component of gravity, but other mechanisms such as pressure gradients may contribute to the movement. On the other hand, transverse oscillations are subject to magnetic forces. The analysis of the parametric survey shows, in agreement with observational studies, that the oscillation period (P) increases with the prominence width. For transverse oscillations we obtained that P increases with density and decreases with B. For longitudinal oscillations we also found that P increases with density, but there are no variations with B. The attenuation of transverse oscillations was investigated by analysing the velocity distribution and computing the Alfvén continuum modes. We conclude that resonant absorption is the mean cause. Damping of longitudinal oscillations is due to some kind of shear numerical viscosity.
Feb 12	Wed	Lyuba Chumakova (Edinburgh)	Applied Mathematics Colloquium
14:00		Why are we not falling apart: cytoskeleton self-organization and some results on intracellular transport
		Hicks, LT 9
	Abstract: For cells and organism to function correctly, cellular components must be robustly delivered to their biologically relevant location. This is achieved through intracellular transport, where vesicles and organelles are transported like cargo via cars (molecular motors) along highways (the microtubule cytoskeleton). Failure of this process can result in pathologies. In this talk I will present a series of studies of microtubule self-organisation and the resulting intracellular transport in epithelium, one of the four fundamental tissue types in all animals. In particular, I will address the questions of the self-organisation of the microtubule network, and how to determine the molecular motor type from the distribution of the cargo it distributes. This will be shown with stochastic simulations, in vivo experiments, and simple probabilistic models, which uncover the mathematical basis of the underlying biological phenomena
Feb 12	Wed	Chris Fewster (University of York)	Cosmology, Relativity and Gravitation
15:00		Singularity theorems with weakened energy hypotheses inspired by QFT
		Hicks Seminar Room J11
	Abstract: The original singularity theorems of Penrose and Hawking were proved for matter obeying the Null Energy Condition or Strong Energy Condition respectively. Various authors have proved versions of these results under weakened hypotheses, by considering the Riccati inequality obtained from Raychaudhuri's equation. Here, we give a different derivation that avoids the Raychaudhuri equation but instead makes use of index form methods. We show how our results improve over existing methods and how they can be applied to hypotheses inspired by Quantum Energy Inequalities. In this last case, we make quantitative estimates of the initial conditions required for our singularity theorems to apply. The talk will be largely based on arXiv:1907.13604 (joint work with E.-A. Kontou) and will introduce index form methods from the start.
Feb 13	Thu	Ines Krissaane (Sheffield)	Statistics Seminar
14:00		Robustness of Variational Inference under Model Misspecification
		LT 6
	Abstract: In many complex scientific problems, we deal with a model that is misspecified relative to the data generating process, in the sense that there is no parameter setting that allows the model to perfectly replicate the data. We will review the recent paper Generalized Variational Inference (https://arxiv.org/pdf/1904.02063.pdf) and expose arguments for using VI under model misspecification. As an application, we will focus on the Hodgkin Huxley model of action potentials, and infer parameters from uncertain experimental measurements using a variational auto encoder method.
Feb 13	Thu	Severin Bunk (Hamburg University)	Topology Seminar
16:00		Smooth Open-Closed Functorial Field Theories from B-Fields and D-Branes
		Hicks Seminar Room J11
	Abstract: Bundle gerbes are a categorification of line bundles, and their connections model the B-field in string theory. In this talk we show how bundle gerbes with connection and their D-branes give rise to smooth open-closed field theories (OCFFTs) on a manifold M in a functorial manner. The key ingredients for this construction are the 2-categorical structure of bundle gerbes, the transgression of gerbes and D-branes to spaces of loops and paths in M, as well as a formalisation of the Wess-Zumino amplitude on surfaces with corners. After giving an overview of these concepts, we will explain how they combine to yield the desired smooth OCFFTs on M. This is based on an ongoing collaboration with Konrad Waldorf.
Feb 13	Thu	Shahin Jafarzadeh (Rosseland Centre for Solar Physics, University of Oslo)	Plasma Dynamics Group
16:00		Magneto-acoustic Waves in the Lower Solar Atmosphere at High Resolution
		Room F28 (Hicks Building)
	Abstract: Fibrillar structures of different appearances and/or properties have ubiquitously been observed throughout the Sun's chromosphere. They are often thought to map the magnetic fields, and are likely rooted in small-scale magnetic elements in the solar photosphere. Here, we present properties of magnetohydrodynamic-wave dynamics in various fibrillar structures as well as in small magnetic elements in the low solar atmosphere, at high-spatial resolution, from the SUNRISE balloon-borne observatory as well as the Swedish Solar Telescope. Our analysis reveals the prevalence of kink and sausage waves in both types of magnetic structures, propagating at similar high frequencies. The estimated energy flux carried by the observed waves is marginally enough to heat the chromosphere (and perhaps the corona). Furthermore, such waves are compared with temperature fluctuations in the fibrils from high-temporal resolution observations with the Atacama Large Millimeter/submillimeter Array (ALMA) and the Interface Region Imaging Spectrograph (IRIS) explorer, simultaneously observed at several millimetre and ultraviolet bands of, e.g., ALMA 1.3 mm as well as IRIS Mg II h & k, Si IV, and C II spectral lines, from which, physical properties of the fibrillar structures are also discussed.
Feb 18	Tue	William Elbaek Mistegaard (IST Vienna)	Algebra / Algebraic Geometry seminar
12:00		Quantum modularity
		F24
	Abstract: Lawrence and Zagier have shown that for a Brieskorn homology sphere there exists a power series with integer coefficients and convergent inside the unit disc, such that the Reshetikhin-Turaev invariant of this three-manifold is the radial limit of that power series, as the parameter tends to a certain root of unity. This power series have interesting modularity properties. Subsequent work by Gukov, Putrov, Pei and Vafa aimed at generalizing this phenomena to other three-manifolds, leading them to the invention of a power series invariants of three-manifolds, which is now known as the so-called Zed-hat invariant. These invariants are conjectured to be examples of (higher depth) quantum modular forms, and this is known to be true for some families of three-manifolds. In this talk we present the following result, which is joint with Jørgen E. Andersen: For a Seifert fibered homology sphere, the zed-hat invariant can be computed via Borel-Laplace resummation of the Reshetikhin-Turaev invariant, as proposed (and proven in examples with three singular fibers) by Gukov, Marino and Putrov.
Feb 19	Wed	Jon Keating (Univerisities of Bristol and Oxford)	Pure Maths Colloquium
14:00		Primes and Polynomials in Short Intervals
		Hicks Seminar Room J11
	Abstract: I will discuss a classical problem in Number Theory concerning the distribution of primes in short intervals and explain how an analogue of this problem involving polynomials can be solved by evaluating certain matrix integrals. I will also explain a generalisation to other arithmetic questions with a similar flavour.
Feb 19	Wed	Mitchell Berger (Exeter)	Applied Mathematics Colloquium
14:00		Localized measures of magnetic helicity and helicity flux
		Hicks, LT 9
	Abstract: Magnetic helicity is an ideal MHD invariant; it measures geometric and topological properties of a magnetic field. The talk will begin by reviewing helicity and its mathematical properties. It can be decomposed in several ways (for example, self and mutual helicity, Fourier spectra, field line helicity, linking, twist, and writhe). The talk will also review methods of measuring the helicity flux. Applications in solar and stellar astrophysics will be reviewed. ​ I will then discuss some new developments in measuring localized concentrations of helicity in a well-defined, gauge -invariant manner. One method involves absolute measures of helicity (rather than relative to a vacuum field), based on generalizations of the Toroidal-Poloidal decomposition in spherical geometries. A second method involves employing wavelets and multiresolution analysis
Feb 19	Wed	Leong Khim Wong (Cambridge)	Cosmology, Relativity and Gravitation
15:00		Dynamics of black holes with induced scalar charges
		Hicks Seminar Room J11
	Abstract: While stringent no-hair theorems forbid isolated black holes from possessing permanent moments beyond their mass, spin and electric charge, the presence of an external scalar field can endow a black hole with additional multipole moments even when the field is minimally coupled to gravity. Recent advancements in effective field theory (EFT) techniques make it possible to study how these induced scalar multipoles affect the dynamics of black holes in binary systems. I will present an overview of the EFT approach and will discuss some interesting phenomena that arise due to this effect, including a novel guise of superradiance.
Feb 19	Wed	Robin Stephenson (Sheffield)	Probability seminar
15:30
		LT7
Feb 19	Wed	Sadiah Zahoor (Sheffield)	ShEAF: postgraduate pure maths seminar
16:00		Modular forms and their congruences
		Hicks Seminar Room J11
	Abstract: Starting with a unit disc embedded inside a complex plane, we act on it by a group of symmetries. Our primary interest lies in holomorphic functions defined over this disc which are invariant under this action. These functions are called modular forms. Modular forms show bizarre symmetries due to the remarkable way they transform. I shall begin with an informal introduction to modular forms building up an insight to my current research project dealing with congruences between modular forms and similar objects.
Feb 19	Wed	Carina Geldhauser (Sheffield)	Probability seminar
16:15
		LT7
Feb 20	Thu	John Armstrong (University of Glasgow)	SP2RC/ESPOS seminar
10:00		ESPOS: Learning to Invert Solar Flares with RADYN Physics
		K14
	Abstract: During a solar flare, it is believed that reconnection takes place in the corona followed by fast energy transport to the chromosphere. The resulting intense heating strongly disturbs the chromospheric structure and induces complex radiation hydrodynamic effects. Interpreting the physics of the flaring solar atmosphere is one of the most challenging tasks in solar physics. We present a novel deep learning approach, an invertible neural network, to understanding the chromospheric physics of a flaring solar atmosphere via the inversion of observed solar line profiles in Hα and Ca II λ8542. The network is trained using flare simulations from the 1D radiation hydrodynamic code RADYN as the expected atmosphere and line profile. This model is then applied to whole images from an observation of an M1.1 solar flare taken with the Swedish 1 m Solar Telescope/CRisp Imaging SpectroPolarimeter instrument. The inverted atmospheres obtained from observations provide physical information on the electron number density, temperature and bulk velocity flow of the plasma throughout the solar atmosphere ranging in height from 0 to 10 Mm. Our method can invert a 1k x 1k field-of-view in approximately 30 minutes and we show results from the whole image inversions and error calculations on the inversions. Furthermore, we delve into the mammoth task of analysing the wealth of data we have accumulated through these inversions.
Feb 20	Thu	Niall Taggart (Queen's University Belfast)	Topology Seminar
16:00		Comparing functor calculi
		Hicks Seminar Room J11
	Abstract: Functor calculus is a categorification of Taylor's Theorem from differential calculus. Given a functor, one can assign a sequence of polynomial approximations, which assemble into a Taylor tower, similar to the Taylor series from differential calculus. In this talk, I will introduce several variants of functor calculus together with their associated model categories, and demonstrate how one may compare these calculi both on a point-set and model categorical level.
Feb 27	Thu	Rodrigo Panosso Macedo (Queen Mary University of London)	Cosmology, Relativity and Gravitation
15:00		Revisiting black-hole perturbation theory: the hyperboloidal slice approach
		Hicks Seminar Room J11
	Abstract: After reviewing the well-stablished notion of black-hole perturbation theory and the concept of quasinormal modes, we present a spectral representation of solutions to relativistic wave equations based on a geometrical approach in which the constant-time surfaces extend until future null infinity. Here, we restrict ourselves to an asymptotically flat, spherical symmetric spacetime (with focus on the Reisnner-Nordstrom solution), though the geometrical framework extends also to the Kerr spacetime. With the help of a Laplace transformation on the wave equation in question, we provide a geometrical interpretation to known algorithms (i.e. Leaver’s approach) apart from deriving an algorithm for obtaining all ingredients of the desired spectral decomposition, including quasi-normal modes, quasi-normal mode amplitudes as well as the jump of the Laplace-transform along the branch cut.
Feb 27	Thu	Ai Guan (Lancaster)	Topology Seminar
16:00		Koszul duality for derived categories of second kind
		Hicks Seminar Room J11
	Abstract: Koszul duality is a phenomenon appearing in many areas of mathematics, such as rational homotopy theory and deformation theory. For differential graded (dg) algebras, the modern formulation of Koszul duality says there is a Quillen equivalence between model categories of dg algebras and conilpotent dg coalgebras, and their corresponding dg modules/comodules. I will give an overview of this circle of ideas, and then consider what happens when the conilpotence condition is removed. The answer to this question leads to an exotic model structure on dg modules that is "of second kind", i.e. weak equivalences are finer than quasi-isomorphisms. This is joint work with Andrey Lazarev based on the preprint https://arxiv.org/abs/1909.11399.
Feb 27	Thu	Sandra Milena Conde Cuellar (University of São Paulo, Brazil)	Plasma Dynamics Group
16:00		Oscillation of coronal loops associated with flaring events
		Room F28 (Hicks Building)
	Abstract: Loops are fascinating structures that bring us a lot of information about the exchange of energy in the solar atmosphere. Oscillations and waves represent one of the most fascinating events in the loops, which also plays a key role in the study of coronal seismology. It is not clear how the disturbances are excited, however, there are several candidates, e.g., flares, emerging flux, and eruptions. In this talk, I present a summary of oscillations observed in different active regions in the presence of flares and other events. This analysis has been done with data provided by IRIS, SDO and GOES-15 spacecraft. We have found excitation sources of some disturbances in lower heights of the solar atmosphere. This matches with oscillations found in the top and the footpoints of the coronal loops. We used this information together with semi-empirical models to study the distribution of physical variables in the loops.
Feb 27	Thu	Mark Dunning, Tim Freeman, Sorkatis Kariotis (Sheffield)	Statistics Seminar
16:30		Statistical and Data Analysis Challenges in Bioinformatics
		K14
	Abstract: Bioinformatics is a multi-disciplinary subject that combines aspects of biology, computer science and statistics. Modern experimental techniques are able to generate vast amounts of data that can profile an individual's genome and offer insights into the development of disease and potential novel therapeutics. In this talk, I will describe the challenges faced by Bioinformaticians trying to deal with such data on a daily basis and the opportunities for collaboration with other disciplines to develop new analytical methods.
Feb 28	Fri	Axel Polaczek and Samuel Skirvin (Sheffield)	Postgraduate seminars
16:00		Aspects of public key cryptography (Axel Polaczek) Effect of a spatially arbitrary flow on MHD waves in solar waveguides (Samuel Skirvin)
		Hicks Seminar Room J11
	Abstract: Aspects of public key cryptography How can you exchange secrets with your friends when the available means of communication is being constantly monitored by your adversary? This is the scenario dealt with in public key cryptography. One widespread solution to this problem is based on the concept of trapdoor functions, i.e. functions that are easy to evaluate but difficult to invert unless you have some additional information. An example for this is the RSA cryptosystem which is based on the problem of integer factorization. This talk aims at providing an overview of the ideas underlying cryptography in general and RSA in particular. Effect of a spatially arbitrary flow on MHD waves in solar waveguides Magnetohydrodynamic (MHD) waves are thought to play a crucial role in the energy budget of the solar atmosphere. It is well thought that these waves contribute to the heating of the solar chromosphere and corona. As a result, understanding the physics and behaviour of these waves within the context of a realistic solar atmospheric environment is of great importance. We derive a new governing equation describing the generalised case for a spatially arbitrary flow in a 2-dimensional magnetic slab. We therefore also introduce the idea for a new method of retrieving the dispersion diagram describing the types of waves which can exist in the system.
Mar 4	Wed	Dmitri Finkelshtein (Swansea)	Probability seminar
14:00
		LT1
Mar 5	Thu	Azaymi Litzi Siu Tapia (Instituto de Astrofísica de Andalucía (IAA-CSIC), Spain)	SP2RC/ESPOS seminar
10:00		ESPOS: Magnetic properties of short-lived penumbral microjets
		K14
	Abstract: Studying the polarization properties of penumbral microjets that have the shortest durations requires spectropolarimetric observations with the fastest temporal cadence possible and is currently a challenging task. Here, we approach this task using fast-cadence spectropolarimetric measurements of the Ca II 8542 A line made with the CRISP instrument at the Swedish 1 m Solar Telescope. We exploited the diagnosis capabilities of this line to retrieve the magnetic field configuration and its evolution in the upper photosphere and low chromosphere by applying the weak field approximation to its wings and line core wavelengths respectively. We found that the short-lived microjets are associated with a transient perturbation in the photospheric magnetic field and sometimes they show clear but weaker changes in the chromospheric field as well. We will describe the different types of evolution that were identified.
Mar 5	Thu	Ariel Weiss (Jerusalem)	Number Theory seminar
14:00		TBA
		Hicks Seminar Room J11
Mar 6	Fri	Cameron Thomas (University of Sheffield)	Cosmology, Relativity and Gravitation
14:00		Predictions of interacting dark energy
		Hicks Seminar Room J11
	Abstract: Dark energy is a form of energy with an unknown physical origin that makes up nearly 70% of the universe and is causing our universe to expand at an accelerating rate. A popular candidate for dark energy is a classical scalar field with a self-interaction potential (quintessence), the other most popular candidate being the cosmological constant Λ which explains cosmological observations very well, but suffers from numerous theoretical problems which quintessence, at least in part, appears to solve. If a quintessence scalar field exists, then it is expected to dynamically couple to all matter species, both baryonic and dark, unless forbidden by some hidden symmetry. Direct coupling between dark energy and baryonic matter is severely constrained by so-called “fifth-force” experiments, however, a direct coupling between dark energy and dark matter is not constrained by conventional experiments, and remains open for investigation. I will review models with conformal couplings and their cosmological consequences, as well as their status in light of the swampland conjectures.
Mar 6	Fri	Ben Snow (University of Exeter)	Plasma Dynamics Group
16:00		Mode conversion of two-fluid shocks in a partially-ionised, isothermal, stratified atmosphere
		Room F28 (Hicks Building)
	Abstract: The plasma of the lower solar atmosphere consists of mostly neutral particles, whereas the upper solar atmosphere is mostly ionised particles and electrons. A shock that propagates upwards in the solar atmosphere therefore undergoes a transition where the dominant fluid is either neutral or ionised. An upwards propagating shock also passes a point where the sound and Alfvén speed are equal. At this point the energy of the acoustic shock can separated into fast and slow components. How the energy is distributed between the two modes depends on the angle of magnetic field. Two-fluid numerical simulations are performed of a wave steepening into a shock in an isothermal, partially-ionised atmosphere. The collisional coefficient is varied to investigate the regimes where the plasma and neutral species are weakly, strongly and finitely coupled. The propagation speeds of the compressional waves hosted by neutral and ionised species vary, therefore velocity drift between the two species is produced as the plasma attempts to propagate faster than the neutrals. This is most extreme for a fast-mode shock. We find that the collisional coefficient drastically changes the features present in the system, specifically the mode conversion height, type of shocks present, and the shock widths. In the finitely-coupled regime fast-mode shock widths can exceed the pressure scale height leading to a new potential observable of two-fluid effects in the lower solar atmosphere.
Mar 12	Thu	Viktor Fedun (Sheffield )	Plasma Dynamics Group
16:00		Vortex motions in the solar atmosphere
		Room F28 (Hicks Building)
	Abstract: Solar photosphere vortices have the potential to form coherent magnetic field structures, e.g. twisted magnetic flux tubes and, therefore, may play a key role in the transport of energy and momentum from the lower atmosphere into the upper solar atmosphere. In this talk I will review existing methods for their identification and discuss our approach, which is based on Gamma detection and LAVD of inter-granular photospheric intensity vortices. I will also present new mechanism for the generation of magnetic waveguide from the lower solar atmosphere to the corona. This waveguide appears as the result of interacting perturbations (initially generated by photospheric vortex motions) in neighbouring magnetic flux tubes (modelled in the framework of self-similar approach).
Mar 17	Tue	Dr Dominik Utz (University of Graz)	SP2RC seminar
15:00		Small-scale solar magnetic fields as seen by MBPs: From quiet-sun basics over activity to coronal holes
		Zoom link: https://us04web.zoom.us/j/343142270
	Abstract: The Sun is our host star and not at all a dull ball of gas, but instead an impressive heavenly body, due to its activity within its atmosphere. All of this activity is caused by magnetic fields, which range from gigantic active regions - consisiting of sunspots or even sunspot groups - down to isolated single flux fibres, often visible as magnetic bright points (MBPs). While sunspots are very important to understand the global solar magnetic field dynamo, as well as the caused large scale-solar activity, and hence the space weather and its influence on Earth, small-scale solar magnetic fields can teach us about important magneto-plasma processes such as MHD wave generation and propagatin. In this sminary talk, we wish to shed light on MBPs, which are due to their size among the smallest solar magnetic feastures we can study currently and thus of great importance to advance the field. Moreover, they have the advantage that identifying them in "simple" filtergram images, is of an easier and especially faster task than analysing cumbersome and low cadence spectro-polarimetric data. We will outline first of all the basic characterstics of MBPs, then have a look in solar-activity processes they are involved in such as magnetic reconnection and MHD wave creation and propagation, before touching shortly large scale-structures - namely coronal holes - and their relationship to MBPs.
Mar 18	Wed	Marcel Ortgiese (Bath)	Probability seminar
14:00
		LT1
Mar 19	Thu	Jack Jenkins (Mullard Space Science Laboratory (MSSL), UK)	SP2RC/ESPOS seminar
10:00		ESPOS: The Small-Scale Structure and Motions Underneath an On-Disk Solar Prominence
		Zoom Link: https://zoom.us/j/2793966563
	Abstract: Solar prominences are typically considered clouds of plasma suspended, bound, and governed within the solar corona solely by their host magnetic field. That said, recent studies have suggested we reconsider the (widely-adopted!) assumption that prominence mass has a negligible role to play in the (in)stability of this host magnetic field. Specifically, such studies have suggested that the contribution of mass to the global equilibrium of quiescent prominences is quite the opposite. Of course, the plethora of observations of the vertical motions within quiescent prominences (typically interpreted as occurrences of the Rayleigh-Taylor instability) have already suggested the importance of mass on smaller scales. The further suggestion that these falling ‘plasmoids’ may then successfully drain from the prominence-hosting magnetic field and subsequently cease to contribute to the global equilibrium is, therefore, of particular interest. We present the latest results of our ongoing study that combines high-resolution ground-based observations (H-α, Ca II 8542, He I 10830) taken at the Dunn Solar Telescope (DST) with multiple inversion methods that involve a varying degree of assumption/complexity. I will briefly present the instrument set-up and resulting observations of an on-disk prominence from 29 May 2017. Each inversion approach and their individual results will then be discussed, before the construction of one possible framework that accounts for all of the observations. I will then finish with details of a tentative detection of an RTI-like structure located beneath the observed prominence.
Mar 19	Thu	Susan Cox (KCL)	Statistics Seminar
14:00
		LT 6
Mar 20	Fri	Mitsuyasu Hashimoto (Osaka City University)	Algebra / Algebraic Geometry seminar
15:00
		Hicks Seminar Room J11
Mar 24	Tue	Prof. Ineke de Moortel (University of St. Andrews)	SP2RC seminar
11:00		UK-SOSS: Aspects of MHD Wave Heating in the Complex Solar Atmosphere
		Zoom
	Abstract: In a series of numerical experiments, we investigate the possible role of MHD waves in the energy and mass cycle in the complex solar corona. Using 3D MHD simulations of transverse, Alfvenic waves, we look at the role of chromospheric evaporation, the complexity of the magnetic field and the power spectrum of the wave driver. We focus on the efficiency of the wave-based heating in our models, in particular whether heating provided by the waves can balance coronal losses and whether proposed wave heating mechanisms are in fact self-consistent.
Mar 26	Thu	Abdulrahman Albidah (Sheffield)	Plasma Dynamics Group
16:00		Multi-faceted approach to decomposing and identifying individual magnetohydrodynamic (MHD) wave modes in sunspots and pores
		Google hangouts https://meet.google.com/oxg-wxhq-gkp
	Abstract: High resolution observations of pores and sunspots show a rich and complex variety of oscillatory temporal and spatial behaviour. To decompose this data into individual magnetohydrodynamic (MHD) wave modes is non-trivial and requires a multi-faceted approach. Here we take a three-pronged approach of combining Fourier analysis, Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD). The Fourier omega-k power spectrum provides us with a useful overall view of the particular temporal and spatial scales of interest but does not provide any cross-pixel correlation. In this regard, POD classifies modes that are orthogonal in space but places no restrictions on their frequencies. DMD has no such restrictions in space but classifies modes that are orthogonal in time, i.e., identified modes cannot have the same frequency. Each of these complementary techniques have their particular strengths which we will illustrate with synthetic data.
Mar 27	Fri	Dr. Dominik Utz (University of Graz)	SP2RC seminar
13:00		Small-scale solar magnetic fields as seen by MBPs: From quiet-sun basics over activity to coronal holes
		https://us04web.zoom.us/j/343142270
	Abstract: The Sun is our host star and not at all a dull ball of gas, but instead an impressive heavenly body, due to its activity within its atmosphere. All of this activity is caused by magnetic fields, which range from gigantic active regions - consisiting of sunspots or even sunspot groups - down to isolated single flux fibres, often visible as magnetic bright points (MBPs). While sunspots are very important to understand the global solar magnetic field dynamo, as well as the caused large scale-solar activity, and hence the space weather and its influence on Earth, small-scale solar magnetic fields can teach us about important magneto-plasma processes such as MHD wave generation and propagatin. In this sminary talk, we wish to shed light on MBPs, which are due to their size among the smallest solar magnetic feastures we can study currently and thus of great importance to advance the field. Moreover, they have the advantage that identifying them in "simple" filtergram images, is of an easier and especially faster task than analysing cumbersome and low cadence spectro-polarimetric data. We will outline first of all the basic characterstics of MBPs, then have a look in solar-activity processes they are involved in such as magnetic reconnection and MHD wave creation and propagation, before touching shortly large scale-structures - namely coronal holes - and their relationship to MBPs.
Apr 2	Thu	Ben Snow (University of Exeter)	European Solar Physics Online Seminars (ESPOS)
10:00		Shock substructure in partially-ionised plasma
		Zoom link: https://zoom.us/j/165498165
	Abstract: The partially-ionised nature of the lower solar atmosphere introduces new and exciting complexities to shock solutions. Here we study numerically the slow-mode shock triggered via a magnetic discontinuity, mimicking the slow-mode shocks that can form as a result of magnetic reconnection. In single-fluid ideal MHD, the slow-mode shock occurs as a discontinuous jump in parameters. However, in the two-fluid partially-ionised plasma, the shock occupies a finite width due to the coupling and decoupling of plasma and neutral species across the shock. It is found that this finite width region allows for shock sub-structure that can affect the overall dynamics of the system. In particular, we find that an intermediate shock can exist where the plasma velocity transitions from super to sub Alfvenic velocities. A key feature of this type of shock is that the magnetic field is reversed across the interface. We present numerical results analysing the formation and evolution of intermediate shocks as sub-structure within slow-mode shocks.
Apr 2	Thu	Ben Snow (Exeter University, UK)	SP2RC/ESPOS seminar
10:00		Shock substructure in partially-ionised plasma
		Zoom Link: https://zoom.us/j/165498165
	Abstract: The partially-ionised nature of the lower solar atmosphere introduces new and exciting complexities to shock solutions. Here we study numerically the slow-mode shock triggered via a magnetic discontinuity, mimicking the slow-mode shocks that can form as a result of magnetic reconnection. In single-fluid ideal MHD, the slow-mode shock occurs as a discontinuous jump in parameters. However, in the two-fluid partially-ionised plasma, the shock occupies a finite width due to the coupling and decoupling of plasma and neutral species across the shock. It is found that this finite width region allows for shock sub-structure that can affect the overall dynamics of the system. In particular, we find that an intermediate shock can exist where the plasma velocity transitions from super to sub Alfvenic velocities. A key feature of this type of shock is that the magnetic field is reversed across the interface. We present numerical results analysing the formation and evolution of intermediate shocks as sub-structure within slow-mode shocks.
Apr 2	Thu	Nicola Bellumat (University of Sheffield)	Topology Seminar
16:00		Iterated chromatic localization
	Abstract: The work of Ravanel, Devinatz, Hopkins and Smith in the Eighties provided the basis of chromatic homotopy theory: its protagonists are the Morava theories E(n) and K(n), whose associated Bousfield localizations provide optimal means to decompose the stable homotopy category. It comes naturally to wonder how the compositions of such localizations behave: there are classical results regarding the relationship of the Bousfield classes of wedges of the above spectra which lead us to expect some kind of regularity. In this talk I will present a joint work with N. Strickland which provides a positive result in this direction: we show that, fixed an upper bound n for the chromatic height, the compositions of localizations with respect to spectra which are wedges of K(i), for i lesser or equal n, are only finitely many up to isomorphism. We formulated our proof in the language of derivators, thus I will provide a brief overview.
Apr 9	Thu	Yasir Aljohani (Sheffield)	Plasma Dynamics Group
16:00		Identifying magnetohydrodynamic vortex tubes in the Sun's photosphere
		Google Meet
	Abstract: Vortex flows in the solar photosphere are fundamentally important for the generation of magnetohydrodynamic (MHD) waves which propagate to the upper layers of the solar atmosphere. Vortex tubes are formed as coherent magnetic field structures in the solar atmosphere, e.g. twisted magnetic flux tubes. In this presentation, I will discuss the method of Lagrangian Averaged Vorticity Deviation (LAVD) developed by Haller (2016) to identify vortex flows, namely the center of circulation and their boundary, then I will present the algorithmic technique I have developed to check whether a structure detected by the LAVD method is a true vortex or not and how to determine the rotational direction(clockwise or anticlockwise). In addition, I will apply these methods to MURaM magneto-convection simulation data to detect and track the evolution of both 2D vortices and 3D vortex tubes in the solar photosphere.
Apr 10	Fri	Dr Chris Nelson (Queen's University, Belfast)	SP2RC seminar
13:00		The signatures of down flowing plasma in sunspots in high-resolution data
		Zoom Link: https://us04web.zoom.us/j/343142270
	Abstract: Sunspots are one of the most widely studied phenomena in the zoo of solar features. Although these events can be observed over the course of days, many dynamical events with lifetimes of the order minutes can be observed within them. In this talk, we will briefly cover the options available to observers when studying sunspots in different regions of the solar atmosphere before discussing specific features which shine light on the physics occurring within these regions of strong magnetic field. Specifically, we will discuss small-scale umbral brightenings forming in the chromosphere and super-sonic downflows occurring in the transition region. These events, which are both linked to falling plasma in sunspots, highlight the fine-scale structuring present in sunspots and could act as excellent test-cases for the next generation of solar telescopes.
Apr 16	Thu	Rahul Yadav (Stockholm University)	European Solar Physics Online Seminars (ESPOS)
10:00		Three-dimensional magnetic field structure of a flux-emerging region in the solar atmosphere
		Zoom link: https://zoom.us/j/165498165
	Abstract: We present spectropolarimetric analysis of a flux-emerging region (FER) in order to understand its magnetic and kinematic structure. Our spectropolarimetric observations, in the He i 10830Å spectral region, were recorded with the GRIS at the 1.5m aperture GREGOR telescope. A Milne–Eddington-based inversion code was employed to extract the photospheric information of the Si i spectral line, whereas the He i triplet line was analyzed with the Hazel code. The spectropolarimetric analysis of the Si i line reveals a complex magnetic structure near the vicinity of the FER, where a weak (350–600 G) and horizontal magnetic field was observed. In contrast to the photosphere, the analysis of the He i triplet presents a smooth variation of the magnetic field vector (ranging from 100 to 400 G) and velocities across the FER. Moreover, we find supersonic downflows of ∼40 km/s appearing near the foot points of loops connecting two pores of opposite polarity, whereas strong upflows of 22 km/s appear near the apex of the loops. Furthermore, nonforce-free field extrapolations were performed separately at two layers in order to understand the magnetic field topology of the FER. The reconstructed loops using photospheric extrapolations along an arch filament system have a maximum height of ∼10.5 Mm from the solar surface with a foot-point separation of ∼19 Mm, whereas the loops reconstructed using chromospheric extrapolations reach around ∼8.4 Mm above the solar surface with a foot-point separation of ∼16 Mm at the chromospheric height. The magnetic topology in the FER suggests the presence of small-scale loops beneath the large loops. Under suitable conditions, due to magnetic reconnection, these loops can trigger various heating events in the vicinity of the FER.
Apr 16	Thu	Rahul Yadav (Stockholm University, Sweden)	SP2RC/ESPOS seminar
10:00		Three-dimensional magnetic field structure of a flux-emerging region in the solar atmosphere
		Zoom Link: https://zoom.us/j/165498165
	Abstract: We present spectropolarimetric analysis of a flux-emerging region (FER) in order to understand its magnetic and kinematic structure. Our spectropolarimetric observations, in the He i 10830Å spectral region, were recorded with the GRIS at the 1.5m aperture GREGOR telescope. A Milne–Eddington-based inversion code was employed to extract the photospheric information of the Si i spectral line, whereas the He i triplet line was analyzed with the Hazel code. The spectropolarimetric analysis of the Si i line reveals a complex magnetic structure near the vicinity of the FER, where a weak (350–600 G) and horizontal magnetic field was observed. In contrast to the photosphere, the analysis of the He i triplet presents a smooth variation of the magnetic field vector (ranging from 100 to 400 G) and velocities across the FER. Moreover, we find supersonic downflows of ∼40 km/s appearing near the foot points of loops connecting two pores of opposite polarity, whereas strong upflows of 22 km/s appear near the apex of the loops. Furthermore, nonforce-free field extrapolations were performed separately at two layers in order to understand the magnetic field topology of the FER. The reconstructed loops using photospheric extrapolations along an arch filament system have a maximum height of ∼10.5 Mm from the solar surface with a foot-point separation of ∼19 Mm, whereas the loops reconstructed using chromospheric extrapolations reach around ∼8.4 Mm above the solar surface with a foot-point separation of ∼16 Mm at the chromospheric height. The magnetic topology in the FER suggests the presence of small-scale loops beneath the large loops. Under suitable conditions, due to magnetic reconnection, these loops can trigger various heating events in the vicinity of the FER.
Apr 16	Thu	Jocelyne Ishak (Vanderbilt University)	Topology Seminar
16:00		The naive commutative structure on rational equivariant $K$-theory
	Abstract: Modeling rational spectra via algebraic data has a long and fruitful history in homotopy theory. More precisely, rational spectra are equivalent to rational chain complexes, and this algebraic data is called an algebraic model for rational spectra. Our goal is to understand rational equivariant $K$-theory as a naive commutative ring spectrum when G is a finite group. We do this by calculating its image in the algebraic model for naive-commutative ring G-spectra given by Barnes, Greenlees and Kędziorek. Our calculations show that these spectra are unique as naive-commutative ring spectra in the sense that they are determined up to weak equivalence by their homotopy groups. This work is joint with Anna Marie Bohmann, Christy Hazel, Magdalena Kędziorek, and Clover May
Apr 21	Tue	Travis Mandel (Edinburgh)	Algebra / Algebraic Geometry seminar
15:30		Tropical multiplicities from polyvector fields and QFT
	Abstract: When considering planar tropical curves satisfying point conditions, Mikhalkin expressed the tropical curves' multiplicities as the product of the multiplicities of their vertices. Such a decomposition of the multiplicity into local computations is very useful in practice, e.g., in the Gross-Siebert program. I will describe joint work with H. Ruddat in which we give such localized tropical multiplicity formulas very generally using mirror polyvector fields. This involves developing a notion of tropical quantum field theory.
Apr 23	Thu	Liran Shaul (Charles University in Prague)	Topology Seminar
16:00		The Cohen-Macaulay property in derived algebraic geometry
	Abstract: In this talk we explain how to extend the theory of Cohen-Macaulay rings and Cohen-Macaulay modules to the setting of commutative DG-rings. We will explain how by studying local cohomology in the DG-setting, one obtains certain amplitude inequalities about certain DG-modules of finite injective dimension. When these inequalities are equalities, we arrive to the notion of a Cohen-Macaulay DG-ring. We show that these arise naturally in many situations, and explain their basic theory. We then explain that this situation is the generic local situation in derived algebraic geometry; under mild hypothesis, every eventually coconnective locally noetherian derived scheme is Cohen-Macaulay on a dense open set.
Apr 23	Thu	Abdulaziz Alharbi (Sheffield)	Plasma Dynamics Group
16:00		Waves in Two-Fluid Gravitationally Stratified Plasmas
		Google Meet
	Abstract: The temperature in the lower part of solar atmosphere is not high enough for a complete ionisation of the plasma. Therefore, this environment region is made up of electrons, positive ions and neutrals that interact through short and long range collisions in the presence of the magnetic field. Due to the low temperature, the gravitational scale-height is also short, meaning that perturbations will be affected by gravity. Here we study the spatial and temporal evolution of slow magnetoacoustics waves propagating in a stratified magnetic flux tube. In the two-fluid plasma the dynamics of neutrals and charged species has to be studied separately. Our analysis shows that the dynamic is described by a system of coupled Klein -Gordon equations that are solved in the strongly ionised limit. For the mentioned two species we study the changes in the cut-off frequency for a range of physical parameters. Asymptotic solutions to the governing equations are obtained for a harmonic driver. Our results reveal that ion-acoustic and neutrals-acoustic slow modes show a different damping scale.
Apr 24	Fri	Dr Ryan Milligan (QUB)	SP2RC seminar
13:00		Lyman-alpha Variability During Solar Flares
		Google Meet
	Abstract: The hydrogen Lyman-alpha line is the brightest emission line in the solar spectrum, and yet observations of solar flares at this wavelength have been surprisingly scarce over the past 50 years. The few publications that do exist are somewhat ambiguous leaving many unanswered questions regarding the nature of short-term solar variability. The study of Lyman-alpha is important for understanding space weather effects as changes in the Sun’s Lyman-alpha output can drive changes in the dynamics and composition of planetary atmospheres. This can also provide insights into the effects of stellar activity and how it might influence the potential habitability of exoplanets. Studies have also shown that Lyman-alpha is a significant radiator of solar flare energy, providing an important diagnostic of energy release and transport processes. In this talk I shall give an overview of a statistical study of ~500 solar flares observed in Lyman-alpha by GOES-15/EUVS-E. I will be discussing flare energetics, opacity effects, acoustic oscillations, and the implications for space weather, as well as looking ahead to future Lyman-alpha observations anticipated during Solar Cycle 25.
Apr 24	Fri	Martin Saal (Pisa/Darmstadt)	Applied Mathematics Colloquium
14:00		White noise solutions for (m)SQG
		Google Hangout Meet
	Abstract: The inviscid surface quasigeostrophic equation (SQG) describes (roughly speaking) the temperature in a rapidly rotating stratified fluid which is transported by the velocity field. The velocity field is connected to the temperature via Riesz-transform, which are singular integral operators. It has applications in both meteorological and oceanic flows, while in mathematics it is often used as a toy model for the 3D Euler equations due to some structural similarities of these equations. We give a brief overview on versions of the SQG equation and of the known mathematical results. For a modified version (mSQG) with a smoother velocity field, which links the SQG equation to the vorticity formulation of the 2D Euler equations, we will show that by using a special Symmetrie in the kernel a white noise solution to mSQG can be constructed and give some comments on Further results. Finally, we outline the difficulties of our approach in the case of SQG itself.
Apr 28	Tue	Piotr Sulkowski (Warsaw)	Algebra / Algebraic Geometry seminar
14:00		Nahm sums, quiver A-polynomials, and topological recursion
		Google Meet
	Abstract: There is a large class of q-series that have the structure of Nahm sums, or equivalently motivic generating series for quivers. First, in this talk I will present first efforts to systematically analyse and classify classical and quantum A-polynomials associated to such q-series. Second, I will formulate a conjecture that states that those series, as well as their quantum quiver A-polynomials, can be reconstructed by means of the topological recursion. There is a large class of interesting quiver A-polynomials of genus zero, and for a number of them this conjecture can be verified by explicit calculations. In view of recently found dualities, for an appropriate choice of quivers, these results have a direct interpretation in topological string theory, knot theory, counting of lattice paths, and related topics. In particular it follows, that various quantities characterizing those systems, such as motivic Donaldson-Thomas invariants, various knot invariants, etc., have the structure compatible with the topological recursion and can be reconstructed by its means.
Apr 28	Tue	Di Zhang (Sheffield)	Number Theory seminar
15:00		An analogue of the Shintani lifting for imaginary quadratic fields
		Google hangout
Apr 29	Wed	Ellen Powell (Durham)	Probability seminar
14:00
		LT1
Apr 29	Wed	Benjamin Elder (University of Nottingham)	Cosmology, Relativity and Gravitation
15:00		Dynamical friction in superfluids
		https://app.vscene.net/r/KjKhl4yTE4
	Abstract: A number of modern theories of dark matter hypothesize that it can condense into a superfluid phase. Such a phase could be distinguished from ordinary particle dark matter by its lack of dynamical friction, a process by which moving objects are slowed by gravitational attraction to their own wake. This process involves both the Jeans instability and the “quantum pressure” of superfluid dark matter. I will present a treatment of this phenomenon via two equivalent formalisms: (i) a standard hydrodynamical description of superfluid density waves, and (ii) a novel quasiparticle description, wherein massive perturbers lose energy via the radiation of phonons. Somewhat surprisingly, we find that even subsonic perturbers can lose energy to dynamical friction. This theoretical work resolves a long-standing puzzle associated with dynamical friction in fluids, and paves the way for more detailed study of superfluid dark matter phenomenology.
	Slides
Apr 30	Thu	Gianluca Napoletano (University of Rome Tor Vergata)	European Solar Physics Online Seminars (ESPOS)
10:00		On the parameters of Drag-Based ensemble models
		Zoom: https://zoom.us/j/165498165
	Abstract: ICMEs (Interplanetary Coronal Mass Ejections) are violent phenomena of solar activity that affect large regions of the heliosphere. The prediction of their impact on the Earth and other solar system bodies is one of the primary goals of the planetary space weather forecasting. The travel time of an ICME from the Sun to the Earth can be computed through the Drag-Based Model (DBM). A DBM is based on a simple equation of motion for the ICME defining its acceleration as a=-Γ(v-w)|v-w|, where a and v are the CME acceleration and speed, w is the ambient solar-wind speed and Γ is the so-called drag parameter (Vršnak et al., 2013). To run the codes, forecasters use empirical input values for Γ and w, derived by pre-existent knowledge of solar wind. In the ‘Ensemble’ approaches (Dumbovich et al., 2018; Napoletano et al. 2018), the uncertainty about the actual values of such inputs are rendered by Probability Distribution Functions (PDFs), accounting for their variability and our lack of knowledge. Employing a list of past ICME events, for which initial conditions when leaving the Sun and arrival conditions at the Earth are known, we apply a statistical approach to the DBM to determine a measure of Γ and w for each case. This allows to obtain distributions for the model parameters on an experimental basis and to test whether different conditions of relative velocity to the solar wind influence the value of the drag efficiency. This is a promising approach when considering the extremely short computation time needed by the model to propagate ICMEs, to forecast ICME arrival to planetary bodies or spacecraft in the whole heliosphere, with relevant application to space-mission short-term planning.
Apr 30	Thu	Gianluca Napoletano (Rome Tor Vergata)	SP2RC/ESPOS seminar
10:00		By-weekly SP2RC/ESPOS joint seminar: On the parameters of Drag-Based ensemble models
		Zoom
	Abstract: ICMEs (Interplanetary Coronal Mass Ejections) are violent phenomena of solar activity that affect large regions of the heliosphere. The prediction of their impact on the Earth and other solar system bodies is one of the primary goals of the planetary space weather forecasting. The travel time of an ICME from the Sun to the Earth can be computed through the Drag-Based Model (DBM). A DBM is based on a simple equation of motion for the ICME defining its acceleration as a=-Γ(v-w)|v-w|, where a and v are the CME acceleration and speed, w is the ambient solar-wind speed and Γ is the so-called drag parameter (Vršnak et al., 2013). To run the codes, forecasters use empirical input values for Γ and w, derived by pre-existent knowledge of solar wind. In the ‘Ensemble’ approaches (Dumbovich et al., 2018; Napoletano et al. 2018), the uncertainty about the actual values of such inputs are rendered by Probability Distribution Functions (PDFs), accounting for their variability and our lack of knowledge. Employing a list of past ICME events, for which initial conditions when leaving the Sun and arrival conditions at the Earth are known, we apply a statistical approach to the DBM to determine a measure of Γ and w for each case. This allows to obtain distributions for the model parameters on an experimental basis and to test whether different conditions of relative velocity to the solar wind influence the value of the drag efficiency. This is a promising approach when considering the extremely short computation time needed by the model to propagate ICMEs, to forecast ICME arrival to planetary bodies or spacecraft in the whole heliosphere, with relevant application to space-mission short-term planning.
Apr 30	Thu	Heather Battey (Imperial)	Statistics Seminar
14:00
		LT 6
Apr 30	Thu	Magdalena Kedziorek (Radboud University Nijmegen)	Topology Seminar
16:00		Genuine commutative structure on rational equivariant K-theory
		meet.google.com/sqb-gwhq-dgk
	Abstract: In a recent talk at this seminar Jocelyne Ishak described a proof that rational equivariant K-theory admits a unique naive-commutative structure when the group of equivariance is finite abelian. A natural question to ask is what can we say about other levels of commutative structures on rational equivariant K-theory? Using the result of Wimmer which provides an algebraic model for rational genuine commutative ring G-spectra when G is a finite group I will sketch a proof that rational equivariant K-theory has a unique genuine-commutative ring structure for some groups G. This is work in progress with Anna Marie Bohmann, Christy Hazel, Jocelyne Ishak and Clover May. I will start by recalling necessary results mentioned by Jocelyne in her talk and give a short introduction to different levels of commutativity present in the equivariant world.
May 5	Tue	Michel van Garrel (Warwick)	Algebra / Algebraic Geometry seminar
14:00
		ONLINE
May 6	Wed	Matt Rosenzweig (Texas Austin)	Applied Mathematics Colloquium
14:00		From Point Vortices to 2D Fluids: Back and Forth
		Google Meet
	Abstract: In this talk, we will discuss the connection between two-dimensional (2D) fluid equations, such as the incompressible Euler or surface quasi-geostrophic (SQG) equations, and systems of interacting particles, which are known as point vortex models. We consider this topic from two angles determined by different scaling limits. The first is localization, where one passes from a fluid equation to a point vortex model. The second is mean-field limit, where one passes from a point vortex model to a fluid equation. Time permitting, we will also discuss these connections in the stochastic setting, where multiplicative noise has been added to the dynamics.
May 6	Wed	Edward Crane (Bristol)	Probability seminar
14:00
May 6	Wed	Suddhasattwa Brahma (McGill University)	Cosmology, Relativity and Gravitation
15:00		Theory confronts Observations: Cosmology in the era of the Swampland
		https://app.vscene.net/r/KjKhl4yTE4
	Abstract: It is well-known that accelerating spacetimes form the basis of our understanding of early and late-time cosmology. On the other hand, there has been a pile of mounting evidence, mainly based on numerous results from String Theory (but not limited to them), that de Sitter space is difficult to embed in a quantum theory of gravity. Thus, these theoretical constraints that any consistent effective field theory must satisfy in order to have a UV-completion -- the so-called "Swampland conjectures" -- form a new challenge for phenomenologically viable model-building in cosmology. In this talk, I shall discuss some aspects of these conjectures, evidence in support of them and how to reconcile them with astronomical observations with a special focus on inflation. The importance of non-perturbative quantum corrections in constructing quasi de-Sitter backgrounds shall also be demonstrated.
May 7	Thu	Peter Symonds (Manchester)	Topology Seminar
16:00		Rank, Coclass and Cohomology.
		meet.google.com/hdp-cfvn-wak
	Abstract: We prove that for any prime p the finite p-groups of fixed coclass have only finitely many different mod-p cohomology rings between them. This was conjectured by Carlson; we prove it by first proving a stronger version for groups of fixed rank first conjectured by Diaz, Garaialde and Gonzalez.
May 7	Thu	Rahul Sharma (Universidad de Alcalá, Spain)	Plasma Dynamics Group
16:00		Complex 3D dynamics of solar spicule structures
		Google Meet
	Abstract: Sun’s outer atmosphere is a million degree hotter than it’s visible surface, which is not understood with any of the known laws of thermodynamics and remains an intriguing problem for the astrophysics in general. It is now believed that most of the energy dissipation phenomenon occurs at the interface region in between solar chromosphere and corona, which is a highly dynamic, gravitationally stratified, nonlinear, inhomogeneous environment. Observed dynamics of thin magnetic fluxtube structures in this layer, reflects the confined magnetohydrodynamic (MHD) wave-modes (kink, sausage and torsional Alfvén). For the first time, the evolution of the resultant transverse displacement of the observed flux tube structures, estimated from perpendicular velocity components, is analyzed along with cross-sectional width, photometric and azimuthal shear/torsion variations, to accurately identify the confined wave-mode(s). In my talk, I will discuss the observational evidence of pulse-like nonlinear kink wave-mode(s), as indicated by the strong coupling in between kinematic observables, with a frequency-doubling, -tripling aspect, supported by mutual phase relations cen- tered around 0° and ±180° (Sharma et al. 2018). The 3D ensemble of the observed dynamic components revealed complexities pertinent to the accurate identification and interpretation of e.g. linear/nonlinear, coupled/uncoupled MHD wave-modes in the observed waveguides (spicules).
May 8	Fri	Aishawnnya Sharma (IUCAA (Pune))	SP2RC seminar
13:00		Coupling and Dynamics of Waves in the Solar Atmosphere
		Google Meet
	Abstract: Waves are omnipresent in the solar atmosphere. With the advancement of technical capabilities, the direct observations and studies of different wave modes have been increased drastically over the years. But despite the decades-long research, we are yet to achieve a complete understanding of the physics behind their origin and their possible role in the coupling of the solar atmosphere. In this talk, the speaker will talk on multiwavelength imaging and spectroscopic observations that will provide pieces of evidence on the nature and extent of the coupling among different waves observed in the different layers of the solar atmosphere. These observations will help to understand the spatio-temporal evolution of propagating waves in the solar atmosphere.
May 13	Wed	Silvia Gazzola (Bath)	Applied Mathematics Colloquium
14:00		Iterative regularization methods for large-scale linear inverse problems
		Google Meet
	Abstract: Inverse problems are ubiquitous in many areas of Science and Engineering and, once discretized, they lead to ill-conditioned linear systems, often of huge dimensions: regularization consists in replacing the original system by a nearby problem with better numerical properties, in order to find a meaningful approximation of its solution. After briefly surveying some standard regularization methods, both iterative (such as many Krylov methods) and direct (such as Tikhonov method), this talk will introduce a recent class of methods that merge an iterative and a direct approach to regularization. In particular, strategies for choosing the regularization parameter and the regularization matrix will be emphasized, eventually leading to the computation of approximate solutions of Tikhonov problems involving a regularization term expressed in some p-norms.
May 13	Wed	Tadahiro Oh (Edinburgh)	Probability seminar
14:00
		LT1
May 13	Wed	Lucia Menendez-Pidal De Cristina (University of Nottingham)	Cosmology, Relativity and Gravitation
15:00		Singularity resolution depends on the clock
		https://app.vscene.net/r/KjKhl4yTE4
	Abstract: We study the quantum cosmology of an FLRW universe filled with a free massless scalar field and a perfect fluid that can be interpreted either as dark energy, radiation or dust. As general relativity does not have a preferred time coordinate, we study two versions of the quantum theory using different dynamical variables as clocks. The general covariance of the classical theory is not conserved after quantisation. The two theories exhibit different behaviour regarding singularity resolution and hence this cosmological model serves as an illustration of the problem of time.
	Slides
May 14	Thu	Marianna Korsos (Aberystwyth University)	European Solar Physics Online Seminars (ESPOS)
10:00		Solar Flare Prediction Using Magnetic Field Diagnostics Above the Photosphere
		Zoom link: https://zoom.us/j/165498165
	Abstract: We present the application of the weighted horizontal gradient of magnetic field (WGM) flare prediction method to 3D extrapolated magnetic configurations of flaring solar ARs. The main aim is to identify an optimal height range, if any, in the interface region between the photosphere and lower corona, where the flare onset time prediction capability of WGM is best exploited. The optimal height is where flare prediction, by means of the WGM method, is achieved earlier than at the photospheric level. 3D magnetic structures, based on potential and non-linear force-free field extrapolations, are constructed to study a vertical range from the photosphere up to the low corona with a 45 km step size. We found that applying the WGM method between 1000 and 1800 km above the solar surface would improve the prediction of the flare onset time by around 2-8 hrs. Certain caveats and an outlook for future work along these lines are also discussed.
May 14	Thu	Marianna Korsos (Solar System Physics Group, Aberystwyth)	SP2RC/ESPOS seminar
10:00		By-weekly SP2RC/ESPOS joint seminar: Solar Flare Prediction Using Magnetic Field Diagnostics Above the Photosphere
		Zoom
	Abstract: We present the application of the weighted horizontal gradient of magnetic field (WGM) flare prediction method to 3D extrapolated magnetic configurations of flaring solar ARs. The main aim is to identify an optimal height range, if any, in the interface region between the photosphere and lower corona, where the flare onset time prediction capability of WGM is best exploited. The optimal height is where flare prediction, by means of the WGM method, is achieved earlier than at the photospheric level. 3D magnetic structures, based on potential and non-linear force-free field extrapolations, are constructed to study a vertical range from the photosphere up to the low corona with a 45 km step size. We found that applying the WGM method between 1000 and 1800 km above the solar surface would improve the prediction of the flare onset time by around 2-8 hrs. Certain caveats and an outlook for future work along these lines are also discussed.
May 14	Thu	Pak-Hin Lee (Warwick)	Number Theory seminar
15:00		A p-adic L-function for non-critical adjoint L-values
		Google hangout
	Abstract: Let f be a classical eigenform, and K be an imaginary quadratic field with associated quadratic character $\alpha$. By works of Hida and Tilouine--Urban, the value $L(1, ad(f) \otimes \alpha)$, which is non-critical in the sense of Deligne, measures congruences between f and (non-base-change) Bianchi modular forms over K. In this talk, we will outline the construction of an analytic p-adic L-function interpolating these special values as f varies in a Hida family. Our approach is based on Greenberg--Stevens' idea of $\Lambda$-adic modular symbols, which considers cohomology with values in a space of p-adic measures.
May 14	Thu	Sarah Whitehouse (Sheffield)	Topology Seminar
16:00		Multicomplexes and their homotopy theory
		meet.google.com/hdp-cfvn-wak
	Abstract: A multicomplex is an algebraic structure generalizing the notion of a (graded) chain complex and that of a bicomplex. The structure involves a family of higher “differentials” indexed by the non-negative integers. The terms twisted chain complex and D-infinity-module are also used. Multicomplexes have arisen in many different places and play an important role in homotopical and homological algebra. I'll try to survey some of this landscape and talk about joint work with Xin Fu, Ai Guan and Muriel Livernet giving a family of model category structures on multicomplexes.
May 14	Thu	Steven Julious (Sheffield)	Statistics Seminar
16:00		Florence Nightingale: The Passionate Statistician
		https://teams.microsoft.com/l/meetup-join/19%3ameeting_YjVlZTY1NTItNGU4Mi00N2ZjLThmYWEtM2Y1NjExNjc5MTA1%40thread.v2/0?context=%7b%22Tid%22%3a%2219c3a1c9-f583-4a18-b6ad-75cc9c14243c%22%2c%22Oid%22%3a%22da5c99d8-843a-4aa7-84c2-29a3732945ed%22%7d
	Abstract: The Passionate Statistician was the title given to Florence Nightingale by her first biographer Sir Edward Cook. Florence Nightingale was a firm believer in the accurate quantification of evidence to inform decisions. It was her belief in the accurate collection and presentation of data that informed the work she undertook to improve military hospitals. She was of the view that “to understand God’s thoughts, we must study statistics for these are the measure of His purpose” and she used her statistical abilities to inform debates that led to a decline in preventable deaths in military and civilian hospitals. This year marks 200 years since the birth of Florence Nightingale and in this talk Steven will pay tribute to her work in statistics and its long lasting impact. The webinar will take place on Microsoft Teams - you can join on the web or on the Teams app (if you have it), but you should not need to have an account.
May 19	Tue	Prof Anthony Yeates (Durham)
11:00		SP2RC/UK-SOSS joint monthly seminar: Where do solar eruptions come from?
	Abstract: An oft-quoted idea in solar physics is that coronal mass ejections are, fundamentally, the Sun's way of shedding the magnetic helicity that is continually generated by its interior flows. In this talk, I will show how models are helping to give us a handle on the build up of magnetic helicity in the corona (the Sun's lower atmosphere): how much is injected, where it collects, and how it is ultimately ejected. This requires time-evolving coronal magnetic field models as well as new tools for analysing the distribution of magnetic helicity.
May 19	Tue	Giordano Cotti (Birmingham)	Algebra / Algebraic Geometry seminar
14:00
		ONLINE
May 20	Wed	Didier Leibovici (SoMaS)	Applied Mathematics Colloquium
14:00		On spatio-temporal entropy based methods for data science
		Google Meet
	Abstract: The entropy, as a metric to describe if a distribution tends to be uniform (high entropy) or not can be useful in data science to highlight spatio-temporal structures (low entropy). The seminar looks into complementary aspects of multiway data analysis deriving from a tensor decomposition and the use of entropy within a spatio-temporal context. Derived from practices in landscape ecology, a framework based on size and shapes of patches within a spatio-temporal context is used in conjunction with the entropy decomposition theorem or with a tensor decomposition approach. Combined with statistics, such as co-occurrences of observations or specific distance ratios instead of occurrence counts, to define pseudo-distributions to derive spatio-temporal entropies, the framework allows a range of analyses. Along the path some examples are illustrating involved connexe methods, some of which can be found in the references below. Leibovici DG and Claramunt C (2019) On Integrating Patch Size and Shape Distributions into a Spatio-Temporal Information Entropy Framework Entropy, 21(11):1112 (special issue) Leibovici DG, Brosset D, Claramunt C, and Jackson M (2015 ) k-Co-occurrences Density Map Estimation. Spatial Statistics Conference: Emerging Patterns, 9-12th of June 2015, Avignon, France, Procedia Environmental Sciences, 26: 105-109. Leibovici DG, and Birkin MH (2015) On Geocomputational Determinants of Entropic Variations for Urban Dynamic Studies. Geographical Analysis, 47 (3): 193-218 Leibovici DG, Bastin L, and Jackson M (2011) " Higher-Order Co-occurrences for Exploratory Point Pattern Analysis and Decision Tree Clustering on Spatial Data." Computers & Geosciences: 37(3): 382-389 Leibovici DG, (2010) " Spatio-temporal Multiway Decomposition using Principal Tensor Analysis on k-modes: the R package PTAk." Journal of Statistical Software, 34(10), 1-34
	Slides
May 20	Wed	Alessandra Caraceni (Oxford)	Probability seminar
14:00
		LT1
May 20	Wed	Kieran Finn (University of Manchester)	Cosmology, Relativity and Gravitation
15:00		Frame Covariance in Quantum Gravity
		https://app.vscene.net/r/KjKhl4yTE4
	Abstract: The laws of physics should not depend on how we choose to describe them. However, this is exactly what happens in the standard formulation of quantum field theories. The effective action receives different quantum corrections depending on how we parametrise our fields and even Feynman diagrams can yield results that depend on the definition of the fields we choose to work with. In this talk I will rectify these problems by introducing the notion of frame covariance, in which the quantum fields are treated as coordinates on a manifold, known as the field space. Field redefinitions are then simply diffeomorphisms of this manifold and thus we can impose reparametrisation invariance using well-known techniques from differential geometry. This talk is based on arXiv:1910.06661.
	Slides
May 21	Thu	Shu Sasaki (Queen Mary)	Number Theory seminar
10:00		Serre's conjecture about weight of mod p modular forms: old conjectures, not so old theorems and new conjectures​
		Google hangout
	Abstract: In 1987, J.-P. Serre made a set of conjectures about weights and levels of two-dimensional (modular) mod p Galois representations of the absolute Galois group of Q. This conjecture of Serre has been completely proved by C. Khare and J.-P. Wintenberger (2009) building on the work of many mathematicians, but it has also inspired a good deal of new mathematics. One strand of research spurred on by the development is about generalising Serre's conjecture over to a (general) totally real number field. This was initiated by the work (2009) of K. Buzzard, F. Diamond and F. Jarvis, while focusing exclusively on regular weights of mod p Hilbert modular forms. In my joint work with F. Diamond, we have improved on the Buzzard-Diamond-Jarvis conjectures and formulated new conjectures about general weights of (geometric) mod p Hilbert modular forms (analogous to what B. Edixhoven did in 1992). I will explain what our conjectures say exactly, and demonstrate some evidence that we are on the right track. In support of our vision, I will also explain a comparatively new result (joint work with F. Diamond and P. Kassaei) about a Jacquet-Langlands relation between mod p geometric `Hilbert modular forms', which may well shed some light on the problem of formulating a putative mod p Langlands philosophy.
May 21	Thu	Gong Show	Topology Seminar
16:00
		Hicks Seminar Room J11
May 21	Thu	José Juan González Avilés (Laboratorio Nacional de Clima Espacial, SCiESMEX-LANCE. Morelia (Mexico))	Plasma Dynamics Group
16:00		Numerical studies of jet formation in the solar atmosphere
		Google Meet
	Abstract: Using the Newtonian CAFE MHD code to perform 2.5D and 3D resistive MHD simulations in the solar atmosphere, we show that magnetic reconnection may be responsible for the formation of jets with some characteristics of Type II spicules and cool coronal jets. We numerically model the photosphere-corona region using the C7 atmosphere model. The initial magnetic configuration in the 2.5D case consists of two symmetric neighboring loops with opposite polarity, used to support reconnection. In the 3D case, the initial magnetic configuration is extrapolated up to the solar corona region from a dynamic realistic simulation of the solar photospheric magnetoconvection model that mimics the quiet-Sun. In the 2.5D simulations, we include the effect of the thermal conduction along the magnetic field lines to study some properties of spicule jets. In this case, we find that thermal conductivity affects morphology, velocity, and temperature of the jets. Also, the heat flux maps indicate the head of the jet and corona interchange energy more efficiently than the body of the jet. In the 3D simulations, we have found that the formation of the jet depends on the Lorentz force, which helps to accelerate the plasma upward. The morphology, the upward velocity covering a range up to 130 km/s, and the timescale formation of the structure between 60 and 90 s, are similar to those expected for Type II spicules. Additionally, we analyze various properties of the jet dynamics, and find that the structure shows rotational and torsional motions which may generate torsional Alfvén waves in the corona region.
May 22	Fri	Matthew Allcock (Sheffield)	SP2RC seminar
13:00		Breaking Symmetry: Theory and Observations of Asymmetric Solar Waveguides
		Google Meet
	Abstract: 50 years of solar MHD wave theory has focussed on waveguides in symmetric plasma environments. Yet the Sun’s inhomogeneous atmosphere allows for waveguides to be held in asymmetric equilibrium. We break symmetry by studying a slab model embedded in an asymmetric external plasma in three ways: Eigenvalue problem: We derive the dispersion relation and show that asymmetric eigenmodes have mixed properties of the traditional sausage and kink modes. Ray theory: We demonstrate how a ray theoretic approach can be used to derive this dispersion relation, giving particular insight into the nature of asymmetric leaky modes. Initial value problem: Given an initial impulse, the time-dependence of MHD waves in these waveguides is studied. Next, we embark on deriving a magneto-seismology technique to estimate the magnetic field strength in waveguides embedded in asymmetric external plasmas. We apply this to a series of solar chromospheric fibrils as a proof of concept and we finish by identifying ambiguities in eigenmode identification.
May 27	Wed	Adam Butler (BIOSS)	Statistics Seminar
14:00
		LT 6
May 27	Wed	Minmin Wang (Sussex)	Probability seminar
14:00
		LT7
May 27	Wed	Philippe Brax (Universite Paris-Saclay)	Cosmology, Relativity and Gravitation
15:00		Charged Dark matter and H0 tension
		https://app.vscene.net/r/KjKhl4yTE4
	Abstract: I will describe recent models of non-linear electrodynamics with charged dark matter and their cosmological consequences. In particular, I will emphasize the inhomogeneous nature of the resulting cosmology. This follows from the screening of the extra U(1) in a way akin to the K-mouflage mechanism of modified gravity. I will eventually argue that this may have some applications to the local dynamics vs large scale structure of the Universe and the H0 tension.
May 28	Thu	Juraj Lorinčík (Astronomical Institute of the Czech Academy of Sciences, ASU (Czech Republic))	European Solar Physics Online Seminars (ESPOS)
10:00		Understanding hooks of solar flare ribbons and the evolution of coronal mass ejections
		Zoom https://zoom.us/j/165498165
	Abstract: Solar flares and eruptions are one of the most energetic phenomena occuring in the solar system. They are typically described by the cartoon-like 2D Standard model of solar flares. This model is however not capable of describing J-shaped (hooked) solar flare ribbons, bright elongated structures typically observed in the UV part of the spectrum. Their description requires 3D MHD modelling of magnetic flux ropes, bundles of twisted field lines rooted in the hooked endings of flare ribbons. The standard flare model in three dimensions, developed in the Observatory of Paris, was recently used to find predictions on how do the field lines reconnect during solar eruptions with respect to the positions of flare ribbons (Aulanier & Dudík 2019, A&A, 621, 72). Authors of this study identified three geometries involving field lines composing and/or surrounding the erupting flux rope. With a help of high-resolution EUV data, these were identified in a series of publications focused on eruptive events. Using data from the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory, we will present the manifestations of the different 3D reconnection scenarios and discuss under what conditions can their constituents be observed.
May 28	Thu	Juraj Lorinčík (Astronomical Institute of the Czech Academy of Sciences)	SP2RC/ESPOS seminar
10:00		By-weekly SP2RC/ESPOS joint seminar: Understanding hooks of solar flare ribbons and the evolution of coronal mass ejections
		Zoom
	Abstract: Solar flares and eruptions are one of the most energetic phenomena occuring in the solar system. They are typically described by the cartoon-like 2D Standard model of solar flares. This model is however not capable of describing J-shaped (hooked) solar flare ribbons, bright elongated structures typically observed in the UV part of the spectrum. Their description requires 3D MHD modelling of magnetic flux ropes, bundles of twisted field lines rooted in the hooked endings of flare ribbons. The standard flare model in three dimensions, developed in the Observatory of Paris, was recently used to find predictions on how do the field lines reconnect during solar eruptions with respect to the positions of flare ribbons (Aulanier & Dudík 2019, A&A, 621, 72). Authors of this study identified three geometries involving field lines composing and/or surrounding the erupting flux rope. With a help of high-resolution EUV data, these were identified in a series of publications focused on eruptive events. Using data from the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory, we will present the manifestations of the different 3D reconnection scenarios and discuss under what conditions can their constituents be observed.
Jun 3	Wed	Visakan Balakumar (University of Sheffield)	Cosmology, Relativity and Gravitation
00:00		Hadamard renormalisation for a charged scalar field
		https://app.vscene.net/r/KjKhl4yTE4
	Abstract: The Hadamard renormalisation method provides a powerful and axiomatic approach to renormalising the stress-energy tensor in the study of quantum fields in curved spacetime. This procedure has been developed by Decanini and Folacci for massive neutral scalar fields in a general spacetime of arbitrary dimension. Motivated by the study of superradiant scattering in Reissner–Nordström black holes, we extend their work to include charged scalar fields in spacetimes with a classical, background gauge field and explicitly demonstrate the Hadamard renormalisation procedure in four dimensions.
	Slides
Jun 4	Thu	Suzana de Souza e Almeida Silva (Technological Institute of Aeronautics, Sao Paulo)	Plasma Dynamics Group
16:00		Dynamics of Vortex Tubes in the Solar Atmosphere
		Google Meet
	Abstract: We use a state of the art vortex detection method, Instantaneous Vorticity Deviation, to define and locate three-dimensional vortices in magneto-convections simulations performed by the MURaM code. The detected vortices extend from the photosphere to the low chromosphere. The dynamics across the vortical flows at different height levels are investigated through radial profiles. We found that the vortices present similar dynamics at all height levels, with nonuniform angular rotational velocity and eddy viscosity effects. The vortices intensify the magnetic field, and in turn, the vortex dynamics are affected by the magnetic field. On the other hand, our findings hint that kinematic vortices need to present high tangential velocities at different height levels to overcome the magnetic tension and generate magnetic vortices.
Jun 5	Fri	Professor Peng-Fei Chen (Nanjing University, China)	SP2RC seminar
13:00		Formation and dynamics of solar filaments
		https://zoom.com.cn/j/169636835
	Abstract: Filaments, or called prominences when appearing above the solar limb, are a spectacular phenomenon in the solar atmosphere. Their formation is strongly related to chromospheric heating, their oscillations can be applied to derive the otherwise unmeasurable coronal magnetic field, and their eruptions are directly related to solar flares and coronal mass ejections (CMEs). All these explain why solar filaments have attracted wide attention in the solar community. More importantly, similar structures exist in the intergalactic medium associated with active galactic nuclei (AGN). Research on solar filaments with high resolutions can definitely shed light on the understanding of AGN filaments. In this talk, I will review our work on solar filaments formation and dynamics in the past decade, with an emphasis on our recent results.
Jun 11	Thu	Ajay Tiwari (Northumbria University)	European Solar Physics Online Seminars (ESPOS)
10:00		Study of damping of propagating kink waves in the solar corona
		Zoom: https://zoom.us/j/165498165
	Abstract: Propagating kink waves have been reported recently and have been found to be ubiquitous in the solar corona including in the quiet Sun. It is imperative to understand the mechanisms that enable their energy to be transferred to the plasma. Carrying on the legacy of the standing kink waves, mode conversion via resonant absorption is thought to be one of the main mechanisms for damping of these propagating kink waves, and is considered to play a key role in the process of energy transfer. We use the Doppler velocity images of the Coronal Multi-channel Polarimeter (CoMP) for the study of propagating kink waves in quiescent coronal loops. A coherence-based method is used to track the Doppler velocity signal of the waves, enabling an investigation into the spatial evolution of velocity perturbations. To enable accurate estimates of these quantities, the first derivation is provided of a likelihood function suitable for fitting models to the ratio of two power spectra obtained from discrete Fourier transforms. Maximum likelihood estimation is used to fit an exponential damping model to the observed variation in power ratio as a function of frequency. This also confirms earlier indications that propagating kink waves are undergoing frequency-dependent damping. Additionally, it is found that the rate of damping decreases for longer coronal loops that reach higher in the corona. The analysis techniques are used to create a statistical sample of quiescent loops to study the statistical properties of propagating kink waves and compare it to the studies of standing kink waves. It is noted that the damping for the propagating waves appears to be significantly weaker than that found from measurements of standing kink modes. The propagating kink waves also exhibit signatures of power amplification of waves. These propagating kink waves provide a new avenue to perform coronal magneto-seismology even during the quiet Sun period and this reliable method is not limited by requiring the eruptive activity of the Sun.
Jun 11	Thu	Ajay Tiwari (Northumbria)	SP2RC/ESPOS seminar
10:00		By-weekly SP2RC/ESPOS joint seminar: Study of damping of propagating kink waves in the solar corona
		Zoom
	Abstract: Propagating kink waves have been reported recently and have been found to be ubiquitous in the solar corona including in the quiet Sun. It is imperative to understand the mechanisms that enable their energy to be transferred to the plasma. Carrying on the legacy of the standing kink waves, mode conversion via resonant absorption is thought to be one of the main mechanisms for damping of these propagating kink waves, and is considered to play a key role in the process of energy transfer. We use the Doppler velocity images of the Coronal Multi-channel Polarimeter (CoMP) for the study of propagating kink waves in quiescent coronal loops. A coherence-based method is used to track the Doppler velocity signal of the waves, enabling an investigation into the spatial evolution of velocity perturbations. To enable accurate estimates of these quantities, the first derivation is provided of a likelihood function suitable for fitting models to the ratio of two power spectra obtained from discrete Fourier transforms. Maximum likelihood estimation is used to fit an exponential damping model to the observed variation in power ratio as a function of frequency. This also confirms earlier indications that propagating kink waves are undergoing frequency-dependent damping. Additionally, it is found that the rate of damping decreases for longer coronal loops that reach higher in the corona. The analysis techniques are used to create a statistical sample of quiescent loops to study the statistical properties of propagating kink waves and compare it to the studies of standing kink waves. It is noted that the damping for the propagating waves appears to be significantly weaker than that found from measurements of standing kink modes. The propagating kink waves also exhibit signatures of power amplification of waves. These propagating kink waves provide a new avenue to perform coronal magneto-seismology even during the quiet Sun period and this reliable method is not limited by requiring the eruptive activity of the Sun.
Jun 16	Tue	Professor Mitch Berger (Exeter University, UK)	SP2RC seminar
11:00		UK Solar Online Seminar Series (UK-SOSS) monthly seminar: Magnetic helicity - decompositions and methods of localization
		Zoom
	Abstract: Magnetic helicity is an ideal MHD invariant; it measures geometric and topological properties of a magnetic field. The talk will begin by reviewing helicity and its mathematical properties. It can be decomposed in several ways (for example, self and mutual helicity, Fourier spectra, field line helicity, linking, twist, and writhe). The talk will also review methods of measuring the helicity flux, as well as applications in solar and stellar astrophysics. I will then discuss some new developments in measuring localized concentrations of helicity in a well-defined, gauge invariant manner, using wavelets.
Jun 17	Wed	Hal Haggard (Bard College)	Cosmology, Relativity and Gravitation
15:00		The Black Hole Spin Puzzle, Black Hole Entropy, and Gravitational Wave Observations
		https://app.vscene.net/r/KjKhl4yTE4
	Abstract: Black hole entropy is a robust prediction of quantum gravity with no observational test to date. This entropy can be used to determine the probability distribution of the spin of black holes at equilibrium in the microcanonical ensemble. This ensemble, relevant for black holes formed in the early universe, predicts the existence of a population of black holes with zero spin. Observations of such a population at LIGO, Virgo, and future gravitational wave observatories would elucidate the statistical nature of black hole entropy and the origin of stellar mass black holes.
	Slides
Jun 18	Thu	Matheus Aguiar-Kriginsky Silva (Universitat de les Illes Balears (Spain))	Plasma Dynamics Group
16:00		Ubiquituous hundred-Gauss magnetic fields in solar spicules
		Google Meet
	Abstract: Even though they were observed for the first time in the 19th century, the nature of spicules is not well understood because they are are thin and elongated chromospheric jets and therefore their study is limited to the resolution of the instruments used. Every time a step forward in the quality of the observations of the lower chromosphere is taken, the interest in spicules sparks. Most recently, the advent of the Hinode telescope provided high-resolution images of spicules that allowed for a better comprehension of their nature and behavior. Studies regarding their magnetic field have been also undertaken, but most of them did not have the ideal spatial/temporal resolution needed to give definitive results. This study is aimed to provide a step forward in this matter, with observations in the Ca II 854.2 nm line taken with the CRISP instrument at the Swedish 1-meter Solar Telescope in La Palma. The sensitivity of the Ca II 854.2 nm line to the magnetic field is exploited and the Weak Field Approximation (WFA) is used to estimate the line-of-sight component of the magnetic field of spicules both off-limb and on the solar disk. The WFA must be used carefully, since there are conditions that need to be met for it to be applicable. This consideration is assessed in every pixel, and a Bayesian approach is taken to infer the line-of-sight magnetic field component from the WFA equations. It is established that magnetic fields over 100 G are abundant, and the reason for the failure of previous studies to conclude this is carefully studied and is speculated to lie in the poor temporal/spatial resolution of the observations used.
Jun 19	Fri	Dr David Long (Mullard Space Science Laboratory)	SP2RC seminar
13:00		Understanding the evolution of global waves in the low solar corona
		Google Meet
	Abstract: Global waves in the low solar corona have been a source of significant interest and investigation since their discovery using SOHO/EIT in 1997. The advent of very high spatial and temporal resolution observations with SDO/AIA has enabled a number of significant advances in our understanding of these phenomena. In particular, the interpretation of these features are large-amplitude waves or shocks is becoming more and more accepted in the community. However, questions still remain, particularly with regard to their relationship to other associated coronal phenomena. I will present recent work looking at the techniques commonly used to identify and track these global EUV waves which shows that current techniques using wave kinematics and perturbation profiles provide a useful insight into the properties of the waves. I then show how these techniques can be used to examine the relationship between global EUV waves and Moreton-Ramsey waves typically observed using H-alpha observations.
Jun 24	Wed	Ippocratis Saltas (CEICO)	Cosmology, Relativity and Gravitation
15:00		New tests of gravity at large and small scales in the Universe
		https://app.vscene.net/r/KjKhl4yTE4
	Abstract: In this talk, I will explain the implications of the recent measurement of the gravitational waves’ speed for large and small scales in the Universe. I will pay special focus on how the physics of stellar structure, and in particular helioseismology, can provide us with tight constraints on the residual scalar-gravity interactions.
Jun 25	Thu	Beatrice Popescu Braileanu (Instituto de Astrofísica de Canarias, IAC, Spain)	European Solar Physics Online Seminars (ESPOS)
10:00		Two-fluid simulations of Rayleigh-Taylor instability in a magnetized solar prominence thread: Effects of prominence magnetization and mass loading
		Zoom: https://zoom.us/j/165498165
	Abstract: Solar prominences are formed by partially ionized plasma with inter-particle collision frequencies generally warranting magnetohydrodynamic treatment. In this work, we explore the dynamical impacts and observable signatures of two-fluid effects in the parameter regimes when ion-neutral collisions do not fully couple the neutral and charged fluids. We perform 2.5D two-fluid (charges - neutrals) simulations of the Rayleigh-Taylor instability (RTI) at a smoothly changing interface between a solar prominence thread and the corona. The purpose of this study is to deepen our understanding of the RTI and the effects of the partial ionization on the development of RTI using non-linear two-fluid numerical simulations. Our two-fluid model takes into account viscosity, thermal conductivity, and collisional interaction between neutrals and charges: ionization/recombination, energy and momentum transfer, and frictional heating. We explore the sensitivity of the RTI dynamics to the prominence equilibrium configuration, including the impact of the magnetic field strength and shear supporting the prominence thread, and the amount of prominence mass-loading. We show that, at small scales, a realistically smooth prominence-corona interface leads to qualitatively different linear RTI evolution than that expected for a discontinuous interface, while magnetic field shear has the stabilizing effect of reducing the growth rate or eliminating the instability. In the non-linear phase, we observe that in the presence of field shear the development of the instability leads to formation of coherent and interacting 2.5D magnetic structures, which, in turn, can lead to substantial plasma flow across magnetic field lines and associated decoupling of the fluid velocities of charges and neutrals.
Jun 25	Thu	Beatrice Popescu Braileanu (Instituto de Astrofísica de Canarias)	SP2RC/ESPOS seminar
10:00		By-weekly SP2RC/ESPOS joint seminar: wo-fluid simulations of Rayleigh-Taylor instability in a magnetized solar prominence thread: Effects of prominence magnetization and mass loading
		Zoom
Jul 1	Wed	Nelson Nunes (University of Lisbon)	Cosmology, Relativity and Gravitation
15:00		Disformal couplings with a LambdaCDM background
		https://app.vscene.net/r/KjKhl4yTE4
	Abstract: The discovery of the accelerated expansion of the Universe is now very well established and the LambdaCDM paradigm is the strongest candidate to explain it. Nonetheless, there are tensions between the relatively high level of clustering found in cosmic microwave background experiments and the smaller one obtained from large-scale observations in the late Universe. A way to alleviate this issue is to consider a scalar field dark energy component conformally coupled to dark matter maintaining a LambdaCDM background cosmology. In this presentation we extend these studies to allow in addition disformal couplings which we explore by performing a dynamical system analysis.
Jul 2	Thu	Nitin Yadav (Max Planck Institute for Solar System Research, Gottingen, Germany)	Plasma Dynamics Group
16:00		Vortex Flows in the Solar Atmosphere
		Google Meet
	Abstract: Vortex flows exist over various spatial and temporal scales throughout the solar atmosphere and are of great importance due to their potential in twisting the magnetic field lines and hence facilitating Poynting flux transport. Recent advances in both, observational techniques and numerical simulations, have enabled us to detect a multitude of small-scale vortices in the solar atmosphere. Smaller vortices are suggested to play an important role in the solar atmospheric heating, however, their physical properties remain poorly understood due to limited resolution in observations. Hence, it is crucial to investigate them using high-resolution simulations since they are more abundant and faster rotating flows than the larger vortices. Using MHD simulations, we explored the the relationship between vortex flows at different spatial scales, analyze their physical properties, and investigate their contribution to Poynting flux transport from the lower to the upper layers of the solar atmosphere. We found that a large vortex, as seen at low spatial resolution, consists of a large number of smaller vortices, when seen at high spatial resolution. Statistically, they have higher densities and higher temperatures than the average values at the same geometrical height. Their Poynting flux contribution is more than adequate to compensate for the radiative losses in the chromosphere indicating their possible role in the solar atmospheric heating.
Jul 3	Fri	Professor Durgesh Tripathi (IUCAA)	SP2RC seminar
13:00		The Aditya-L1 Mission of Indian Space Research Organisation
		https://us02web.zoom.us/j/82382995948?pwd=aUFzNGhQYkNMckdCdU5CekpXZHdXZz09
	Abstract: The Aditya-L1 is the first mission of the Indian Space Research Organization (ISRO) dedicated to solar observations. The spacecraft will be located at the first Lagrangian point and will provide continuous observations of the Sun using remote sensing as well as in-situ measurements. The spacecraft will carry seven payloads, including a coronagraph that will image the corona in visible and IR wavelength and will provide measurements of coronal magnetic field and will study the dynamics of coronal mass ejections; a NUV imaging telescope to study the coupling between solar photosphere and chromosphere and to measure spatially resolved solar spectral irradiance and its variation. There will be two payloads to study the soft X-ray and hard X-ray emission from the Sun, two payloads for in-situ measurements of the charged particles and a magnetometer to study the magnetic field variations during energetic events. Some of the salient features of the experiments onboard Aditya-L1 mission will be discussed.
Jul 8	Wed	Robert Brandenberger (McGill University)	Cosmology, Relativity and Gravitation
15:00		Is Inflationary Cosmology Consistent with Fundamental Physics?
		https://app.vscene.net/r/KjKhl4yTE4
	Abstract: The inflationary scenario is currently the paradigm of early universe cosmology. However, an embedding of inflation into a fundamental theory is missing. I will first show that there are alternative early universe scenarios which are consistent with current observations. Hence, we do not require inflation to explain the data. Then I will discuss recent challenges which indicate that standard inflation is NOT consistent with fundamental physics. Specifically, I will discuss the "Swampland Criteria" and the "Trans-Planckian Censorship Conjecture".
Jul 17	Fri	Vaibhav Pant (KU Leuven)	SP2RC seminar
13:00		MHD simulations and forward modeling of transverse MHD waves in the solar atmosphere
		Google Meet
	Abstract: Several spectroscopic and imaging observations have established the ubiquity of transverse MHD waves in the solar atmosphere. Recently, an apparent discrepancy was noted in the measured wave energy flux in the transition region using SDO/AIA compared to those measured in the corona using Coronal Multi-channel Polarimeter (CoMP). Earlier studies have speculated that this discrepancy could be due to the unresolved wave amplitudes along the line-of-sight (LOS) in the solar atmosphere but they required the use of an additional, unknown source of wave energy to provide agreement with the measurements of the coronal non-thermal line widths. In this talk, I will resolve this discrepancy by presenting 3D MHD simulations of propagating transverse MHD waves in a gravitationally stratified plasma with properties similar to the coronal holes in the Sun. I will present the amount of underestimation of true energy in the MHD simulations due to the LOS superposition of different structures in the solar corona. This study could be useful in estimating the true wave energy flux using the observations of the nonthermal line widths from the upcoming solar observatories such as Solar orbiter, Aditya, UCoMP, etc.
Jul 23	Thu	Jonny Higham (University of Liverpool)	Plasma Dynamics Group
16:00		Modal Decompositions: What are they, why should we use them and how?
		Google Meet
	Abstract: The dynamics of natural systems are often complex and highly non-linear, understanding these procedures is difficult as their dynamics and complexities are usually intertwined and colluded. Whilst we might be able to identify these systems using sets of nonlinear equations, determining the individual process is underlying a complex mechanism are non-trivial. Over the past few decades, there has been much work to develop data driven methods to extract coherent features either in space or in time. Two prominent methods are the proper orthogonal decomposition and the dynamic mode decomposition; in this seminar these two methods will be introduced, the underpinning mathematics and algorithms will be outlined, and variants of the algorithms and methods will also be described. However, much of the seminar will focus on applying these methods, using them at all different scales from idealised small-scale laboratory experiments to large-scale real-world applications. The primary aim of this seminar will be to equip you with an arsenal of spatially and temporally orthogonal tools which you can use to elucidate the complex features from your data sets.
Jul 24	Fri	Fionnlagh Dover (SP2RC, University of Sheffield)	SP2RC seminar
13:00		MHD simulations of the morphology of spicular solar jets
		Google Meet
	Abstract: Solar spicules are one of the dominant dynamic phenomena of the lower solar atmosphere. Here, we show our results on modelling the propagation of such localised jets with a momentum pulse as the driving force near photospheric heights. Using the MPI-AMRVAC code to perform 2D MHD simulations in an idealised stratified solar atmosphere, we investigate how key parameters (e.g., driver time, equilibrium magnetic field strength and velocity amplitude of driver) determine the morphology of these small-scale solar jet. A parametric study is carried out and using jet tracking software we analyse the jet properties (e.g., widths, apex heights, etc). We find that jet boundary deformation occurs naturally due to speeds involved in driving these jets within the range of spicule heights that could be then a possible alternative explanation for the appearance of sausage and kink waves in solar jets. By resolving structures up to 10 km, we also find unforeseen substructures inside the spicular jet beam. We propose observers to confirm this latter finding that may be challenging due to current spatial resolution limits.
Jul 30	Thu	Isabell Piantschitsch (Universitat de les Illes Balears, Spain)	Plasma Dynamics Group
16:00		A new method for estimating global coronal wave properties from their interaction with solar coronal holes
		Google Meet
	Abstract: Global coronal waves (CWs) and their interaction with coronal holes (CHs) result, among other effects, in the formation of reflected and transmitted waves. Observations of such events provide us with measurements of different CW parameters, such as phase speed and intensity amplitudes. However, several of these parameters are provided with only intermediate observational quality, other parameters, such as the phase speed of transmitted waves, can hardly be observed in general. We present a new method to estimate crucial CW parameters, such as density and phase speed of reflected as well as transmitted waves, Mach numbers and density values of the CH's interior, by using analytical expressions in combination with basic and most accessible observational measurements. The transmission and reflection coefficients are derived from linear theory and subsequently used to calculate estimations for phase speeds of incoming, reflected and transmitted waves. The obtained analytical expressions are validated by performing numerical simulations of CWs interacting with CHs. This new method enables to determine in a fast and straightforward way reliable CW and CH parameters from basic observational measurements which provides a powerful tool to better understand the observed interaction effects between CWs and CHs.
Jul 31	Fri	William Oxley (SP2RC)	SP2RC seminar
12:30		Magnetohydrodynamic (MHD) Waves and Asymmetric Magnetic Slabs
		Google Meet
	Abstract: The field of solar magneto-seismology (SMS) is heavily reliant upon our understanding of magnetohydrodynamic (MHD) waves that occur in many solar features. In this talk I will discuss my two recent papers which build on previous studies of propagating MHD waves in asymmetric magnetic slabs. The new ideas in these studies are the assumptions of a line-tying boundary condition that causes standing waves to form. As with many wave studies, after setting up the model, the idea is to derive the dispersion relation which connects the wave number and the frequency of the waves supported by the waveguide. The goal is to derive expressions for observable quantities to lead order in the variables that represent the slab width and the asymmetry (which are both assumed to be small). After presenting these results I will discuss what we have learned, and how this is useful through solar magneto-seismology. The same techniques have been applied to the magnetic slab in both a magnetic and non-magnetic asymmetric environment, and comparisons between the two models will be made.
Sep 10	Thu	Olena Podladchikova (Physikalisch-Meteorologisches Observatorium Davos, PMOD/WRC, Switzerland)	European Solar Physics Online Seminars (ESPOS)
10:00		Stereoscopic Measurements of Coronal Doppler Velocities with Solar Orbiter
		Zoom
	Abstract: The Solar Orbiter mission, whose orbit is outside the Sun-Earth line, opens up novel opportunities for the combined analysis of measurements by solar imagers and spectrometers. For the first time different spectrometers will be located at wide angles with each other allowing 3D spectroscopy in the solar atmosphere. In order to develop a methodology for these opportunities, we make use of the Hinode EUV Imaging Spectrometer (EIS) and Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO) and by employing solar rotation we simulate the measurements of two spectrometers that have different views of solar corona. The resulting data allows us to apply stereoscopic tie-pointing and triangulation techniques designed for SECCHI (Sun Earth Connection Coronal and Heliospheric Investigation) imaging suite on the STEREO (Solar Terrestrial Relations Observatory) spacecraft pair and perform three-dimensional analysis of Doppler shifts of quasi-stationary active region. We present a technique that allows the accurate reconstruction of the 3D velocity vector in plasma flows along open and closed magnetic loops. This technique will be applied to the real situation of two spacecraft at different separations with spectrometers onboard. This will include the Solar Orbiter Spectral Imaging of the Coronal Environment (SPICE), the Solar Orbiter Extreme Ultraviolet Imager (EUI), the Interface Region Imaging Spectrograph (IRIS) and Hinode EIS spectrometers and we summarise how these can be coordinated. This 3D spectroscopy is a new research domain that will aid the understanding of the complex flows that take place throughout the solar atmosphere.
Sep 10	Thu	Olena Podladchikova (Physikalisch-Meteorologisches Observatorium Davos, PMOD/WRC, Switzerland)	SP2RC/ESPOS seminar
10:00		Stereoscopic Measurements of Coronal Doppler Velocities with Solar Orbiter
		Zoom
	Abstract: The Solar Orbiter mission, whose orbit is outside the Sun-Earth line, opens up novel opportunities for the combined analysis of measurements by solar imagers and spectrometers. For the first time different spectrometers will be located at wide angles with each other allowing 3D spectroscopy in the solar atmosphere. In order to develop a methodology for these opportunities, we make use of the Hinode EUV Imaging Spectrometer (EIS) and Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO) and by employing solar rotation we simulate the measurements of two spectrometers that have different views of solar corona. The resulting data allows us to apply stereoscopic tie-pointing and triangulation techniques designed for SECCHI (Sun Earth Connection Coronal and Heliospheric Investigation) imaging suite on the STEREO (Solar Terrestrial Relations Observatory) spacecraft pair and perform three-dimensional analysis of Doppler shifts of quasi-stationary active region. We present a technique that allows the accurate reconstruction of the 3D velocity vector in plasma flows along open and closed magnetic loops. This technique will be applied to the real situation of two spacecraft at different separations with spectrometers onboard. This will include the Solar Orbiter Spectral Imaging of the Coronal Environment (SPICE), the Solar Orbiter Extreme Ultraviolet Imager (EUI), the Interface Region Imaging Spectrograph (IRIS) and Hinode EIS spectrometers and we summarise how these can be coordinated. This 3D spectroscopy is a new research domain that will aid the understanding of the complex flows that take place throughout the solar atmosphere.
Sep 17	Thu	Prof. William Chaplin (University of Birmingham)	SP2RC seminar
10:00		UK Solar Online Seminar Series (UK-SOSS) monthly seminar: Probing the Solar Cycle with BiSON: The Solar-Stellar Connection
		Zoom
	Abstract: In this talk I will review how we are utilizing helioseismic observations made by the Birmingham Solar-Oscillations Network (BiSON) to provide unique inferences on the solar activity cycle, using its unprecedented long timebase dataset that is now extending into a fifth cycle. I will also discuss how we are using these data together with asteroseismic data, collected on other Sun-like stars by the NASA Kepler Mission, to provide a broader perspective on stellar activity and dynamo action in main-sequence stars.
Sep 24	Thu	Abhishek Rajhans (Inter-University Center for Astronomy and Astrophysics (IUCAA), Pune, India)	European Solar Physics Online Seminars (ESPOS)
10:00		Forward modelling and energetics of Hi-C brightenings
		Zoom
	Abstract: The Solar coronal heating problem remains a persistent challenge in astrophysics. Parker postulated back in 1988 that the heating of corona should be dominated by small energy dissipation events, referred to as nanoflares. However, there have not yet been any confirmed observations of individual nanoflares. Hi-C reported unique bright points with energies ranging between log[E(ergs)] = 24-25. Those brightenings were also identified in AIA passbands. Here, I will describe 0-D hydrodynamical simulations to forward model these tiny brightenings, study their energetics, and discuss possible implications for coronal heating.
Sep 24	Thu	Abhishek Rajhans (Inter-University Centre for Astronomy and Astrophysics, IUCAA (IN))	SP2RC/ESPOS seminar
11:00		Forward modelling and energetics of Hi-C brightenings
		Zoom
	Abstract: The Solar coronal heating problem remains a persistent challenge in astrophysics. Parker postulated back in 1988 that the heating of corona should be dominated by small energy dissipation events, referred to as nanoflares. However, there have not yet been any confirmed observations of individual nanoflares. Hi-C reported unique bright points with energies ranging between log[E(ergs)] = 24-25. Those brightenings were also identified in AIA passbands. Here, I will describe 0-D hydrodynamical simulations to forward model these tiny brightenings, study their energetics, and discuss possible implications for coronal heating.
Sep 30	Wed	Evgeny Shinder (Sheffield)
02:00		Algebraic Surfaces 1/12: Basic invariants and examples
		online in Blackboard collaborate (please e-mail Evgeny for the link)
Sep 30	Wed	Visakan Balakumar (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Quantum superradiance on static black hole space-times
		Blackboard Collaborate
	Abstract: We study the quantum analogue of the classical process of superradiance for a massless charged scalar field on a charged black hole space-time. We show that an “in” vacuum state, which is devoid of particles at past null infinity, contains an outgoing flux of particles at future null infinity. This radiation is emitted in the superradiant modes only, and is nonthermal in nature.
Oct 1	Thu	Rekha Jain (Sheffield)	Plasma Dynamics Group
16:00		Frequency power spectra of Alfvén waves in a solar coronal arcade: Discrete or Continuous?
		Google Meet
	Abstract: In this talk I will present theoretically computed frequency power spectra for shear Alfvén waves excited in a solar coronal arcade. I investigate two separate perturbations, a cosine-modulated Gaussian perturbation and an impulsive driver. The arcade is assumed to consist of potential magnetic field lines embedded in stratified plasma. In principle, the nature of the frequency power spectra can constrain the size and the type of driver.
Oct 2	Fri	Dr Teimuraz Zaqarashvili (University of Graz, Austria)	SP2RC seminar
13:00		Rossby waves and solar activity variations
		Google Meet
	Abstract: Recent progress in observations of Rossby-type waves on the Sun revived the interests towards the waves. Though the hydrodynamic Rossby waves are well studied in the Earth context, the ubiquitous existence of magnetic fields in the atmosphere/interior of the Sun requires to study the waves in magnetohydrodynamics. The talk will cover the recent direct observations of Rossby waves on the Sun, theoretical development of magneto-Rossby wave theory and the possible connection of the waves to observed long and short term variations in solar magnetic activity.
Oct 7	Wed	Reinder Meinsma
02:00		Algebraic Surfaces 2/12: Curves on surfaces, rational and algebraic equivalence of divisors
		online in Blackboard collaborate (please e-mail Evgeny for the link)
Oct 7	Wed	Katy Clough (Oxford)	Cosmology, Relativity and Gravitation
15:00		Initial conditions for inflation
		Blackboard Collaborate
	Abstract: Inflation solves a number of problems in early universe cosmology but potentially introduces some new ones regarding how it was able to get started in the first place. In this talk I will explain these issues in the context of single field slow roll inflationary models, and discuss how they might restrict the phase space of initial conditions and early universe models that we consider valid. I will describe work I have done using numerical relativity to investigate the problem in the non-linear regime.
Oct 8	Thu	Lucia Kleint (Leibniz Institute for Solar Physics (KIS), Germany))	European Solar Physics Online Seminars (ESPOS)
10:00		GREGOR - Optics Redesign, Updates, and First Images
		Zoom
	Abstract: GREGOR is Europe’s largest solar telescope. It has undergone significant upgrades and changes from 2018-2020 to improve the image quality, instrumentation, and operation. Particularly, a complete redesign of the optics laboratory was performed by KIS to obtain diffraction-limited images from the blue to the infrared. The new optics setup was completed while “trapped” on the mountain during the lockdown and we obtained first light images in July 2020. In this talk, I will summarize the most important updates, explain the new optics setup, and show the improved images.
Oct 8	Thu	Lucia Kleint (Leibniz Institute for Solar Physics (KIS), Germany)	SP2RC/ESPOS seminar
10:00		GREGOR - Optics Redesign, Updates, and First Images
		Zoom
	Abstract: GREGOR is Europe’s largest solar telescope. It has undergone significant upgrades and changes from 2018-2020 to improve the image quality, instrumentation, and operation. Particularly, a complete redesign of the optics laboratory was performed by KIS to obtain diffraction-limited images from the blue to the infrared. The new optics setup was completed while “trapped” on the mountain during the lockdown and we obtained first light images in July 2020. In this talk, I will summarize the most important updates, explain the new optics setup, and show the improved images.
Oct 14	Wed	Alberto Cobos Rabano (Sheffield)
02:00		Algebraic Surfaces 3/12: Intersection theory on surfaces, adjunction formula
		online in Blackboard collaborate (please e-mail Evgeny for the link)
Oct 14	Wed	Indira Chatterji (University of Nice)	Pure Maths Colloquium
14:00		Group ring conjectures and relative hyperbolicity
		Google Meet
	Abstract: The idempotent conjecture is that there should be no idempotent in the group ring of a torsion-free group. I will discuss this conjecture, as well as associated conjectures in some geometric context, and will use them as an excuse to discuss hyperbolicity and introduce relative hyperbolicity, a context in which some of these conjectures are still open.
Oct 14	Wed	Jose Cembranos (Complutense, Madrid)	Cosmology, Relativity and Gravitation
15:00		Disformal dark matter from brane-worlds
		Blackboard Collaborate
	Abstract: Scalar particles coupled to the Standard Model fields through a disformal coupling arise in different theories, such as massive gravity or brane-world models. We will review the main phenomenology associated with such particles. Distinctive disformal signatures could be measured at colliders and with astrophysical observations. The phenomenological relevance of the disformal coupling demands the introduction of a set of symmetries, which may ensure the stability of these new degrees of freedom. In such a case, they constitute natural dark matter candidates since they are generally massive and weakly coupled. We will illustrate these ideas by paying particular attention to the branon case, since these questions arise naturally in brane-world models with low tension, where they were first discussed.
Oct 15	Thu	Prof. Robertus Erdelyi (University of Sheffield)	SP2RC seminar
10:00		UK-SOSS: Waves and oscillations in the solar atmosphere
		Zoom (Meeting ID: 953 3817 1418)
	Abstract: Satellite and ground-based observations from e.g. SOHO, TRACE, STEREO, Hinode, SDO and IRIS to DST/ROSA, IBIS, CoMP, STT/CRISP have all provided a wealth of evidence of waves and oscillations present in a wide range of spatial and temporal scales of the magnetised solar atmosphere. Our understanding about localised solar structures has been considerably changed in light of these superb spatial and temporal resolution observations. However, MHD waves not only enable us to perform sub-resolution solar magneto-seismology (SMS) but are also potential candidates to carry and damp the observed non-thermal energy in localised MHD waveguides. First, we will briefly outline the basic recent developments in MHD wave theory focussing on linear MHD waves both in symmetric and asymmetric waveguides. This latter may be an important aspect for the fantastic kitty: DKIST. Next, we will concentrate on the role of the most frequently studied wave classes, including the mysterious Alfven, and magneto-acoustic sub-classes of kink and sausage waves. Finally, we will address how solar MHD waves, swirls and solar jet formation may be related. We will argue to unite MHD wave and jet theories and make efforts to develop a common modelling platform with solar applications. An example will be shown where prevalent swirls, in the form of Alfven pulses, propagate upwards through the solar atmosphere dragging with them jets and reach the chromospheric layers. We will argue why this maybe seen as an important step towards understanding better the heating problem of the solar atmosphere.
Oct 15	Thu	George Haller (ETH Zurich (Switzerland))	Plasma Dynamics Group
13:00		Objective material barriers to the transport of momentum and vorticity
		Google Meet
	Abstract: I discuss a recent theory for material surfaces that maximally inhibit the diffusive transport of a dynamically active (i.e., velocity-dependent) vector field, such as the linear momentum, the angular momentum or the vorticity, in three-dimensional unsteady flows. These diffusion barriers provide physics-based, observer-independent boundaries of dynamically active coherent structures. Instantaneous limits of these Lagrangian diffusion barriers mark objective Eulerian barriers to short-term active transport. I show how active diffusion barriers can be identified with active versions of Lagrangian coherent structure (LCS) diagnostics. In comparison to their passive counterparts, however, active LCS diagnostics require no significant fluid particle separation and hence provide substantially higher-resolved Lagrangian and Eulerian coherent structure boundaries from shorter velocity data sets. I illustrate these results on two-dimensional turbulence and three-dimensional wall-bounded turbulence.
Oct 20	Tue	Haluk Sengun (Sheffield)	Number Theory seminar
11:00		C*-algebras associated to locally compact groups and the Selberg trace formula
		Google meet
	Abstract: Given a locally compact group G, one can obtain C*-algebras by taking various completions of the convolution algebra of integrable functions on G. These C*-algebras sit in the intersection of representation theory, index theory and non-commutative geometry. In this talk, we will describe an identity, obtained in joint work with Bram Mesland (Leiden) and Hang Wang (Shanghai), that involves the K-groups of the C*-algebras of a semisimple Lie group G and of a cocompact lattice H in G. We will then argue that this identity is a K-theoretic analgoue of the celebrated Selberg trace formula. The talk is planned to be of expository nature.
Oct 20	Tue	Alberto Cobos Rabano
14:00		Alberaic Surfaces 4/12: Numerical equivalence, effective cone, numerical criterion for ampleness
		online in Blackboard collaborate (please e-mail Evgeny for the link)
Oct 21	Wed	Helen Alexander (Edinburgh)	Mathematical Biology Seminar
13:00		Stochastic establishment of antibiotic resistance
		Zoom
	Abstract: The probability of establishment (i.e. non-extinction) of a lineage is a fundamental quantity in stochastic process models, and a classical question in population genetics. One practical application, where the possibility of stochastic extinction has been largely overlooked, is the emergence of antibiotic-resistant lineages in bacterial populations. Once prevalent, antibiotic resistance can be very difficult to eradicate and has become a major public health concern. But could we stop de novo resistance evolution at the source by promoting extinction of initially rare resistant mutants? In this project, we quantified the probability of establishment of resistant bacterial cells by fitting a simple stochastic model to experimental data. Our key finding was that antibiotic doses that are too low to clear an established resistant population may nonetheless prevent outgrowth from single cells with high probability. In this talk I will also explain some experimental design considerations when attempting to quantify stochastic processes, and briefly discuss plans for future work combining experiments and population dynamics models.
Oct 21	Wed	Atsushi Higuchi (York)	Cosmology, Relativity and Gravitation
15:00		The Hartle-Hawking vacuum state in the Schwinger-Keldysh formalism for interacting scalar field theory
		Blackboard Collaborate
	Abstract: Schwarzschild and de Sitter spacetimes are spacetimes with bifurcate Killing horizons. It is known that the preferred vacuum state (the Hartle-Hawking state) in quantum field theory in these spacetimes is a thermal state in the static patch. For example, it is the thermal state with the Hawking temperature outside the horizon in the Schwarzschild case. It is also accepted that this state is obtained by analytic continuation from the corresponding Euclidean theory. In this talk, I will make this statement more precise in the context of the Schwinger-Keldysh (or in-in) perturbation theory. (This is a joint work in progress with William C C de Lima.)
Oct 22	Thu	Ricardo Gafeira (University of Coimbra, Portugal)	European Solar Physics Online Seminars (ESPOS)
10:00		Modernization of the spectroheliograph of Coimbra
		Zoom
	Abstract: The details study of the solar activity and variability on long term data series is an important element on the understanding of the solar dynamics and evolution. In addition, their activity influences several aspects of our lives, such as climate, communications, energy, aviation, and many other fields, sustaining and threatening, simultaneously, our entire technologically-based way of life. Hence, it is paramount to secure the continuity of unbroken and self-consistent data series of solar observations and its study. The associated physical processes and structures on the Sun span over a wide range of values regarding their lifetimes, intensities, and spatial scales. Ideally, to study all these different structures in detail, we need facilities that allow us to observe the full solar disk and spectrum with very high spectral, spatial, and temporal resolutions. Unfortunately, due to technical limitations that cannot be done and there are clear trade-offs to deal with. Even today, elements like spatial resolution versus field of view (FoV), spectral coverage versus temporal resolution, observation of spectral lines in local or non-local thermodynamic equilibrium (depending on the science driver) are among the obstacles that scientists need to keep in mind as limitations for their work. State-of-the-art solar telescopes like the US American 4-meter telescope DKIST, the German GREGOR telescope, or the Solar Orbiter, plus the next generation facilities like the balloon borne SUNRISE III mission, or the future European Solar Telescope will observe the Sun with unprecedented spatial and spectral resolutions. Even though they will use the most advanced technology they do not cover all possible modes of observation. Some key aspects like small FoVs, in some cases limited number of spectral lines or the short lifetime of instruments are among those that some other types of instruments can cover. The spectroheliograph of OGAUC is one of the most durable solar instruments still operating. Having been upgraded only twice, one for new optics and another for digital image recording, it keeps daily observations since 1927. Until now this instrument has been used to study structures visible in the solar atmosphere from their intensity images at specific wavelengths, ignoring most of the visible spectral range. One of the main reasons for that is the lack of tools to extract more information from that type of observations that need to be analysed in Non-Local Thermodynamic Equilibrium (NLTE) regime. However, with the new generation of spectropolarimetric inversion codes, we are now able to invert NLTE spectral lines to extract information about the temperature, the velocity and the magnetic field vector. Such analysis is already possible with several of the aforementioned telescopes, but they do not cover all the possible observing modes. In this project, we propose to take advantage of the operating infrastructure of the OGAUC spectroheliograph and to upgrade it, improving its spectral resolution, adding other spectral regions of interest and increasing the spatial sampling and add polarimetric sensitivity. Due to its flexibility, long term run and set of observed spectral lines and polarimetric sensitivity it will be a competitive state of the art instrument competing with the other solar synoptic (full disk) ground-based spectroheliograph of its category in the. This upgrade, in combination with the new NLTE inversion codes and neural network techniques will allow us to probe at chromospheric and photospheric heights the solar temperature, velocity and magnetic field.
Oct 22	Thu	Ricardo Gafeira (University of Coimbra (PT))	SP2RC/ESPOS seminar
10:00		Modernization of the spectroheliograph of Coimbra
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: The details study of the solar activity and variability on long term data series is an important element on the understanding of the solar dynamics and evolution. In addition, their activity influences several aspects of our lives, such as climate, communications, energy, aviation, and many other fields, sustaining and threatening, simultaneously, our entire technologically-based way of life. Hence, it is paramount to secure the continuity of unbroken and self-consistent data series of solar observations and its study. The associated physical processes and structures on the Sun span over a wide range of values regarding their lifetimes, intensities, and spatial scales. Ideally, to study all these different structures in detail, we need facilities that allow us to observe the full solar disk and spectrum with very high spectral, spatial, and temporal resolutions. Unfortunately, due to technical limitations that cannot be done and there are clear trade-offs to deal with. Even today, elements like spatial resolution versus field of view (FoV), spectral coverage versus temporal resolution, observation of spectral lines in local or non-local thermodynamic equilibrium (depending on the science driver) are among the obstacles that scientists need to keep in mind as limitations for their work. State-of-the-art solar telescopes like the US American 4-meter telescope DKIST, the German GREGOR telescope, or the Solar Orbiter, plus the next generation facilities like the balloon borne SUNRISE III mission, or the future European Solar Telescope will observe the Sun with unprecedented spatial and spectral resolutions. Even though they will use the most advanced technology they do not cover all possible modes of observation. Some key aspects like small FoVs, in some cases limited number of spectral lines or the short lifetime of instruments are among those that some other types of instruments can cover. The spectroheliograph of OGAUC is one of the most durable solar instruments still operating. Having been upgraded only twice, one for new optics and another for digital image recording, it keeps daily observations since 1927. Until now this instrument has been used to study structures visible in the solar atmosphere from their intensity images at specific wavelengths, ignoring most of the visible spectral range. One of the main reasons for that is the lack of tools to extract more information from that type of observations that need to be analysed in Non-Local Thermodynamic Equilibrium (NLTE) regime. However, with the new generation of spectropolarimetric inversion codes, we are now able to invert NLTE spectral lines to extract information about the temperature, the velocity and the magnetic field vector. Such analysis is already possible with several of the aforementioned telescopes, but they do not cover all the possible observing modes. In this project, we propose to take advantage of the operating infrastructure of the OGAUC spectroheliograph and to upgrade it, improving its spectral resolution, adding other spectral regions of interest and increasing the spatial sampling and add polarimetric sensitivity. Due to its flexibility, long term run and set of observed spectral lines and polarimetric sensitivity it will be a competitive state of the art instrument competing with the other solar synoptic (full disk) ground-based spectroheliograph of its category in the. This upgrade, in combination with the new NLTE inversion codes and neural network techniques will allow us to probe at chromospheric and photospheric heights the solar temperature, velocity and magnetic field.
Oct 26	Mon		Topology Reading Group
12:00		String Topology: Chas-Sullivan loop product
		Blackboard collaborate
Oct 27	Tue	Abhishek Saha (Queen Mary)	Number Theory seminar
11:00		The Manin constant and p-adic bounds on denominators of the Fourier coefficients of newforms at cusps
		Google meet
	Abstract: The Manin constant $c$ of an elliptic curve $E$ over $\mathbb{Q}$ is the nonzero integer that scales the differential $\omega_f$ determined by the normalized newform $f$ associated to $E$ into the pullback of a Néron differential under a minimal modular parametrization$\phi\colon X_0(N)_{\mathbb{Q}} \twoheadrightarrow E$. Manin conjectured that $c = \pm 1$ for optimal parametrizations. I will talk about recent work that makes progress towards this conjecture by establishing an integrality property of $\omega_f$ necessary for this conjecture to hold. Our result implies in particular that $c \mid \mathrm{deg}(\phi)$ under a minor assumption at $2$ and $3$ that is not needed for cube-free $N$ or for parametrizations by $X_1(N)_{\mathbb{Q}}$. We reduce the above results to $p$-adic bounds on denominators of the Fourier expansions of $f$ at all the cusps of $X_0(N)_{\mathbb{C}}$. We succeed in proving stronger bounds in the more general setup of newforms of general weight and levels by approaching the problem representation-theoretically. These idea is to study the $p$-adic valuations of the values of the Whittaker newform of $\mathrm{GL}_2$ over a nonarchimedean local field of characteristic 0, using techniques that were originally developed by me in the context of the analytic sup-norm problem. For local fields of odd residue charactertistic, this allows us to ultimately reduce to the classical facts about $p$-adic valuations of Gauss sums. To overcome obstacles at 2, we analyze nondihedral supercuspidal representations of $\mathrm{GL}_2 (\mathbb{Q}_2)$. This is joint work with K\k{e}stutis \v{C}esnavi\v{c}ius and Michael Neururer.
Oct 27	Tue	George Moulantzikos
14:00		Algebraic Surfaces 5/12: Birational maps, blow ups, contractions of (-1)-curves
		online in Blackboard collaborate (please e-mail Evgeny for the link)
Oct 28	Wed	Fordyce Davidson (Dundee)	Mathematical Biology Seminar
13:00		The Architecture of Biofilms
		Zoom
	Abstract: Biofilms are social communities of microbial cells that underpin diverse processes including sewage bioremediation, plant growth promotion and plant protection, chronic infections and industrial biofouling. They are hallmarked by the production of an extracellular polymeric matrix. One of the phenotypic consequences of biofilm formation is that resident microbes are highly resistant to physical stresses and antimicrobial agents. Rapid advances in molecular and microscopy techniques are revealing a rich array of novel, complex behaviours associated with biofilm formation. For example new data of the authors reveals that the leading edge of a class of biofilms advances as a result of an extraordinary complex process that defies simple mechanical analogue. Behind this leading edge the biofilm matures differentially in response to environmental conditions. We propose that in order to keep pace with these rapid advances in experimental methods demands the application of new theoretical tools. We discuss some standard theoretical approaches used by the authors, highlighting their limitation by presenting images and movies that have changed our perception. We invite a discussion of novel perspectives on modelling biofilm formation that may yield a deeper and more useful understanding. As a starting point, we propose that one such approach may result from a holistic view that treats these complex cell-matrix composites as dynamically active materials.
Oct 28	Wed	Clara Loeh (University of Regensburg)	Pure Maths Colloquium
14:00		Amenable covers
		Google Meet
	Abstract: A cover of a space by open subsets is amenable if these subsets all induce amenable images on the level of the fundamental group. In analogy with the LS-category, one can ask how small of an amenable cover one can find for a given space. By Gromov's vanishing theorem, simplicial volume is an example of an obstruction against the existence of small amenable covers. In this talk, I will put this result into context and I will briefly sketch an alternative proof for the vanishing theorem (joint work with Roman Sauer).
Oct 28	Wed	Harry Desmond (Oxford)	Cosmology, Relativity and Gravitation
15:00		Fifth force searches in galaxies
		Blackboard Collaborate
	Abstract: Fifth forces generically follow from new dynamical fields, and hence are ubiquitous in extensions to the standard model. Broad classes of Lagrangian exhibit "screening mechanisms" which hide the fifth force in high-density environments such as the Milky Way, while keeping it operative on larger scales. I will describe the search for fifth forces which act differently on different components of galaxies, e.g. through screening. First, I model the gravitational environments of the local Universe to determine the screening properties of real galaxies and the strength of the fifth-force field over space. I then use this information to forward-model two signals in galaxy morphology -- displacements of stars and gas and warping of stellar disks -- and hence infer fifth-force parameters with a Bayesian likelihood framework. Taking ~16,000 HI-cross-optical detections from the ALFALFA and SDSS surveys and ~4,000 galactic disk images from the Nasa Sloan Atlas, I set the strongest constraints to date on astrophysical fifth forces. Two particularly interesting applications are to f(R) and models such as coupled quintessence in which the fifth force acts only in the dark sector: for the former I require f_R0 < 1.4x10^-8 in the Hu-Sawicki model, and for the latter a fifth-force strength <10^-4 times that of gravity.
Oct 29	Thu	Inigo Arregui (Instituto de Astrofisica de Canarias (Spain))	Plasma Dynamics Group
16:00		Bayesian coronal seismology
		Google Meet
	Abstract: Coronal seismology is based on the remote diagnostics of physical conditions in the solar corona by comparison between model predictions and observations of wave activity. Our lack of direct access to the physical system of interest makes information incomplete and uncertain so our conclusions are at best probabilities. Bayesian inference is increasingly being employed in the area, following a general trend in solar and astrophysical research. In this seminar, I first justify the use of a Bayesian probabilistic approach to seismology diagnostics and explain its philosophy and methodology. Then, I report on recent results that demonstrate its feasibility and advantage in applications to coronal loops, prominences and extended regions of the corona. To finish, I suggest other areas of current interest where the use of Bayesian methods could contribute to improve our understanding on the structure, dynamics and heating of the corona.
Oct 30	Fri	Dr Norbert Gyenge (University of Sheffield)	SP2RC seminar
13:00		Temporal Analysis in Solar Physics
		Google Meet
	Abstract: This talk focuses on the latest tools and techniques of temporal analysis in solar physics. Performing a temporal analysis could be challenging because all the available commonly used tools, namely, Autocorrelation, Fourier-Transformation and Wavelet Analysis, have several advantages and disadvantages. The emphasis of this talk will be on choosing the proper technique for investigation, initialising raw data, choosing a noise profile to create significance intervals and interpreting the results. All these steps will be demonstrated by active research, focusing on the oscillatory behaviour of SDO Intensity images through all the available wavelengths.
Nov 2	Mon		Topology Reading Group
12:00		String Topology: Batalin-Vilkovisky Structure and String Bracket
		Blackboard collaborate
Nov 3	Tue	Pol van Hoften (KCL)	Number Theory seminar
11:00		On the discrete part of the Hecke-orbit conjecture
		Google meet
	Abstract: The Hecke-orbit conjecture, proposed by Chai and Oort, gives strong restrictions on the shape of Hecke-invariant subvarieties of special fibers of Shimura varieties. It consists of a continuous part, which predicts the dimensions of Hecke orbits, and a discrete part, which predicts that certain subvarieties called central leaves are irreducible. In this talk I will give an introduction to the discrete part of the Hecke orbit conjecture, focussing mostly on explicit low-dimensional examples, and discuss a geometric proof for Shimura varieties of Hodge type. The main idea is to use the geometry of Shimura varieties with bad reduction to prove the irreducibility of "distinguished" central leaves, and to deduce the general case using the almost-product structure of Newton strata.
Nov 3	Tue	Yannik Schuler
14:00		Algebraic Surfaces 6/12: Ruled surfaces
		online in Blackboard collaborate (please e-mail Evgeny for the link)
Nov 4	Wed	Matthew Hartfield (Edinburgh)	Mathematical Biology Seminar
13:00		Adaptation and Self–Fertilisation
		Zoom
	Abstract: Many organisms are hermaphrodites that are capable of self-fertilisation, where individuals produce both male and female sex cells that can fertilise one another. The degree of self-fertilisation affects the fixation of adaptive mutations; for example, selfers are more likely to fix recessive mutations than outcrossing organisms. Yet the effects of linked mutations on adaptive alleles, and the genetic footprint that beneficial mutations leave in genome sequence data obtained from self-fertilisation organisms, remain understudied topics. I will first discuss theoretical studies on how the spread of beneficial mutations affect the fixation of other linked selected alleles. Higher self-fertilisation rates increase the probability that linked deleterious alleles will fix alongside beneficial mutations, due to the resulting reduction in polymorphism and effective recombination. When considering a distribution of deleterious alleles, beneficial mutations generally need to be more recessive than predicted from single-locus results, for selfers to have higher overall fitness than outcrossers following a selective sweep. If recurrent adaptive mutation arises at a target site, then intermediate selfing rates maximize the fixation probability of linked recessive beneficial mutations. I will end by presenting results on the genetic footprint of adaptive mutations for different levels of dominance and self-fertilisation.
Nov 4	Wed	Ulrich Pennig (University of Cardiff)	Pure Maths Colloquium
14:00		Bundles of Algebras - Dixmier-Douady Theory and Beyond
		Google Meet
	Abstract: Intuitively a bundle of algebras is a collection of algebras continuously parametrised by a topological space. In operator algebras there are (at least) two different definitions that make this intuition precise: Continuous C(X)-algebras provide a flexible analytic point of view, while locally trivial C*-algebra bundles allow a classification via homotopy theory. The section algebra of a bundle in the topological sense is a C(X)-algebra, but the converse is not true. In this talk I will compare these two notions using the classical work of Dixmier and Douady on bundles with fibres isomorphic to the compacts as a guideline. I will then explain joint work with Marius Dadarlat, in which we showed that the theorems of Dixmier and Douady can be generalized to bundles with fibers isomorphic to stabilized strongly self-absorbing C*-algebras. An important feature of the theory is the appearance of higher analogues of the Dixmier-Douady class.
Nov 4	Wed	Jean-Luc Lehners (Max-Planck-Institute, Potsdam)	Applied Mathematics Colloquium
14:00		Path integrals, black holes and the beginning of the universe
		Google Meet
	Abstract: Quantum gravity promises to unveil the deepest mysteries about space, time and matter. But that is for the far future. In this talk, I will review recent progress in a less ambitious setting, namely in semi-classical gravity, which may be thought of as the leading order in hbar approximation to quantum gravity. I will discuss techniques for evaluating gravitational path integrals, both in the context of black holes and regarding the implications for the Hartle-Hawking no-boundary proposal. This not only shows a close relation between black holes and the big bang, but also provides clues for an effective description of the quantum origin of the universe.
Nov 5	Thu	Florian Regnault (Institut d'Astrophysique Spatiale, IAS, France)	European Solar Physics Online Seminars (ESPOS)
10:00		20 years of ACE data: how superposed epoch analysis reveal generic features in interplanetary CME profiles
		Zoom
	Abstract: Interplanetary Coronal Mass Ejections (ICMEs) result from the reconfiguration of magnetic fields in our star’s atmosphere. These large-scale magnetized structures propagate in the interplanetary medium where they can be probed by spacecraft. Depending on their speed, ICMEs may accumulate enough solar wind plasma to form a turbulent sheath ahead of them. They therefore consist of two main substructures : a sheath and a magnetic ejecta (ME). The magnetic ejecta is the main body of an ICME where the magnetic field is more intense and with less variance than that of the ambient solar wind. We present a statistical study using the superposed epoch analysis technique on a catalog of around 400 ICMEs where we consider the profiles of the physical parameters of the ICMEs (the magnetic field intensity, the speed, temperature, …) seen at 1 AU by the ACE spacecraft. We analyze the effects of the relative speed of ICMEs compared with the ambient solar wind to extract possible interactions between both.
Nov 5	Thu	Florian Regnault (Institut d’Astrophysique Spatiale, IAS (FR))	SP2RC/ESPOS seminar
10:00		20 years of ACE data: how superposed epoch analysis reveal generic features in interplanetary CME profiles
		Zoom (Meeting ID: 165 498 165)
Nov 9	Mon		Topology Reading Group
12:00		String Topology: Stable viewpoint and relation to Hochschild cohomology
Nov 10	Tue	George Moulantzikos
14:00		Algebraic Surfaces 7/12: Rational and del Pezzo surfaces
		online in Blackboard collaborate (please e-mail Evgeny for the link)
Nov 11	Wed	Sira Gratz (University of Glasgow)	Pure Maths Colloquium
14:00		Grassmannians, Cluster Algebras and Hypersurface Singularities
		Google Meet
	Abstract: Grassmannians are objects of great combinatorial and geometric beauty, which arise in myriad contexts. Their coordinate rings serve as a classical example of cluster algebras, as introduced by Fomin and Zelevinsky at the start of the millennium. Jensen, King and Su construct an additive categorification of these Grassmannian cluster algebras via maximal Cohen-Macaulay modules over certain plane curve singularities. Such a Grassmannian cluster category encodes key aspects of the cluster structure on the respective coordinate ring of a Grassmannian. Notably, Plücker coordinates naturally correspond to rank 1 modules. An interesting aspect of this relation is that it affords a formal connection between two famous examples of a priori unrelated ADE classifications, providing a bridge between skew-symmetric cluster algebras of finite type and simple plane curve singularities. In this talk, we take the above ideas to the limit: Taking colimits of Grassmannian cluster algebras gives rise to Grassmannian cluster algebras of infinite rank. We explore these structures combinatorially, and construct an infinite rank analogue of Jensen, King and Su’s Grassmannian cluster categories via maximal Cohen-Macaulay modules over certain hypersurface singularites – the Grassmannian categories of infinite rank. In particular, we investigate how Plücker coordinates are in natural correspondence with generically free modules of rank 1. This talk is based on joint work with Grabowski, and with August, Cheung, Faber, and Schroll.
Nov 11	Wed	Lisa Glaser (Vienna)	Cosmology, Relativity and Gravitation
15:00		Simulating spectral triples
		Blackboard Collaborate
	Abstract: A spectral triple consists of an algebra, a Hilbert space and a Dirac operator, the information contained in these is equivalent to that of a differential manifold. However it also offers avenues for generalization, since a general algebra can be non-commutative, which leads us to non-commutative geometry. In this talk I will introduce spectral triples and non-commutative geometry, and then from there move on to talking about my own work, using computer simulations to better understand the structure of spectral triples, and to visualize them.
Nov 12	Thu	Prof. Silvia Dalla (University of Central Lancashire)	SP2RC seminar
10:00		UK-SOSS: Solar Energetic Particles: origins and propagation
		Zoom link: https://zoom.us/j/95338171418 Meeting ID: 953 3817 1418
	Abstract: Solar Energetic Particles (SEPs) are ions and electrons detected in interplanetary space in association with flare and coronal mass ejection events. By propagating through the solar wind’s magnetic field, these particles may reach near-Earth locations, where they pose a radiation risk to humans in space and satellite hardware. This talk will review our understanding of the origin and transport of SEPs, based on a large body of data gathered by spacecraft detectors and on theoretical models. It will focus on recent results of test particle simulations, which show that accurate modelling of SEP propagation requires a 3D approach, due to guiding centre drifts and magnetic field line meandering.
Nov 12	Thu	Francisco Guzman (Universidad Michoacana de San Nicolas de Hidalgo, Mexico)	Plasma Dynamics Group
16:00		A code that solves the equations of MHD coupled to radiation
		Google Meet
	Abstract: Our code is based on a finite volume discretization, uses high-resolution shock-capturing flux formulae of the HLL class. Concerning the MHD part, we use the divergence cleaning method to preserve the non-monopoles constraint. For radiation, at the moment, we use the M1 closure relation within the gray body approximation. The evolution equations for radiation become stiff for high opacities, for which we use an implicit-explicit evolution method, which allows the use of a standard integration time-step. We present our code's status and mention the solar physics scenarios where we expect to produce some applications.
Nov 16	Mon		Topology Reading Group
12:00		String Topology: Operads (little framed discs)
		Blackboard collaborate
Nov 17	Tue	Ariel Weiss (Jerusalem)	Number Theory seminar
11:00		Lafforgue pseudocharacters and the construction of Galois representations
		Hicks Seminar Room J11
	Abstract: A key goal of the Langlands program is to attach Galois representations to automorphic representations. In general, there are two methods to construct these representations. The first, and the most effective, is to extract the Galois representation from the étale cohomology of a suitable Shimura variety. However, most Galois representations cannot be constructed in this way. The second, more general method is to construct the Galois representation, via its corresponding pseudocharacter, as a p-adic limit of Galois representations constructed using the first method. In this talk, I will demonstrate how the second construction can be refined by using V. Lafforgue’s G-pseudocharacters in place of classical pseudocharacters. As an application, I will prove that the Galois representations attached to certain irregular automorphic representations of U(a,b) are odd, generalising a result of Bellaïche-Chenevier in the regular case. This work is joint with Tobias Berger.
Nov 17	Tue	Yirui Xiong (Sheffield)
14:00		Algebraic Surfaces 8/12: Minimal models (nef K^2 or P^2 or ruled), uniqueness
		online in Blackboard collaborate (please e-mail Evgeny for the link)
Nov 18	Wed	Francesco Iorio (Human Technopole)	Mathematical Biology Seminar
13:00		CRISPR-cas9 screens and multi-omic data integration for identifying and new cancer therapeutic targets
		Zoom
	Abstract: Functional genomics approaches can overcome limitations -such as the lack of identification of robust targets and poor clinical efficacy- that hamper cancer drug development. We performed genome-scale CRISPR–Cas9 screens in 324 human cancer cell lines from 30 cancer types and developed a data-driven framework to prioritize candidates for cancer therapeutics. We integrated cell fitness effects with genomic biomarkers and target tractability for drug development to systematically prioritize new targets in defined tissues and genotypes. We verified one of our most promising dependencies, the Werner syndrome ATP-dependent helicase, as a synthetic lethal target in tumours from multiple cancer types with microsatellite instability. Our analysis provides a resource of cancer dependencies, generates a framework to prioritize cancer drug targets and suggests specific new targets. The principles described in this study can inform the initial stages of drug development by contributing to a new, diverse and more effective portfolio of cancer drug targets.
Nov 18	Wed	Andreagiovanni Reina (CS, Sheffield)
14:00		Collective Decision Making: From Bees to Robots via Multiscale Modelling
		Google Meet
	Abstract: I will give an overview of my studies on modelling and simulating collective decision making in distributed systems. Such systems, found in biology, sociology, and engineering, are composed of a large number of interacting individuals that coordinate in order to reach a consensus. The main phases of the collective decision making process consist of identifying the available options, estimating their quality, and selecting the best option or any of them. I will present the main results of my research in understanding and designing each of these phases. Collective systems are inherently difficult to analyse as the stochastic nonlinear interactions between individuals can give rise to complex emergent dynamics. Therefore, I employ a collection of advanced techniques, commonly defined as multiscale modelling. Relying on a set of methods, rather than a single one, gives the benefit of having complementary techniques addressing one another's limitations. In fact, through multiscale modelling, it is possible to analyse the systems at various levels of complexity and detail, from macroscopic group-level dynamics to microscopic individual-level behaviour, and from noise-free deterministic models to stochastic spatial descriptions. I finally shed a light on the recently developed opensource software for automated multiscale modelling. This software, called MuMoT, can also be a useful resource for remote teaching. For more info on MuMoT see (Marshall et al. PlosOne 2019) or MuMoT live notebook (https://mumot.readthedocs.io/). Bio: Dr Andreagiovanni Reina is a Research Fellow in Collective Robotics at the University of Sheffield, UK. He is currently working on the DiODe project (Distributed Algorithms for Optimal Decision-Making) led by Prof. James Marshall, and is the Principal Investigator of the Swarm Awareness project (https://swarmawareness.group.shef.ac.uk/). Andreagiovanni is the researcher responsible for more than 900 Kilobot robots and the related Augmented Reality for Kilobot (ARK) infrastructure at Sheffield Robotics. He holds a PhD in applied sciences from IRIDIA (Marco Dorigo's AI-Laboratory) of the Université Libre de Bruxelles, Belgium, and an M.Sc. in computer engineering from Politecnico di Milano, Italy. He has been a researcher in five European projects on distributed robotic systems since 2009. In December 2020, he plans to return to Brussels with an FNRS Fellowship on modelling heterogeneity in decentralised consensus. Full info at http://areina.staff.shef.ac.uk.
Nov 18	Wed	Sara Arias de Reyna (University of Seville)	Pure Maths Colloquium
14:00		Modular forms and the arithmetic of fields
		Google Meet
	Abstract: Modular forms are holomorphic functions on the upper half-plane which display some symmetry with respect to the action of a subgroup of $SL(2,\mathbb{Z})$. However, it turns out that they encode a great deal of arithmetic information about some field extensions of the rational numbers. This relationship has been fruitfully exploited to prove results in number theory, perhaps the more notorious being the proof of Fermat's Last Theorem by A. Wiles. In this talk we want to describe the interplay between these two subjects and provide an application of field arithmetic to the existence of certain families of weight one modular forms. This is joint work with François Legrand and Gabor Wiese.
Nov 18	Wed	Andreagiovanni Reina (CS, Sheffield)	Applied Mathematics Colloquium
14:00		Collective Decision Making: From Bees to Robots via Multiscale Modelling
		Google Meet
	Abstract: I will give an overview of my studies on modelling and simulating collective decision making in distributed systems. Such systems, found in biology, sociology, and engineering, are composed of a large number of interacting individuals that coordinate in order to reach a consensus. The main phases of the collective decision making process consist of identifying the available options, estimating their quality, and selecting the best option or any of them. I will present the main results of my research in understanding and designing each of these phases. Collective systems are inherently difficult to analyse as the stochastic nonlinear interactions between individuals can give rise to complex emergent dynamics. Therefore, I employ a collection of advanced techniques, commonly defined as multiscale modelling. Relying on a set of methods, rather than a single one, gives the benefit of having complementary techniques addressing one another's limitations. In fact, through multiscale modelling, it is possible to analyse the systems at various levels of complexity and detail, from macroscopic group-level dynamics to microscopic individual-level behaviour, and from noise-free deterministic models to stochastic spatial descriptions. I finally shed a light on the recently developed opensource software for automated multiscale modelling. This software, called MuMoT, can also be a useful resource for remote teaching. For more info on MuMoT see (Marshall et al. PlosOne 2019) or MuMoT live notebook (https://mumot.readthedocs.io/). Bio: Dr Andreagiovanni Reina is a Research Fellow in Collective Robotics at the University of Sheffield, UK. He is currently working on the DiODe project (Distributed Algorithms for Optimal Decision-Making) led by Prof. James Marshall, and is the Principal Investigator of the Swarm Awareness project (https://swarmawareness.group.shef.ac.uk/). Andreagiovanni is the researcher responsible for more than 900 Kilobot robots and the related Augmented Reality for Kilobot (ARK) infrastructure at Sheffield Robotics. He holds a PhD in applied sciences from IRIDIA (Marco Dorigo's AI-Laboratory) of the Université Libre de Bruxelles, Belgium, and an M.Sc. in computer engineering from Politecnico di Milano, Italy. He has been a researcher in five European projects on distributed robotic systems since 2009. In December 2020, he plans to return to Brussels with an FNRS Fellowship on modelling heterogeneity in decentralised consensus. Full info at http://areina.staff.shef.ac.uk.
Nov 18	Wed	Elisa Maggio (Sapienza, Rome)	Cosmology, Relativity and Gravitation
15:00		Gravitational wave signatures of exotic compact objects
		Blackboard Collaborate
	Abstract: Gravitational waves from the coalescence of compact binaries provide a unique opportunity to test gravity in strong field regime. In particular, the postmerger phase of the gravitational signal is a proxy for the nature of the remnant. This is of particular interest in view of some quantum-gravity models which predict the existence of horizonless exotic compact objects that overcome the paradoxes associated to black holes. Such exotic compact objects can emit a modified ringdown with respect to the black hole case and late-time gravitational wave echoes as characteristic fingerprints. In this talk, I develop a generic framework to the study of the ringdown of exotic compact objects and provide a gravitational-wave template for the echo signal. Finally, I assess the detectability of exotic compact objects with current and future gravitational-wave detectors.
Nov 19	Thu	Ryan Milligan (Queen’s University Belfast)	European Solar Physics Online Seminars (ESPOS)
10:00		Lyman-alpha Variability During Solar Flares
		Zoom
	Abstract: The chromospheric hydrogen Lyman-alpha line at 1216A is the brightest emission line in the solar spectrum, and yet studies of solar flares at this wavelength have been scarce in the literature over the past 50 years. The study of Lyman-alpha is important for understanding space weather effects as changes in the Sun’s Lyman-alpha output can drive changes in the dynamics and composition of planetary atmospheres. Lyman-alpha is also a significant radiator of solar flare energy, providing an important diagnostic of energy release and transport processes. Milligan et al. (2020) published a statistical study of ~500 M- and X-class flares using GOES/EUVS data, showing that although the Lyman-alpha irradiance increases by only a few percent during large events, it can radiate up to 100 times more energy than the corresponding X-rays. Flares that occurred closer to the solar limb, however, were found to exhibit a smaller Lyman-alpha enhancement relative to those on the disk due to opacity and/or foreshortening effects. It was also shown that acoustic oscillations in the chromosphere can be detected through Lyman-alpha flare observations, and that impulsive Lyman-alpha emission, not X-rays, can induce currents in the E-layer of Earth’s ionosphere. A follow-up study now includes B- and C-class flares, which although not readily observable in disk-integrated measurements, can be investigated using a superposed epoch analysis. Despite increases of <1% above the solar background, a clear centre-to-limb variation was found in agreement with larger events. These findings should serve as a baseline for the advent of new Lyman-alpha flare observations and advanced numerical simulations that will become available during Solar Cycle 25.
Nov 19	Thu	Ryan Milligan (Queen’s University Belfast, Astrophysics Research Centre (UK))	SP2RC/ESPOS seminar
10:00		Lyman-alpha Variability During Solar Flares
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: The chromospheric hydrogen Lyman-alpha line at 1216A is the brightest emission line in the solar spectrum, and yet studies of solar flares at this wavelength have been scarce in the literature over the past 50 years. The study of Lyman-alpha is important for understanding space weather effects as changes in the Sun’s Lyman-alpha output can drive changes in the dynamics and composition of planetary atmospheres. Lyman-alpha is also a significant radiator of solar flare energy, providing an important diagnostic of energy release and transport processes. Milligan et al. (2020) published a statistical study of ~500 M- and X-class flares using GOES/EUVS data, showing that although the Lyman-alpha irradiance increases by only a few percent during large events, it can radiate up to 100 times more energy than the corresponding X-rays. Flares that occurred closer to the solar limb, however, were found to exhibit a smaller Lyman-alpha enhancement relative to those on the disk due to opacity and/or foreshortening effects. It was also shown that acoustic oscillations in the chromosphere can be detected through Lyman-alpha flare observations, and that impulsive Lyman-alpha emission, not X-rays, can induce currents in the E-layer of Earth’s ionosphere. A follow-up study now includes B- and C-class flares, which although not readily observable in disk-integrated measurements, can be investigated using a superposed epoch analysis. Despite increases of <1% above the solar background, a clear centre-to-limb variation was found in agreement with larger events. These findings should serve as a baseline for the advent of new Lyman-alpha flare observations and advanced numerical simulations that will become available during Solar Cycle 25.
Nov 23	Mon		Topology Reading Group
12:00		String Topology: Cacti operad and the action on loop spaces
		Blackboard collaborate
Nov 24	Tue	Jaclyn Lang (Oxford)	Number Theory seminar
11:00		Images of two-dimensional pseudorepresentations
		Google meet
	Abstract: There is a general philosophy that the image of a Galois representation should be as large as possible, subject to its symmetries. This can be seen in Serre's open image theorem for non-CM elliptic curves, Ribet and Momose's work on Galois representations attached to modular forms, and recent work of the speaker and Conti-Iovita-Tilouine on Galois representations attached to p-adic families of modular forms. Recently, Bellaïche developed a way to measure the image of an arbitrary pseudorepresentations taking values in a local ring A. Under the assumptions that A is a domain and the residual representation is not too degenerate, we explain how the symmetries of such a pseudorepresentation are reflected in its image. This is joint work with Andrea Conti and Anna Medvedovsky.
Nov 24	Tue	Cristina Manolache (Sheffield)
14:00		Algebraic Surfaces 9/12: Surfaces with k = 0 (K3, Enriques, abelian, bielliptic)
		online in Blackboard collaborate (please e-mail Evgeny for the link)
Nov 25	Wed	Katrina Lythgoe (Oxford)	Mathematical Biology Seminar
13:00		Short-sighted viruses
		Zoom
	Abstract: With extremely short generation times and high mutability, many viruses can rapidly evolve and adapt to changing host environments. This ability allows viruses to evade host immune responses, evolve new behaviours, and exploit within-host ecological niches. However, natural selection typically generates adaptation in response to the immediate selection pressures that a virus experiences in its current host. Consequently, I will argue that some viruses, particularly those characterised by long durations of infection and ongoing replication, may be susceptible to short-sighted evolution, whereby a virus’ adaptation to its current host will be detrimental to its onward transmission within the host population. I will propose that viruses that are vulnerable to short-sighted evolution exhibit life history strategies that minimise its effects, and describe the various mechanisms by which this may be achieved. These concepts provide a new perspective on the way in which some viruses have been able to establish and maintain global pandemics.
Nov 25	Wed	Ailsa Keating (University of Cambridge)	Pure Maths Colloquium
14:00		Two-variable singularities and symplectic topology
		Google Meet
	Abstract: Start with a two-variable complex polynomial f with an isolated critical point at the origin. We will survey a range of classical structures associated to f, and explain how these can be revisited and enhanced using insights from symplectic topology. No prior knowledge of singularity theory or symplectic topology will be assumed.
Nov 25	Wed	Ivonne Zavala (Swansea)	Cosmology, Relativity and Gravitation
15:00		Multifield Inflation: Fat inflatons, large turns and the η-problem
		Blackboard Collaborate
	Abstract: I will discuss multifield models of inflation where all scalar fields are heavier than the Hubble scale, thus evading the η-problem. I will show how this is achieved in multifield inflation thanks to large turns in the field space, which I will introduce. I will then illustrate this scenario in a D5-brane model in Type IIB string flux compactifications, where the brane moves along the angular and radial directions in a warped throat driving fat D-brane natural-like inflation, with interesting cosmological predictions.
Nov 26	Thu	Petr Heinzel (Astronomical Institute, Czech Academy of Sciences)	Plasma Dynamics Group
16:00		Partial ionization of hydrogen plasma in the solar atmosphere - a non-LTE modeler's view
		Google Meet
	Abstract: Based on our extensive experience with the non-LTE radiative-transfer modeling of different atmospheric structures (chromosphere, flares, prominences, CME-cores), I will demonstrate the importance of partial hydrogen ionization and review the most relevant atomic processes. I will also discuss the role of non-equilibrium ionization of hydrogen.
Nov 27	Fri	Dr Krisztián Vida (CSFK)	SP2RC seminar
13:00		Coronal mass ejections on late-type stars
		Google Meet
	Abstract: In search of finding stellar CMEs we analyzed a large number of archive spectral observations of F-M dwarfs. While the F-K sample showed no events, M stars produced enough eruptions for statistical analysis. In this talk, I’ll summarize what we can learn from these detections and non-detections, and how this improves our knowledge on the possible habitability around these systems.
Dec 1	Tue	Neil Dummigan (Sheffield)	Number Theory seminar
11:00		Lifting congruences of modular forms to half-integral weight
		Google meet
	Abstract: In the situation where two newforms of the same level are congruent modulo some prime divisor, one can ask whether half-integral weight modular forms assigned to them by Kohnen's correspondence enjoy the same property. Under certain conditions, it is possible to prove this by proving a congruence (of Fourier coefficients, not just Hecke eigenvalues) between certain associated Siegel modular forms, the Saito-Kurokawa lifts.
Dec 1	Tue	Reinder Meinsma
14:00		Algebraic Surfaces 10/12: Elliptic surfaces
		online in Blackboard collaborate (please e-mail Evgeny for the link)
Dec 2	Wed	Mariya Ptashnyk (Heriot-Watt)	Mathematical Biology Seminar
13:00		Multiscale modelling of plants: Coupling between mechanics, chemistry and growth.
		Zoom
	Abstract: In multiscale modelling and analysis of the interplay between the mechanics, microscopic structure and the chemistry in plant tissues we shall assume that elastic properties of cell walls depend on the chemical processes, whereas chemical reactions depend on mechanical stresses within the cell walls. Numerical solutions for macroscopic models demonstrate heterogeneity in the cell wall displacement due to interactions between mechanical stresses, microstructure, and chemical processes. For plant growth we will consider macroscopic density-based models and microscopic description of growth processes on the plant cell level.
Dec 2	Wed	Yemon Choi (University of Lancaster)	Pure Maths Colloquium
14:00		Fourier algebras and dual convolution
		Google Meet
	Abstract: The Fourier transform provides a map between function spaces on a given abelian group G and function spaces on its dual group, which interchanges convolution and pointwise product. The functions on G that correspond to integrable functions on its dual group form a natural Banach algebra, known as the Fourier algebra of G. In the 1960s it was shown that one can extend the definition of the Fourier algebra to non-abelian groups, and the resulting Banach algebra has since been the subject of much study. In many cases there is also a corresponding version of the Fourier transform, but scalar-valued Fourier coefficients must be replaced by operator-valued Fourier coefficients. In this talk, which will mostly be expository, I will give a sketch of these constructions, focusing on some specific examples arising from groups such as SU(2) or the real ax+b group. I will then discuss the following natural but slightly ill-posed question: what operation on the "dual side" corresponds to pointwise product of functions in G? In particular, I will report on recent work (joint with M. Ghandehari) where we are able to describe the dual convolution explicitly for the real ax+b group. Time permitting, I will mention some applications to the study of derivations and cocycles on certain Fourier algebras.
Dec 2	Wed	Andrew Krause (Oxford)	Applied Mathematics Colloquium
14:00		Recent Progress & Open Frontiers in Turing-Type Morphogenesis
		Google Meet
	Abstract: Motivated by recent work with biologists, I will showcase some mathematical results on Turing instabilities in complex domains. This is scientifically related to understanding developmental tuning in the whiskers of mice, and more generally pattern formation on multiple scales and evolving domains. Such phenomena are typically modelled using reaction-diffusion systems of morphogens, and one is often interested in emergent spatial and spatiotemporal patterns resulting from instabilities of a homogeneous equilibrium, which have been well-studied. In comparison to the well-known effects of how advection or manifold structure impacts unstable modes in such systems, I will present results on instabilities in heterogeneous systems, as well as those arising in the setting of evolving manifolds. These contexts require novel formulations of classical dispersion relations, and may have applications beyond developmental biology, such as in population dynamics (e.g. understanding colony or niche formation of populations in heterogeneous environments). These approaches also help close the vast gap between the simple theory of diffusion-driven pattern formation, and the messy reality of biological development, though there is still much work to be done in validating even complex theories against the rich dynamics observed in nature.
Dec 2	Wed	Andrew Gow (Sussex)	Cosmology, Relativity and Gravitation
15:00		A History of the Universe in 100 Primordial Black Holes
		Blackboard Collaborate
	Abstract: A summary of the work completed during the course of my PhD so far, centred on the hypothesised Primordial Black Holes (PBHs). The talk will begin at the curvature power spectrum, and advance forward in time through the creation of PBHs and the intricacies of their mass distribution, culminating in the possibility of the LIGO gravitational wave signals being from PBH mergers, instead of astrophysics.
Dec 3	Thu	Meetu Verma (Leibniz-Institut für Astrophysik Potsdam (AIP), Germany)	European Solar Physics Online Seminars (ESPOS)
10:00		Classification of High-resolution Solar Hα Spectra using t-distributed Stochastic Neighbor Embedding
		Zoom
	Abstract: The Hα spectral line is a well-studied absorption line revealing properties of the highly structured and dynamic solar chromosphere. The presented work is based on high-spectral resolution Hα spectra obtained with the echelle spectrograph of the Vacuum Tower Telescope (VTT) located at Observatorio del Teide (ODT), Tenerife, Spain. The number of spectra accumulated at VTT over one observing day easily reaches up to millions. Hence, we require tools to identify and classify spectra with minimal human intervention. I will present exploratory work, which provides the framework and some ideas on how to tailor a classification scheme towards specific spectral data and science questions. t-distributed Stochastic Neighbor Embedding (t-SNE) is a machine learning algorithm, which is used for nonlinear dimensionality reduction. In this application, it projects Hα spectra onto a two-dimensional map, where it becomes possible to classify the spectra according to results of Cloud Model (CM) inversions. The CM parameters optical depth, Doppler width, line-of-sight velocity, and source function describe properties of the cloud material. Initial results of t-SNE indicate its strong discriminatory power to separate quietSun and plage profiles from those that are suitable for CM inversions. Furthermore, I will discuss our choice of various t-SNE parameters, the impact of seeing on classification, the results arising from various types of input data, and the link of the identified clusters to chromospheric features. Although t-SNE proves to be efficient in clustering high-dimensional data, human inference is required at each step to interpret the results.
Dec 3	Thu	Meetu Verma (Leibniz Institute for Astrophysics Potsdam (DE))	SP2RC/ESPOS seminar
11:00		Classification of High-resolution Solar Hα Spectra using t-distributed Stochastic Neighbor Embedding
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: The Hα spectral line is a well-studied absorption line revealing properties of the highly structured and dynamic solar chromosphere. The presented work is based on high-spectral resolution Hα spectra obtained with the echelle spectrograph of the Vacuum Tower Telescope (VTT) located at Observatorio del Teide (ODT), Tenerife, Spain. The number of spectra accumulated at VTT over one observing day easily reaches up to millions. Hence, we require tools to identify and classify spectra with minimal human intervention. I will present exploratory work, which provides the framework and some ideas on how to tailor a classification scheme towards specific spectral data and science questions. t-distributed Stochastic Neighbor Embedding (t-SNE) is a machine learning algorithm, which is used for nonlinear dimensionality reduction. In this application, it projects Hα spectra onto a two-dimensional map, where it becomes possible to classify the spectra according to results of Cloud Model (CM) inversions. The CM parameters optical depth, Doppler width, line-of-sight velocity, and source function describe properties of the cloud material. Initial results of t-SNE indicate its strong discriminatory power to separate quietSun and plage profiles from those that are suitable for CM inversions. Furthermore, I will discuss our choice of various t-SNE parameters, the impact of seeing on classification, the results arising from various types of input data, and the link of the identified clusters to chromospheric features. Although t-SNE proves to be efficient in clustering high-dimensional data, human inference is required at each step to interpret the results.
Dec 8	Tue	Jun Su (Cambridge)	Number Theory seminar
11:00		Arithmetic group cohomology with generalised coefficients
		Google Meet
	Abstract: Cohomology of arithmetic subgroups, with algebraic representations as coefficients, has played an important role in the construction of Langlands correspondence. Traditionally the first step to access these objects is to view them as cohomology of sheaves on locally symmetric spaces and hence connect them with spaces of functions. However, sometimes infinite dimensional coeffients also naturallhy arise, e.g. when you try to attach elliptic curves to weight 2 eigenforms on GL_2/an imaginary cubic field, and the sheaf theoretic viewpoint might no longer be fruitful. In this talk we'll explain a very simple alternative understanding of the connection between arithmetic group cohomology (with finite dimensional coefficients) and function spaces, and discuss its application to infinite dimensional coefficients.
Dec 8	Tue	Ananyo Dan
14:00		Algebraic Surfaces 11/12: Surfaces of general type
		online in Blackboard collaborate (please e-mail Evgeny for the link)
Dec 9	Wed	Philip O'Neill (Nottingham)	Mathematical Biology Seminar
13:00		Statistical Inference for epidemic models via likelihood approximation
		Zoom
	Abstract: Individual-level stochastic models for infectious diseases invariably describe how the disease is transmitted from one individual to another. Conversely, in real life we rarely observe transmission, but instead we observe symptoms of disease. In many settings this complicates statistical inference because the likelihood of the observed data is intractable. Although methods such as data-augmented MCMC can deal with this, they can struggle in large-population settings. In this talk we describe a way to approximate the likelihood using interactions between pairs of individuals in the population.
Dec 9	Wed	Kathryn Hess (École Polytechnique Fédérale de Lausanne)	Pure Maths Colloquium
14:00		Topological insights in neuroscience
		Google Meet
	Abstract: Over the past decade, research at the interface of topology and neuroscience has grown remarkably fast. Topology has, for example, been successfully applied to objective classification and digital synthesis of neuron morphologies, to automatic detection of network dynamics, and to the construction of a powerful and parameter-free mathematical framework for relating the activity of a network of neurons or brain regions to its underlying structure, both locally and globally. In this talk I will present a medley of recent applications of topology to neuroscience, many of which resulted from close collaboration with the Blue Brain Project.
Dec 9	Wed	Gary Mirams (Nottingham)	Applied Mathematics Colloquium
14:00		Selecting and parameterising a model for a potassium ion channel's dynamics
		Google Meet
	Abstract: There are a wide range of suggested models in the literature for how the hERG potassium channel opens and closes in response to changes in the voltage across cell membranes. These are typically ODE models with a handful of state variables and up to tens of parameters. Experiments can clamp voltage and measure the resulting current, but we'd like to be able to predict the current in new (unseen) situations that might occur in different cells, people and conditions. In this talk, I'll describe our efforts to choose and parameterise a model, by using novel experimental designs with rapidly fluctuating input waveforms, as well as a strict separation between training and validation of the models. The rapid experiments have allowed us to make cell-specific models and to create a parameterisation for a mutant channel which sheds light on why the mutant may increase the risk of cardiac arrhythmias. We've also used high-throughput measurements to look at cell-cell variability and to examine the temperature-dependence of channel opening. I'll discuss some of the open challenges in tying together experimental design for ion channel models with selection, parameterisation, validation and assessment of discrepancy/misspecification.
Dec 10	Thu	Prof Philippa Browning (University of Manchester)	SP2RC seminar
10:00		UK-SOSS: Heating and particle acceleration in twisted flux ropes in solar and stellar flares
		LT 11
	Abstract: Twisted magnetic flux ropes are reservoirs of free magnetic energy. I will describe some recent advances in modelling plasma heating and non-thermal particle acceleration in twisted magnetic flux ropes in the context of solar flares. After an overview of twisted magnetic flux ropes in the corona, I will show how magnetic reconnection in fragmented current structures in kink-unstable twisted loops can both heat plasma and efficiently accelerate both electrons and ions. Forward modelling of the observational signatures of this process in EUV, hard X-rays and microwaves will be described, and the potential for observational identification of twisted magnetic fields in the solar corona discussed. Furthermore, the reconnection activity can drive oscillations which may be observable as oscillations in the microwave emission. Then, coronal loops with multiple twisted threads will be considered, showing how instability in a single unstable twisted thread may trigger reconnection with stable neighbours, releasing their stored energy and causing an “avalanche” of heating events, with important implications for solar coronal heating. This avalanche can also accelerate charged particles throughout the structure. Many other stars exhibit flares, and I will briefly describe recent work on modelling radio emission in flares in young stars (T Tauri stars). In particular, the enhanced radio luminosity of these stars relative to scaling laws for the Sun and other Main Sequence stars will be discussed.
Dec 10	Thu	Richard Morton (University of Northumbria)	Plasma Dynamics Group
16:00		A new seismology of the corona
		Google Meet
	Abstract: The Coronal Multi-channel Polarimeter (CoMP) instrument has proved itself invaluable for the study of propagating kink waves in the corona. After making the initial discovery back in 2007, CoMP has been able to provide a number of insights into the properties of the kink waves. The kink mode is found to be present throughout the corona and appears to be continuous. The widespread and reliable presence means that the propagating kink mode can make a fantastic tool for magneto-seismology. While CoMP shows a persistent Doppler velocity signal related to the propagating kink mode, the continuous transverse motions of the coronal structures can also be detected with Solar Dynamics Observatory (SDO/AIA). However the scale of the displacements are at the edge of the SDO's capabilities, requiring careful measurements to be able to study them and exploit them for seismology. In this talk I discuss the new possibilities for coronal seismology using the propagating kink mode, demonstrating how we’ve used both CoMP and SDO/AIA to measure the young solar wind, the density structure in a coronal hole and provide the first estimates for the global coronal magnetic field.
Dec 15	Tue	Evgeny Shinder (Sheffield)
14:00		Algebraic Surfaces 12/12: Final overview of the classification of surfaces
		online in Blackboard collaborate (please e-mail Evgeny for the link)
Dec 16	Wed	Marina Iliopoulou (University of Kent)	Pure Maths Colloquium
14:00		A discrete Kakeya-type inequality
		Google Meet
	Abstract: The Kakeya conjectures of harmonic analysis claim that congruent tubes that point in different directions rarely meet. In this talk we discuss the resolution of an analogous problem in a discrete setting (where the tubes are replaced by lines), and provide some structural information on quasi-extremal configurations. This is joint work with A. Carbery.
Dec 16	Wed	Konstantinos Zygalakis (Edunburgh)	Applied Mathematics Colloquium
14:00		Hybrid modeling for the stochastic simulation of multi-scale chemical kinetics
		Google Meet
	Abstract: It is well known that stochasticity can play a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be adequately modeled by Markov processes and, for such systems, methods such as Gillespie’s algorithm are typically employed. While such schemes are easy to implement and are exact, the computational cost of simulating such systems can become prohibitive as the frequency of the reaction events increases. This has motivated numerous coarse-grained schemes, where the “fast” reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation for systems where all reactants are present in large concentrations, the approximation breaks down when the fast chemical species exist in small concentrations, giving rise to significant errors in the simulation. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as computing observables of cell cycle models. In this talk, we present a hybrid scheme for simulating well-mixed stochastic kinetics, using Gillespie–type dynamics to simulate the network in regions of low reactant concentration, and chemical Langevin dynamics when the concentrations of all species are large. These two regimes are coupled via an intermediate region in which a “blended” jump-diffusion model is introduced. Examples of gene regulatory networks involving reactions occurring at multiple scales, as well as a cell-cycle model are simulated, using the exact and hybrid scheme, and compared, both in terms of weak error, as well as computational cost. If there is time, we will also discuss the extension of these methods for simulating spatial reaction kinetics models, blending together partial differential equation with compartment based approaches, as well as compartment based approaches with individual particle models.
Dec 16	Wed	Antonia Micol Frassino (ICC, Barcelona)	Cosmology, Relativity and Gravitation
15:00		Exotic and quantum BTZ black holes
		Blackboard Collaborate
	Abstract: In this talk, I will discuss some black hole solutions in three-dimensional gravity that manifest interesting properties. In particular, I will consider the three-dimensional Einstein-AdS action in the presence of a gravitational Chern-Simons term and focus on a family of geometries that goes from the BTZ black hole to its 'exotic' counterpart. Then, in the context of braneworld holography, I will describe the holographic construction of the quantum rotating BTZ black hole (quBTZ) using an exact four-dimensional bulk solution. I will present some of the thermodynamic properties of these black holes, focus on the generalized first law and discuss possible further developments.
Dec 17	Thu	Fionnlagh Mackenzie Dover (Sheffield)	European Solar Physics Online Seminars (ESPOS)
10:00		MHD simulations and the morphology of spicular solar jets
		Zoom
	Abstract: Solar spicules are one of the dominant dynamic phenomena of the lower solar atmosphere. Here, we show our results on modelling the propagation of such localised jets driven by a momentum pulse as the exciting force near photospheric heights. Using the MPI-AMRVAC code to perform 2D MHD simulations in an idealised stratified solar atmosphere, we investigate how key parameters (e.g., driver time, equilibrium magnetic field strength, velocity amplitude of driver and tilt with respect to the magnetic field) determine the morphology of these small-scale solar jets. A parametric study is carried out and using jet tracking software we analyse the jet properties (e.g., widths, apex heights, etc). We find that jet boundary deformation occurs naturally due to speeds involved in driving these jets within the range of spicule heights that could be then a possible alternative explanation for the appearance of transverse motions (both axisymmetric and non-axisymmetric deformations). By resolving structures up to 10 km, we also find unforeseen substructures inside the spicular jet beam. We propose observers to confirm this latter finding that may be challenging due to current spatial resolution limits.
Dec 17	Thu	Fionnlagh Mackenzie Dover (University of Sheffield, Solar Physics and Space Plasma Research Centre (UK))	SP2RC/ESPOS seminar
10:00		MHD simulations and the morphology of spicular solar jets
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: Solar spicules are one of the dominant dynamic phenomena of the lower solar atmosphere. Here, we show our results on modelling the propagation of such localised jets driven by a momentum pulse as the exciting force near photospheric heights. Using the MPI-AMRVAC code to perform 2D MHD simulations in an idealised stratified solar atmosphere, we investigate how key parameters (e.g., driver time, equilibrium magnetic field strength, velocity amplitude of driver and tilt with respect to the magnetic field) determine the morphology of these small-scale solar jets. A parametric study is carried out and using jet tracking software we analyse the jet properties (e.g., widths, apex heights, etc). We find that jet boundary deformation occurs naturally due to speeds involved in driving these jets within the range of spicule heights that could be then a possible alternative explanation for the appearance of transverse motions (both axisymmetric and non-axisymmetric deformations). By resolving structures up to 10 km, we also find unforeseen substructures inside the spicular jet beam. We propose observers to confirm this latter finding that may be challenging due to current spatial resolution limits.
Jan 14	Thu	Sudheer K. Mishra (Indian Institute of Technology, BHU, India)	European Solar Physics Online Seminars (ESPOS)
10:00		The Kelvin-Helmholtz Instability in the Fan-spine Magnetic Topology in the Solar Corona
		Zoom
	Abstract: Using multi-wavelength imaging observation obtained from the Atmospheric Imaging Assembly (AIA) onboard Solar Dynamics Observatory (SDO), we study the evolution of Kelvin-Helmholtz (K-H) instability in a fan-spine magnetic topology. This fan-spine configuration is situated near the Active Region 12297 and is rooted in a nearby sunspot. The two layers of the cool plasma flows lift up from the fan plane in parallel and interact with each other at the maximum height of the elongated spine in the lower corona. The first layer of the plasma flow (F1) moving with a slow velocity (5 km/s) reflected from the spine’s field lines. Subsequently second layer of plasma flow (F2) with impulsive velocity (114-144 km/s) interacts with the first layer at the maximum height and generating the shear motion , which is responsible for the evolution of the Kelvin-Helmholtz instability inside the elongated spine. The amplitude and characteristics wavelength of the K-H unstable vortices increases, which satisfy the linear growing mode of this instability. Using linear stability theory of the K-H instability, we calculate the Alfvén velocity in the lower layer. We conjecture that the estimated shearing velocity is higher than the estimated the Alfvén velocity in the second denser layer, which also satisfies the classical criterion of K-H instability. The fan-spine configuration possesses magnetic field and sheared velocity component, we estimate the parametric constant [Λ≥1] which confirms that the velocity shear dominates and the linear phase of the K-H instability is evolved. The present observation indicate that in the presence of complex magnetic field structuring and plasma flows, the K-H instability evolve in the fan-spine configuration may evolve the rapid heating, and connectivity changes may occur due to the fragmentation via the K-H instability. It also act as a rapid mechanism to transfer the mass and energy release between two distinct regions separated by the fan-spine configuration.
Jan 14	Thu	Sudheer K. Mishra (Indian Institute of Technology, BHU, India)	SP2RC/ESPOS seminar
10:00		The Kelvin-Helmholtz Instability in the Fan-spine Magnetic Topology in the Solar Corona
		Zoom link: https://zoom.us/j/165498165
	Abstract: Using multi-wavelength imaging observation obtained from the Atmospheric Imaging Assembly (AIA) onboard Solar Dynamics Observatory (SDO), we study the evolution of Kelvin-Helmholtz (K-H) instability in a fan-spine magnetic topology. This fan-spine configuration is situated near the Active Region 12297 and is rooted in a nearby sunspot. The two layers of the cool plasma flows lift up from the fan plane in parallel and interact with each other at the maximum height of the elongated spine in the lower corona. The first layer of the plasma flow (F1) moving with a slow velocity (5 km/s) reflected from the spine’s field lines. Subsequently second layer of plasma flow (F2) with impulsive velocity (114-144 km/s) interacts with the first layer at the maximum height and generating the shear motion , which is responsible for the evolution of the Kelvin-Helmholtz instability inside the elongated spine. The amplitude and characteristics wavelength of the K-H unstable vortices increases, which satisfy the linear growing mode of this instability. Using linear stability theory of the K-H instability, we calculate the Alfvén velocity in the lower layer. We conjecture that the estimated shearing velocity is higher than the estimated the Alfvén velocity in the second denser layer, which also satisfies the classical criterion of K-H instability. The fan-spine configuration possesses magnetic field and sheared velocity component, we estimate the parametric constant [Λ≥1] which confirms that the velocity shear dominates and the linear phase of the K-H instability is evolved. The present observation indicate that in the presence of complex magnetic field structuring and plasma flows, the K-H instability evolve in the fan-spine configuration may evolve the rapid heating, and connectivity changes may occur due to the fragmentation via the K-H instability. It also act as a rapid mechanism to transfer the mass and energy release between two distinct regions separated by the fan-spine configuration.
Jan 21	Thu	Professor Valery M Nakariakov (Centre for Fusion, Space & Astrophysics, University of Warwick, United Kingdom)	SP2RC seminar
10:00		UK-SOSS: Magnetohydrodynamic Seismology of the Solar Coronal Plasma with Kink Oscillations
		Zoom link: https://zoom.us/j/95338171418
	Abstract: Standing transverse oscillations of the plasma loops of the solar corona have been intensively studied for the last 20 years as a tool for the diagnostics of the coronal magnetic field. Those oscillations are confidently interpreted as standing fast magnetoacoustic kink modes of the plasma non-uniformities. Statistical analysis demonstrates that, in the majority of cases, the oscillations are excited by a mechanical displacement of the loop from an equilibrium by a low coronal eruption. Standing kink oscillations are observed to operate in two regimes: rapidly decaying large amplitude oscillations and undamped small amplitude oscillations. In both these regimes, different loops oscillate with different periods that scale with the oscillating loop length. The oscillation amplitude does not show dependence on the loop length or the oscillation period. In the decayless regime the damping should be compensated by energy supply which allows the loop to perform almost monochromatic oscillations with almost constant amplitude and phase. We developed a low-dimensional model explaining the undamped kink oscillations as a self-oscillatory process caused by the effect of negative friction, which is analogous to producing a tune by moving a bow across a violin string. The period of self-oscillations is determined by the frequency of the kink mode. The ubiquity of decayless kink oscillations makes them an excellent tool for MHD seismology, in particular, for probing free magnetic energy in preflaring active regions.
Jan 27	Wed	Theo Torres Vicente (Nottingham)	Cosmology, Relativity and Gravitation
15:00		Electromagnetic self-force on a charged particle on Kerr spacetime
		Blackboard Collaborate
	Abstract: In this talk, we consider the electromagnetic radiation-reaction/self-force process for a charged particle orbiting a rotating black hole. We will present and complement the existing results for the scalar and gravitational cases, to give a full picture of integer spins in the Kerr spacetime. We restrict ourselves to the case of circular orbits and we will compute the dissipative and conservative components of the electromagnetic self-force numerically, by solving the inhomogeneous Teukolsky equations using the BHperturbation toolkit. The results will be compared to the scalar and gravitational cases found in the literature.
Jan 28	Thu	Ben Snow (University of Exeter)	European Solar Physics Online Seminars (ESPOS)
10:00		Collisional ionisation, recombination, and ionisation potential in two-fluid shocks
		Zoom
	Abstract: Shocks are a universal feature of warm plasma environments, such as the lower solar atmosphere and molecular clouds, which consist of both ionised and neutral species. Including partial ionisation leads to the existence of a finite width for shocks, where the ionised and neutral species decouple and recouple. As such, drift velocities exist within the shock that lead to frictional heating between the two species, in addition to adiabatic temperature changes across the shock. The local temperature enhancements within the shock alter the recombination and ionisation rates and hence change the composition of the plasma. We study the role of collisional ionisation and recombination in slow-mode partially ionised shocks. In particular, we incorporate the ionisation potential energy loss and analyse the consequences of having a non-conservative energy equation. A semi-analytical approach is used to determine the possible equilibrium shock jumps for a two-fluid model with ionisation, recombination, ionisation potential, and arbitrary heating. Two-fluid numerical simulations are performed using the (PIP) code. Results are compared to the magnetohydrodynamic (MHD) model and the semi-analytic solution. Accounting for ionisation, recombination, and ionisation potential significantly alters the behaviour of shocks in both substructure and post-shock regions. In particular, for a given temperature, equilibrium can only exist for specific densities due to the radiative losses needing to be balanced by the heating function. A consequence of the ionisation potential is that a compressional shock will lead to a reduction in temperature in the post-shock region, rather than the increase seen for MHD. The numerical simulations pair well with the derived analytic model for shock velocities.
Feb 5	Fri	Dr. Sijie Yu (Center for Solar-Terrestrial Research, New Jersey Institute of Technology)	SP2RC seminar
13:00		Dynamic imaging spectroscopy at radio wavelength: new insight into energetic processes on the Sun
		Google Meet
	Abstract: Thanks to recent advances in radio interferometric instrumentation, we've entered a new era of solar radio observations---broadband dynamic imaging spectroscopy. In this talk, I will first introduce the history of solar radio observations based on either total-power (integrated over the Sun) dynamic spectral measurements or imaging at a few discrete frequencies, then review some recent progress based on dynamic imaging spectroscopy over a wide frequency range that has placed us in a strong position to make revolutionary breakthroughs in understanding high-energy processes in the solar corona. Future perspectives will also be briefly discussed.
Feb 10	Wed	Kevin Painter (Politecnico di Torino)	Applied Mathematics Colloquium
14:00		Sticking together by going against the flow
		Google Meet
	Abstract: The formation of swarms, schools, flocks, herds, aggregates etc is a classical example of self-organisation, with the benefits of forming a high density group ranging from efficient migration to higher fecundity. Often, groups form through a mechanism of chemical signalling between population members, an evolutionary ancient communication used by both microscopic and macroscopic species. Populations in fluid environments, though, must contend with complex and turbulent flows, potentially detrimental (e.g. splitting up groups) or beneficial (e.g. coalescing individuals) to the formation and maintenance of a group. As a counter to flow, rheotaxis describes a behaviour in which individuals orient their body axis with respect to the current and is observed in both unicellular and multicellular organisms . Here we investigate the extent to which rheotaxis and flow impact on chemically-mediated aggregation, revealing these can impact both negatively and positively according to the population state and flow conditions. A hypothesised density-dependent rheotaxis appears capable of optimising group formation and maintenance, exploiting the positive benefits from each of flow and rheotaxis. The results are discussed in the context of broadcast swarming phenomena in marine invertebrates.
Feb 10	Wed	Luke Hart (Manchester)	Cosmology, Relativity and Gravitation
15:00		Reading between the lines: the hidden secrets of recombination
		Blackboard Collaborate
	Abstract: Cosmological recombination has been widely regarded a solid pillar of understanding the cosmic microwave background (CMB) and its anisotropies. For many years, the questions have been answered over the accuracy of these calculations due to exceptional codes as CosmoRec and HyRec as well as numerous publications on the intricate atomic processes. However, the era that dawned the formation of hydrogen and helium atoms has still given us brilliant insights into exotic physics as well as tribalistic disputes in the various pockets of modern cosmology. In this talk, we will briefly recap the physics of recombination before highlighting extensions to the standard model (parametric and non-parametric) that affect the surface of last scattering. Finally, we will look to the future probes that provide a direct, spectral handprint of the atomic transitions in hydrogen and helium: the recombination radiation. Here we will conclude with the feasibility of studying these lines with prospective missions such as SuperPIXIE, Voyage 2050 and what happens when the exotic physics modifications that we can test with the CMB anisotropies are propagated through to the SEDs from recombination.
Feb 10	Wed	Paul Johnson
15:00		Cones and affine toric varieties
		meet.google.com/mob-kmps-rhe
Feb 11	Thu	Vasco Henriques (Rosseland Centre for Solar Physics, Norway)	European Solar Physics Online Seminars (ESPOS)
10:00		The corrugated umbra model
		Zoom
	Abstract: The chromosphere of the umbra of sunspots is a remarkably dynamic layer featuring extremely fine sub-arcsec structure. Such structures appear dark against enveloping umbral flashes, but also bright before or after a flash, other features still are bright throughout. Only recently did we start understanding such fine features and semi-empirical modelling is converging with simulations to provide insight, not only into such fine structure, but also into the umbral flash phenomenon itself. The observational evidence weighs overwhelmingly towards a strong corrugation of the umbra where the material in short dynamic fibrils over-extends in a column of upflowing material while the adjacent areas flash. The delayed small-scale umbral brightenings at the bottom of such columns are an out-of-phase flash where the late-stage downflowing column meets the upflowing under-layers. Recent inversions using NICOLE at both umbral flashes and small-scale brightenings result in a downflow over upflow stratification perfectly bridging the transition of downflowing fibrils to upflowing fibrils as well as red-shifted absorption cores to blue-shifted absorption cores in the broader surroundings. Locally, each inverted column is remarkably similar in velocity profile to those from forward modelling, provided the formation height of the observed Ca II 8542 line is slightly lower in the Sun than in the simulations. Conspicuously, resonant cavities naturally cause the upper downflowing layers to become visible in forward modelling and the top-layer downflows to last longer than otherwise. Open questions, and how these can be addressed by future observations, are briefly discussed.
Feb 11	Thu	Vasco Henriques (Rosseland Centre for Solar Physics, Norway)	SP2RC/ESPOS seminar
11:00		The corrugated umbra model
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: The chromosphere of the umbra of sunspots is a remarkably dynamic layer featuring extremely fine sub-arcsec structure. Such structures appear dark against enveloping umbral flashes, but also bright before or after a flash, other features still are bright throughout. Only recently did we start understanding such fine features and semi-empirical modelling is converging with simulations to provide insight, not only into such fine structure, but also into the umbral flash phenomenon itself. The observational evidence weighs overwhelmingly towards a strong corrugation of the umbra where the material in short dynamic fibrils over-extends in a column of upflowing material while the adjacent areas flash. The delayed small-scale umbral brightenings at the bottom of such columns are an out-of-phase flash where the late-stage downflowing column meets the upflowing under-layers. Recent inversions using NICOLE at both umbral flashes and small-scale brightenings result in a downflow over upflow stratification perfectly bridging the transition of downflowing fibrils to upflowing fibrils as well as red-shifted absorption cores to blue-shifted absorption cores in the broader surroundings. Locally, each inverted column is remarkably similar in velocity profile to those from forward modelling, provided the formation height of the observed Ca II 8542 line is slightly lower in the Sun than in the simulations. Conspicuously, resonant cavities naturally cause the upper downflowing layers to become visible in forward modelling and the top-layer downflows to last longer than otherwise. Open questions, and how these can be addressed by future observations, are briefly discussed.
Feb 17	Wed	Kang Li (KU Leuven)	Pure Maths Colloquium
14:00		Ghost projections and expanderish graphs​
		Google Meet
	Abstract: Roughly speaking, a ghost operator is often an infinite matrix such that its matrix entries vanish at the infinity. This notion was introduced by Guoliang Yu in the study of the so-called coarse Baum-Connes conjecture. It is a very central topic in coarse geometry and operator algebras with applications to provide counterexamples to the coarse Baum–Connes conjecture, the existence of non-exact groups and the rigidity problem for Roe-type algebras. In this talk, we will visualize a class of ghost projections in terms of expanderish graphs.
Feb 17	Wed	Daniele Oriti (LMU Munich)	Cosmology, Relativity and Gravitation
15:00		Emergent relational cosmology from quantum gravity
		Blackboard Collaborate
	Abstract: We overview recent results on the extraction of an effective cosmological dynamics from fundamental quantum gravity formalisms in which spacetime is not fundamental, focusing on so called tensorial group field theories (strictly related to lattice quantum gravity and loop quantum gravity). This line of research is inspired by the idea of our universe as a quantum gravity condensate, and at the same time realizes it concretely. We emphasize how reaching the desired objective requires addressing several outstanding issues in quantum gravity: identifying quantum states in the fundamental theory with a good geometric interpretation, performing some form of coarse graining of the fundamental dynamics, defining diffeomorphism invariant observables to express the resulting coarse grained dynamics in physically transparent language. We also discuss what the theory says about the fate of the big bang singularity at the beginning of our universe.
Feb 17	Wed	Evgeny Shinder
15:00		Properties of affine toric varieties and projective toric varieties
		online in Google Meet (please e-mail Evgeny for the link)
Feb 18	Thu	Dr Huw Morgan (Aberystwyth University)	SP2RC seminar
10:00		UK-SOSS: The Characteristics of Coronal Streamers Over a Solar Cycle: Resolving the Line-of-Sight with Coronal Rotational Tomography
		Zoom Link: https://zoom.us/j/95338171418
	Abstract: Any remote measurement of the solar corona in white light (or other) wavelength is an integration of emission along an extended line of sight. Historically, most studies necessarily assumed an axi-symmetric distribution to the density, thus derived properties contained an inherent and unquantified uncertainty. From the SOHO era onwards, space-based coronagraphs (LASCO/SOHO, and COR/STEREO) make frequent, uninterrupted, and high-quality observations of the corona which allow estimates of the true density distribution using coronal rotational tomography (CRT). A recent breakthrough in CRT is revealing a new view of the corona which is gained directly from observation. For the first time, we can view long-term trends in the coronal rotation rate, find meaningul links between coronal and interplanetary density structures, and use estimated densities at a range of heights to constrain outflow velocity and acceleration. The density distributions provide a ground truth for model extrapolations of the photospheric magnetic field, and new empirical boundary conditions for solar wind models. Tentative evidence of the Parker spiral onset can be seen close to the Sun. The next step in CRT methods is the inclusion of a time-dependent density distribution: initial results show promising correlations with Parker Solar Probe measurements, and the discovery of large variations on daily timescales not associated with mass ejections.
Feb 18	Thu	Mijie Shi (KU Leuven, Belgium)	Plasma Dynamics Group
16:00		Coronal loop model heated by transverse waves against radiative losses
		Google Meet
	Abstract: In the quest to solve the long-standing coronal heating problem, it has been suggested that coronal loops could be heated by waves. Despite the accumulating observational evidence of the possible importance of coronal waves, still very few 3D MHD simulations exist that show significant heating by MHD waves. In this seminar, I will present our recent 3D coronal loop model heated by transverse waves against radiative cooling. The coronal loop is driven at the footpoint by transverse oscillations and subsequently the induced Kelvin-Helmholtz instability deforms the loop cross-section to a fully turbulent state. Wave energy is transferred to smaller scales where it is dissipated, overcoming the internal energy losses by radiation. These results open up a new avenue to address the coronal heating problem.
Feb 24	Wed	Reinder Meinsma
15:00		Normal toric varieties
		online in Google Meet (please e-mail Evgeny for the link)
Feb 25	Thu	Suzana de Souza e Almeida Silva (Sheffield)	European Solar Physics Online Seminars (ESPOS)
10:00		Detection and dynamics of the vortex tubes in the solar atmosphere
		Zoom
	Abstract: We present the state-of-art detection method of three-dimensional vortices and apply it to realistic magneto-convections simulations performed by the MURaM code. The detected vortices extend from the photosphere to the low chromosphere, presenting similar behaviour at all height levels. The vortices concentrate the magnetic field, and thereby the plasma dynamics inside the vortex is considerably influenced by the Lorentz force. Rotational motions also perturb the magnetic field lines, but they lead to only slightly bent flux tubes as the magnetic field tension is too high for the vortex flow to significantly twist the magnetic lines. We find that twisted magnetic flux tubes are created by shear motions in regions where plasma-beta>1, regardless of the existence of flow vortices.
Feb 25	Thu	Suzana de Souza e Almeida Silva (University of Sheffield, Plasma Dynamics Group (UK))	SP2RC/ESPOS seminar
10:00		Detection and dynamics of the vortex tubes in the solar atmosphere
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: We present the state-of-art detection method of three-dimensional vortices and apply it to realistic magneto-convections simulations performed by the MURaM code. The detected vortices extend from the photosphere to the low chromosphere, presenting similar behaviour at all height levels. The vortices concentrate the magnetic field, and thereby the plasma dynamics inside the vortex is considerably influenced by the Lorentz force. Rotational motions also perturb the magnetic field lines, but they lead to only slightly bent flux tubes as the magnetic field tension is too high for the vortex flow to significantly twist the magnetic lines. We find that twisted magnetic flux tubes are created by shear motions in regions where plasma-beta>1, regardless of the existence of flow vortices.
Mar 3	Wed	Jasmin Matz (University of Copenhagen)	Pure Maths Colloquium
14:00		Quantum ergodicity of compact quotients of SL(n,R)/SO(n) in the level aspect
		Google Meet
	Abstract: Suppose M is a closed Riemannian manifold with an orthonormal basis B of $L^2(M)$ consisting of Laplace eigenfunctions. Berry's Random Wave Conjecture tells us that under suitable conditions on M, in the high energy limit (ie, large Laplace eigenvalue) elements of B should roughly behave like random waves of corresponding wave number. A classical result of Shnirelman and others that $M$ is quantum ergodic if the geodesic flow on the cotangent bundle of $M$ is ergodic, can then be viewed as a special case of this conjecture. We now want to look at a level aspect, namely, instead of taking a fixed manifold and high energy eigenfunctions, we take a sequence of Benjamini-Schramm convergent compact Riemannian manifolds together with Laplace eigenfunctions f whose eigenvalue varies in short intervals. This perspective has been recently studied in the context of graphs by Anantharaman and Le Masson, and for hyperbolic surfaces and manifolds by Abert, Bergeron, Le Masson, and Sahlsten. In my talk I want to discuss joint work with F. Brumley in which we study this question in higher rank, namely sequences of compact quotients of $SL(n,R)/SO(n)$ for $n>2$.
Mar 3	Wed	Valerio Lucarini (Reading)	Applied Mathematics Colloquium
14:00		Fingerprinting Heatwaves and Cold Spells and Assessing Their Response to Climate Change using Large Deviation Theory
		Google Meet
	Abstract: Extreme events provide relevant insights on the dynamics of the climate system and their understanding is key to defining useful strategies for mitigating the impact of climate variability and climate change. Here we approach the study of persistent weather extremes using the lens of large deviation theory. We first consider a simplified yet Earth-like general circulation model of the atmosphere and numerically estimate large deviation rate functions of near-surface temperature in the mid-latitudes. We find that, after a re-normalisation based on the integrated auto-correlation, the rate function one obtains at a given latitude by looking, locally in space, at long time averages agrees with what is obtained, instead, by looking, locally in time, at large spatial averages along the latitude. This is a result of scale symmetry in the spatial-temporal turbulence and of the fact that advection is primarily zonal. This agreement hints at the universality of large deviations of the temperature field. Furthermore, we discover that the obtained rate function is able to describe spatially extended and temporally persistent heat waves or cold spells, if we consider temporal averages of spatial averages over intermediate spatial scales. We then extend our analysis by looking at the output of a state-of-the-art climate model and at observational data. We show how to const ruction in a mathematically rigorous way the climatology of persistent heatwaves and cold spells in some key target regions of the planet by constructing empirically the corresponding rate functions for the surface temperature, and we assess the impact of increasing CO2 concentration on such persistent anomalies. In particular, we can better understand the increasing hazard associated to heatwaves in a warmer climate. We show that two 2010 high impact events - summer Russian heatwave and winter Dzud in Mongolia - are associated with atmospheric patterns that are exceptional compared to the typical ones, but typical compared to the climatology of extreme events. Finally, we propose an approximate formula for describing large and persistent temperature fluctuations from easily accessible statistical properties. Refs: V. Galfi, V. Lucarini, Fingerprinting Heatwaves and Cold Spells and Assessing Their Response to Climate Change using Large Deviation Theory, PRL, in review (2020) V. Galfi, V. Lucarini, J. Wouters, A Large Deviation Theory-based Analysis of Heat Waves and Cold Spells in a Simplified Model of the General Circulation of the Atmosphere, J. Stat. Mech. 033404 doi: 10.1088/1742-5468/ab02e8 (2019)
Mar 3	Wed	Elsa Teixeira (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Cosmological Predictions of a Disformal Dark Sector
		Blackboard Collaborate
	Abstract: In this talk I will give an overview of interacting dark energy, with emphasis on disformal couplings and its cosmological implications. I will then focus on the general Dark D-Brane setting, for which the interaction in the dark sector arises naturally through the induced metric on a moving brane. In particular, I will discuss the background and linear perturbation equations in this setting, together with a numerical analysis, with brief connection to observational constraints. Testing gravity in the dark sector will be an exciting topic in the upcoming decade, with next-generation cosmological data probing gravitational phenomena in finer detail.
Mar 3	Wed	Karoline Van Gemst
15:00		Toric orbits and toric morphisms
		online in Google Meet (please e-mail Evgeny for the link)
Mar 4	Thu	Erico L. Rempel (Aeronautics Institute of Technology - ITA, São José dos Campos, Brazil)	Plasma Dynamics Group
16:00		Dynamical Systems Approach to Solar Physics: From Lyapunov Exponents to Lagrangian Coherent Structures
		Google Meet
	Abstract: Dynamical systems, or chaos theory, has enjoyed huge success in the analysis of systems described by ordinary differential equations, such as nonlinear oscillators, chemical reactions, electronic devices, population dynamics, etc. Usually, in the dynamical systems approach, one is concerned with the identification of the basic building blocks of the system under investigation and how they interact with each other to produce the observable dynamics, as well as how they can be manipulated to produce a desired output, in the cases where control is pursued. Examples of those building blocks are unstable equilibrium and periodic solutions, nonattracting chaotic sets and their manifolds, which are special surfaces in the phase space that basically control the dynamics, guiding solutions in preferred directions. Despite its success in those areas, many still think that the theory has limited value when applied to fully developed turbulence, like observed in solar convection, due to the infinite dimension of the phase space. In this talk, we show that this difficulty can be overcome by adopting a Lagrangian reference frame, where the phase space for each fluid particle becomes three-dimensional and the building blocks of the turbulence can be efficiently extracted by appropriate numerical tools. We reveal how finite-time Lyapunov exponents, a traditional measure of chaos, can be used to detect attracting and repelling time-dependent manifolds that divide the fluid in regions with different behavior. These manifolds are shown to accurately mark the boundaries of granules in observational data from the photosfere. In addition, stagnation points and vortices detected as elliptical Lagrangian coherent structures complete the set of building blocks of the photospheric turbulence. Such structures are crucial for the trapping and transport of mass and energy in the solar plasma.
Mar 10	Wed	Anssi Lahtinen (University of Copenhagen)	Pure Maths Colloquium
14:00		An introduction to string topology
		Google Meet
	Abstract: Founded by Chas and Sullivan's observation that the homology of the free loop space of an oriented manifold has the structure of a Batalin--Vilkovisky algebra, string topology studies the rich algebraic structure present on the homology of the free loop spaces of certain spaces such as manifolds and classifying spaces of compact Lie groups. In this talk, I will provide a gentle and subjective introduction to the subject, and also indicate how it connects with objects such as moduli spaces of Riemann surfaces, automorphism groups of free groups, and finite groups of Lie type.
Mar 10	Wed	Aaron Held (Imperial College)	Cosmology, Relativity and Gravitation
15:00		Shadows and Binaries: Stationary and dynamical spacetimes beyond GR
		Blackboard Collaborate
	Abstract: The recent wealth of experimental data from the LIGO/Virgo as well as from the EHT collaboration is fully consistent with GR. However, the true nature of the observed compact objects must involve some new physics (quantum or classical) to ameliorate the singularities present in the interior of the respective GR description. In the spirit of local EFTs, the talk will be based on the main assumption that the new physics, whatever its origin, is tied to local curvature scales. Based on this locality principle, I construct a new class of everywhere-regular, stationary spacetimes parameterized by a mass function in horizon-penetrating coordinates. This construction allows me to identify characteristic image features of the shadows of this class of regular black holes, in particular, in distinction to other models not following the locality principle. Moving on to dynamical spacetime evolution, still following the principles of local EFT, I will present first results on a fully non-linear but well-posed numerical simulation of (quadratic) higher-derivative gravity in the spherically-symmetric sector.
Mar 10	Wed	Yannik Schüler
15:00		Divisors
		online in Google Meet (please e-mail Evgeny for the link)
Mar 11	Thu	Sergio J. González Manrique (Astronomical Institute of Slovak Academy of Sciences (SK))	SP2RC/ESPOS seminar
11:00		The Dynamic and Magnetic Evolution of Arch Filament Systems
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: We study the dynamics of plasma along the legs of an arch filament system (AFS) observed with relatively high-cadence spectropolarimetric data from the ground-based solar GREGOR telescope (Tenerife) using the GREGOR Infrared Spectrograph in the He I 10830 Å range. The temporal evolution of the plasma of an AFS was followed using the chromospheric He I 10830 Å triplet and Si I 10827 Å. Measurements of vector magnetic fields in the solar chromosphere, especially in AFS, are extremely scarce, but very important. The magnetic field configuration reveals how AFSs are sustained in the chromosphere and hints at their formation, evolution, and disappearance. The magnetic field in the AFS follows loop-like structures traced by chromospheric absorption lines. However, if magnetic field lines follow chromospheric threads as seen by filtergrams of H⍺, Ca II, or He I, is still not fully resolved. Previous studies have modeled AFS as multiple flux ropes with mixed signs of helicity consistently with the observed multiple filament bundles constituting AFS. Nevertheless, further spectropolarimetric observations are needed to address this issue. Many spectral lines are sensitive to the atmospheric parameters up to the upper chromosphere. Moreover, when combined with photospheric Zeeman sensitive spectral lines, one can infer the topology of the magnetic field from the bottom of the solar atmosphere to the chromosphere. In this talk, we are going to follow the nature of AFSs by reconstructing the magnetic field configuration of an EFR from the very beginning and follow its evolution and dynamics to support current AFS models. To that aim we used the spectropolarimetric data available at the upper photosphere (Si I) and the upper chromosphere.
Mar 17	Wed	Ulrich Bunke (University of Regensburg)	Pure Maths Colloquium
14:00		Motivic ideas in coarse homotopy theory
		Google Meet
	Abstract: Coarse geometry studies the large-scale properties of metric spaces, groups and other mathematical objects. Interesting invariants are constructed using coarse homology theories. In this exposition I will explain an axiomatic approach to coarse homology theories. A motivic statement is a statement of the form: For every coarse homology theory E assertion P(E) holds. For example, one can turn the coarse Baum-Connes conjecture into a motivic statement. I will explain how motivic statements can be captured in terms of a universal coarse homology theory. The talk is based on joint work with Alexander Engel.
Mar 17	Wed	Richard Daniel (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Scale-invariant, $R^2$ Inflation
		Blackboard Collaborate
	Abstract: In this talk, I will briefly recap slow roll inflation, before demonstrating that an $f(R^2)$ theory of inflation is able to dynamically generate a Planck mass from the vacuum expectation values of the scalar fields. We see that in such models if the self interaction is non-zero, a potentially large cosmological constant will emerge. To avoid this problem we introduce another scalar field, producing a Higgs-like potential. This naturally drives the cosmological constant to zero soon after inflation. We will analyse both models in the Einstein frame, where we find a conserved Noether current simplifying the model to a N-1 scalar field model. Finally, I will discuss the non-trivial features in the power spectrum, which produce testable parameters for future cosmological experiments.
Mar 17	Wed	Cristina Manolache
15:00		Line bundles
		online in Google Meet (please e-mail Evgeny for the link)
Mar 18	Thu	Dr Helen Mason (University of Cambridge)	SP2RC seminar
10:00		UK-SOSS: Solar Diagnostic Spectroscopy - a Personal Perspective
		Zoom link: https://zoom.us/j/95338171418 Meeting ID: 953 3817 1418
	Abstract: Spectroscopic diagnostics have enabled us to determine the physical parameters of plasma for different solar features (active regions, jets, flares etc). Helen started her career studying the visible coronal lines from the 1952 eclipse observations. She then studied the UV and X-ray spectrum of the Sun, working on many joint UK, NASA, ESA and Japanese solar space projects including Skylab, the SMM (Solar Maximum Mission), Yohkoh, SoHO (Solar and Heliospheric Observatory), Hinode, SDO (Solar Dynamics Observatory) and IRIS (Interface Region Imaging Spectrograph). She was a founder member of the CHIANTI team, an atomic database which has been extensively used for solar data analysis. In this talk, she will pick out a few key results as examples of the value of spectroscopic diagnostics (in the transition region and corona). She will also look towards the current opportunities for research in this field and the future prospects for spectrometers. For a recent review, see: Del Zanna and Mason, 2018, Solar UV and X-ray spectral diagnostics’, Sol. Phys. Liv. Reviews.
Mar 18	Thu	Kostas Tziotziou (National Observatory of Athens)	Plasma Dynamics Group
16:00		Detection of small-scale chromospheric vortices and their intricate dynamics
		Google Meet
	Abstract: Small-scale vortex motions are detected at various spatial and temporal scales in the solar atmosphere, from the photosphere to the low corona. They often exhibit complex structure and dynamics and, as largely magnetic structures, can foster a variety of oscillations and wave modes. Despite, however, recent advancements in observational and theoretical studies, as well as in simulations and modelling, their proper detection, especially in chromospheric lines such as Hα and Ca II 8542 Å is still an open issue, and their structure and dynamics remain poorly understood. We present a novel automated method of chromospheric swirl detection based on their morphological characteristics that nicely complements previous LCT-related approaches. We further discuss in detail the intricate dynamics of a persistent small-scale vortex flow with significant substructure, observed with the CRisp Imaging SpectroPolarimeter (CRISP) at the Swedish Solar Telescope (SST), as well as oscillations and observational signatures of different types of waves within it and their propagation characteristics. Both discussed aspects, better detection leading to a more precise estimation of their occurrence rate and wave identification and their properties, are key elements for accurately assessing the role of vortex structures in the energy budget of the solar atmosphere.
Mar 24	Wed	Magnus Goffeng (Lund University)	Pure Maths Colloquium
14:00		A problem of magnitude
		Google Meet
	Abstract: An invariant that has attracted quite some attention in the last decade is the magnitude of a compact metric space. Magnitude gives a way of encoding the size of a metric space, resembling both the Euler characteristic and the capacity. In this colloquium I will give a short introduction to magnitude and present some recent results for compact metric spaces of geometric origin (i.e. domains in Euclidean space or manifolds). One of the results states that the magnitude recovers geometric invariants such as volume and certain integrals of curvatures. Based on joint work with Heiko Gimperlein and Nikoletta Louca.
Mar 24	Wed	George Moulantzikos
15:00		Toric surfaces
		online in Google Meet (please e-mail Evgeny for the link)
Mar 25	Thu	Valeriia Liakh (INAF-OAR National Institute for Astrophysics (IT))	SP2RC/ESPOS seminar
10:00		Large-amplitude oscillations in solar prominences derived from high-resolution simulations
	Abstract: We report 2D MHD simulations of the large-amplitude oscillations (LAOs) in the solar prominences performed with MHD code Mancha. We aim to study the properties of LAOs using high-resolution simulations in a simple 2D magnetic configuration that contains a dipped part. We loaded the dense prominence plasma in the dips region. In order to excite oscillations, we used a perturbation directed along the magnetic field. For the same numerical model, the four spatial resolutions were considered: 240, 120, 60, and 30 km. The longitudinal LAOs (LALOs) are strongly damped even in the high-resolution simulation in the region of the weaker and more curved magnetic field (at the center and bottom of the prominence). At the prominence top, the oscillations have relatively longer damping times. Furthermore, during the first 100 minutes, the longitudinal velocity shows growing with respect to its initial amplitude. The amplification becomes even more significant in the experiments with high-resolution. The damping and amplification mechanisms involved in our experiments can be important for explaining the observed amplification and attenuation of the LALOs.
Apr 1	Thu	Iulia Chifu (University of Goettingen)	Plasma Dynamics Group
16:00		3D solar coronal loop reconstructions with machine learning
		Google Meet
	Abstract: The magnetic field plays an essential role in the initiation and evolution of different solar phenomena in the corona. The structure and evolution of the 3D coronal magnetic field are still not very well known. A way to ascertain the 3D structure of the coronal magnetic field is by performing magnetic field extrapolations from the photosphere to the corona. In previous work, it was shown that by prescribing the 3D-reconstructed loops’ geometry, the magnetic field extrapolation produces a solution with a better agreement between the modeled field and the reconstructed loops. This also improves the quality of the field extrapolation. Stereoscopy, which uses at least two view directions, is the traditional method for performing 3D coronal loop reconstruction. When only one vantage point of the coronal loops is available, other 3D reconstruction methods must be applied. Within this work, we present a method for the 3D loop reconstruction based on machine learning. Our purpose for developing this method is to use as many observed coronal loops in space and time for the modeling of the coronal magnetic field. Our results show that we can build machine-learning models that can retrieve 3D loops based only on their projection information. Ultimately, the neural network model will be able to use only 2D information of the coronal loops, identified, traced, and extracted from the extreme-ultraviolet images, for the calculation of their 3D geometry.
Apr 2	Fri	Dr Michael Griffiths (Research IT, University of Sheffield)	SP2RC seminar
13:00		Computational MHD for solar physics with Graphical Processing Units
		Google Meet
	Abstract: Parallel magnetohydrodynamic (MHD) algorithms are important for numerical modelling of highly inhomogeneous solar, astrophysical and geophysical plasmas. Parallelisation techniques have been exploited most successfully by the gaming/graphics industry with the adoption of graphical processing units (GPUs) possessing hundreds of processor cores. The opportunity has been recognised by the computational sciences and engineering communities who have recently harnessed successfully the numerical performance of GPUs. Here, we introduce the implementation of SMAUG, the Sheffield Magnetohydrodynamics Algorithm Using GPUs. SMAUG is a 1-3D MHD code capable of modelling magnetised and gravitationally stratified plasmas. We illustrate an application of SMAUG with a discussion of the results of a study of the atmospheric motions generated by the solar global resonant oscillations. Utilising a spatially structured driver across the base of the computational model, we embark on how the ensemble of performed simulations, that provide insight into the energy supplied by various wave modes, is redistributed in the atmosphere. The results shed light on the mechanisms leading to ubiquitous intensity oscillations in the stratified solar atmosphere and establish a link between signals at photospheric levels and the solar coronal response. In the final section of the talk we describe how to access the different resources which are available for running computational MHD codes with GPU’s.
Apr 8	Thu	Mayukh Panja (Max Planck Institute for Solar System Research, MPS (DE))	SP2RC/ESPOS seminar
10:00		Sunspot MHD simulations: subsurface structure and penumbral filament formation
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: Penumbral filaments do not form naturally in MHD simulations of sunspots. This is typically circumvented by modifying the top boundary: the field is made 2-3 times more horizontal than a potential field configuration. In this talk, I will explore the possibility that penumbral filament formation is governed by the subsurface structure of sunspots. We conducted a series of numerical experiments where we used flux tubes with different initial curvatures to study the effect of the fluting instability on the subsurface structure of spots using the MURaM code. We find that the curvature of a flux tube indeed determines the degree of fluting the flux tube will undergo—the more curved a flux tube is, the more fluted it becomes. In addition, sunspots with strong curvature have strong horizontal fields at the surface and therefore readily form penumbral filaments. The fluted sunspots eventually break up from below, with lightbridges appearing at the surface several hours after fluting commences. We also propose that intruding lightbridges can be used as tracers of the subsurface magnetic field.
Apr 15	Thu	Prof Richard A Harrison (RAL Space)	SP2RC seminar
10:00		UK-SOSS: Taking stock of our understanding of Coronal Mass Ejections
		UK-SOSS Zoom Link: https://zoom.us/j/95338171418
	Abstract: This presentation will take stock of where we are with Coronal Mass Ejection (CME) research, taking a brief look at the history of CME observations and the early interpretations of the phenomenon, through to the present day where we have multi-spacecraft observations with coronagraphs and heliospheric imagers and a wide range of modelling techniques, many of which are now geared towards space weather impacts. This is a research area that has matured dramatically, since the launch of the SOHO spacecraft in particular, but especially with the increased interest in space weather and missions such as STEREO and Lagrange. It is a good time to take stock and in doing so to revisit some basic issues, including the flare-CME relationship, stealth CMEs, coronal dimming and CME-CME interactions, as well as lessons learnt from imaging and tracking CMEs in the corona and in the heliosphere. Perhaps it is also a useful time to pause and ask the questions, what else do we want to know about CMEs, and how are we going to satisfy that desire?
Apr 15	Thu	Juie Shetye (New Mexico State University)	Plasma Dynamics Group
16:00		Zooming into the solar chromosphere
		Google Meet
	Abstract: The solar chromosphere serves as a bridging layer between the photosphere and the corona. This dynamic layer is filled with a plethora of features that vary in time and space. With the advent of high-resolution ground-based observations we can discover new features. We use some of the World’s biggest solar telescopes to zoom into this layer and it reveals never seen before dynamics. Here I present detailed observations of two science topics that are guided by observations. I show a statistical study of spicules, which are long-thin grass-like features observed on the sun. These events wiggle-jiggle and sway around their axes or along a common centre of mass to create wave-like motions on the Sun. These waves can travel with speeds on 100s of km per second to energise the solar chromosphere. The second example I show are swirling-whirling events, that look like Tornadoes on the Earth. These churn the matter from the Lowe photosphere to the chromosphere. Studying the behaviour of such events is vital in understanding a decade long question in the solar physics, that tells us how the Sun’s atmosphere is heated. In addition, the current work presented already tests the limits of current telescopes in terms of the temporal and spatial resolution. The answer to exploring the depth of chromosphere lies in building next-generation solar physics observatories such as DKIST that have 3 times more spatial resolution than CRISP and much higher temporal resolution.
Apr 16	Fri	Dr Daria Y Shukhobodskaia (SP2RC (UoS))	SP2RC seminar
13:00		Magnetohydrodynamic Waves in Cylindrical and Multi-slab Environments
		Google meet link: https://meet.google.com/ciq-zovu-rzm
	Abstract: The investigation of magnetohydrodynamic (MHD) wave propagation in different equilibrium configurations is important for the development of solar magneto-seismology (SMS). The applicable models of solar atmospheric waveguides are studied in the framework of Cartesian and cylindrical geometries. First, a magnetised plasma slab sandwiched between an arbitrary number of non-magnetic/ magnetic layers are considered and an analytical approach is used for the derivation of its dispersion relation. The amplitudes of the eigenmodes depend on the equilibrium structuring and the model parameters; this motivates an application as a solar magneto-seismology tool. Specific cases of two- and three-layered slabs are studied in detail and their potential applicability to magnetic bright points is discussed. Furthermore, the resonant damping of propagating kink waves is studied in a straight magnetic flux tube with the density varying along the tube taking into account the magnetic loop expansion. Also non-stationary magnetic tubes to model, for example, cooling coronal loops is considered. In particular, it was found that cooling enhances the wave amplitude and the loop expansion makes this effect more pronounced. After, we analyse $10$ driven kink oscillations in coronal loops to further investigate the ability of expansion and cooling to explain complex damping profiles. The used approach could allow to infer some important diagnostic information (such as, for example, the density ratio at the loop foot-points) from the oscillation profile alone, without detailed measurements of the loop and without complex numerical methods. The current study indicates that thermal evolution should be included in kink-mode oscillation models in the future to help us to better understand oscillations that are not purely Gaussian or exponential. Finally, fluting oscillations in a thin straight expanding magnetic flux tube in the presence of background flow are considered. The method of multiple scales is used for the derivation of the system of governing equations. We have found that the amplitude increases due to cooling and is higher for a higher expansion factor. Higher values of the wave number lead to localisation of the oscillation closer to the boundary. We show that the higher the value of the ratio of internal and external plasma densities, the higher the amplification of oscillation due to cooling. So, not only the wave number plays an important role in the evolution of the cooling system, but also the density ratio and the variation of tube expansion are relevant parameters in the cooling process of an oscillating flux tube.
Apr 20	Tue	Petru Constantinescu (University College London)	Number Theory seminar
13:00		Distribution of Modular Symbols
		Google Meet
	Abstract: Motivated by a series of conjectures of Mazur, Rubin and Stein, the study of the arithmetic statistics of modular symbols has received a lot of attention in recent years. In this talk, I will highlight several results about the distribution of modular symbols, including their Gaussian distribution and the residual equidistribution modulo p. I will also talk about generalisations to quadratic imaginary fields and higher dimensions.
Apr 20	Tue	James Cranch (Sheffield)	MiaowMiaow (2d category theory) seminar
14:00		Parallelism and Multiple Monoidal Categories
		online
	Abstract: Notes: 14:00-15:30. Contact Joseph Martin for meeting link.
Apr 21	Wed	Cihan Okay (Bilkent University)	Pure Maths Colloquium
14:00		Topology of quantum resources
		Google Meet
	Abstract: A central question in quantum information theory is to determine physical resources required for quantum computational speedup. Such resources are characterized in terms of intrinsic features of quantum states and include various notions such as quantum contextuality, quasiprobability representations, and topological phases. Each of these notions correspond to a different perspective taken on the question of where the computational power is hidden. We take a topological approach based on the recently established connection between classifying spaces from algebraic topology and the study of quantum contextuality from quantum foundations in joint work with Robert Raussendorf. In this talk I will explain this connection and discuss possible ways of extending the role of topology to study other kinds of quantum resources.
Apr 21	Wed	Peter Clarkson (University of Kent)	Applied Mathematics Colloquium
14:00		Rational solutions of three integrable equations and applications to rogue waves
		Google Meet
	Abstract: In this talk I shall discuss rational solutions of the Boussinesq equation, the focusing nonlinear Schrodinger (NLS) equation and the Kadomtsev-Petviashvili I (KPI) equation, which are all soliton equations solvable by the inverse scattering. The Boussinesq equation was introduced by Boussinesq in 1871 to describe the propagation of long waves in shallow water. Rational solutions of the Boussinesq equation, which are algebraically decaying and depend on two arbitrary parameters, are expressed in terms of special polynomials that are derived through a bilinear equation, have a similar appearance to rogue-wave solutions of the focusing NLS equation and have an interesting structure. Conservation laws and integral relations associated with rational solutions of the Boussinesq equation will also be discussed. Rational solutions of the KPI equation will be derived in three ways: from rational solutions of the NLS equation; from rational solutions of the Boussinesq equation; and from the spectral problem for the KPI equation. It'll be shown that these three families of rational solutions are fundamentally different.
Apr 21	Wed	Bianca Dittrich (Perimeter Institute, Waterloo)	Cosmology, Relativity and Gravitation
15:00		Quantization of spacetime and its (effective) dynamics
		Blackboard Collaborate
	Abstract: General relativity taught us that spacetime geometry is dynamical and quantum theory posits that dynamical objects are quantum. In this talk I will sketch the notion of quantum geometry, which arises in loop quantum gravity. Somewhat surprisingly, this quantum geometry, although it arises from a quantization of a torsion-free theory, does include torsion degrees of freedom. I will then introduce an effective dynamics for such quantum geometries and sketch how to derive corrections that arise due to the inclusion of torsion degrees of freedom.
Apr 21	Wed	Yannik Schüler
15:00		The Cox ring / quotient construction
		online in Google Meet (please e-mail Evgeny for the link)
Apr 22	Thu	Alex Prokopyszyn (University of St Andrews)	SP2RC/ESPOS seminar
10:00		Mode coupling at the transition region and the validity of line-tied boundary conditions
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: In this seminar, we aim to show why Fast/Alfvén waves couple at the solar surface. We will also show that the polarisation of the waves changes upon reflection at the solar surface. Finally, we will test the validity of line-tied boundary conditions for highly phase-mixed Alfvén waves. For most parameters, line-tied boundary conditions provide a good approximation. However, for highly phase-mixed waves, the coronal transverse length scales can be shorter than the corresponding parallel length scales in the chromosphere. In that case, we find that the line-tied model produces unphysically large boundary layers. Hence, we have the counter-intuitive result that the length scales parallel to the solar surface play a key role in determining the validity of line-tied boundary conditions.
Apr 27	Tue	Tobias Berger (University of Sheffield)	Number Theory seminar
13:00		Eisenstein cohomology and CM congruences
		Google Meet
	Abstract: This is a report on joint work in progress with Adel Betina (Vienna) to prove congruences between Eisenstein and cuspidal cohomology classes for imaginary quadratic fields. I plan to discuss applications to R=T theorems and congruences for classical CM modular forms.
Apr 27	Tue	Dan Graves	MiaowMiaow (2d category theory) seminar
14:00		Crossed Simplicial Groups, Double Categories and PROPs for (Involutive) Bimonoids
		online
Apr 28	Wed	Tom Bridgeland (University of Sheffield)	Pure Maths Colloquium
14:00		Stability conditions and quadratic differentials
		Google Meet
	Abstract: I'm planning to talk about some quite old joint work with Ivan Smith which realises moduli spaces of quadratic differentials on Riemann surfaces as spaces of stability conditions on a certain class of three-dimensional Calabi-Yau triangulated categories. I expect to spend the whole talk explaining what all those words mean, and why such a result might be interesting!
Apr 28	Wed	Eleni Kontou (Amsterdam)	Cosmology, Relativity and Gravitation
15:00		A singularity theorem for evaporating black holes
		Blackboard Collaborate
	Abstract: The classical singularity theorems of General Relativity rely on energy conditions that are easily violated by quantum fields. In this talk I will provide motivation for an energy condition obeyed by semiclassical gravity: the smeared null energy condition (SNEC), a proposed bound on the weighted average of the null energy along a finite portion of a null geodesic. I will then then present the proof of a semiclassical singularity theorem using SNEC as an assumption. This theorem extends the Penrose theorem to semiclassical gravity and has interesting applications to evaporating black holes. Based on: arXiv: 2012.11569
Apr 28	Wed	Ananyo Dan
15:00		Projective morphisms and resolution of singularities
		online in Google Meet (please e-mail Evgeny for the link)
Apr 30	Fri	Dr Indrani Roy (University College London)	SP2RC seminar
13:00		Can Solar cyclic variability modulate winter Arctic climate?
		Google Meet
	Abstract: This study investigates the role of the eleven-year solar cycle on the Arctic climate during 1979–2016. It reveals that during those years, when the winter solar sunspot number (SSN) falls below 1.35 standard deviations (or mean value), the Arctic warming extends from the lower troposphere to high up in the upper stratosphere and vice versa when SSN is above. The warming in the atmospheric column reflects an easterly zonal wind anomaly consistent with warm air and positive geopotential height anomalies for years with minimum SSN and vice versa for the maximum. Despite the inherent limitations of statistical techniques, three different methods – Compositing, Multiple Linear Regression and Correlation – all point to a similar modulating influence of the sun on winter Arctic climate via the pathway of Arctic Oscillation. Presenting schematics, it discusses the mechanisms of how solar cycle variability influences the Arctic climate involving the stratospheric route. Compositing also detects an opposite solar signature on Eurasian snow-cover, which is cooling during Minimum years, while warming in maximum. It is hypothesized that the reduction of ice in the Arctic and a growth in Eurasia, in recent winters, may in part, be a result of the current weaker solar cycle.
May 4	Tue	Andrea Conti (University of Luxembourg)	Number Theory seminar
13:00		Lifting trianguline Galois representations along isogenies
		Google Meet
	Abstract: When interpolating p-adically Galois representations attached to automorphic forms, one obtains many new representations that are not de Rham locally at p. It is expected that such representations are characterized by the condition of being trianguline at p. We study how this notion behaves under functoriality: it is easy to show that if S: GL_m -> GL_n is an algebraic representation and rho is an m-dimensional trianguline Galois representation, the composition S(rho) is again trianguline. We prove that under reasonable assumptions the reverse implication is true, with the goal of applying the result to the study of congruence loci on eigenvarieties.
May 5	Wed	Reinder Meinsma / Yirui Xiong
15:00		Canonical class and sheaf cohomology
		online in Google Meet (please e-mail Evgeny for the link)
May 6	Thu	Matheus Aguiar-Kriginsky Silva (University of the Balearic Islands, UIB (ES))	SP2RC/ESPOS seminar
10:00		Magnetic field inference in spicules and coronal rain clumps
		Zoom
	Abstract: In this seminar, we aim to present the results of two recent works centred at the use of spectropolarimetric data obtained with the CRISP instrument at the SST in the Ca II 845.2 nm line. With these observations, we obtain information about the magnetic field present in chromospheric spicules and coronal rain clumps. For this purpose, we have used the Weak-field approximation (WFA), which albeit being computationally simple to implement, needs careful assessment of the conditions of the plasma to be correctly applied. Magnetic fields of the order of hundreds of Gauss are inferred. We also combine the Ca II 845.2 nm observations with simultaneous Hα observations to estimate the temperature and non-thermal velocity of the plasma in coronal rain and spicules using the observed Doppler amplitude.
May 11	Tue	Lassina Dembele (University of Luxembourg)	Number Theory seminar
13:00		Revisiting the modularity of the abelian surfaces of conductor 277
		Google Meet
	Abstract: There is an isogeny class of semistable abelian surfaces A with good reduction outside 277 and $End_Q(A) = Z$. The modularity (or paramodularity) of this class was proved by a team of six people: Armand Brumer, Ariel Pacetti, Cris Poor, Gonzalo Tornaria, John Voight and David Yuen. They did so by using the so-called Faltings-Serre method. This was the first known case of the paramodularity conjecture. In this work in progress, I will discuss how to (re-)prove the modularity of these surfaces by directly applying deformation theory. This could be seen as an explicit approach to deformation theory.
May 11	Tue	Emily Roff (Edinburgh)	MiaowMiaow (2d category theory) seminar
14:00		Magnitude Homology of Semidirect Products and "Spheres"
		Google Meet. Link will be emailed.
	Abstract: Seminar will run for 90 mins.
May 12	Wed	Isha Kotecha (Okinawa Institute for Science and Technology)	Cosmology, Relativity and Gravitation
13:30		Generalised Gibbs States and Application in Discrete Quantum Gravity
		Blackboard Collaborate
	Abstract: Thermal states are absolutely important for statistical descriptions of physical systems; likewise also in discrete quantum gravity, where classical continuum spacetime is thought to emerge from the collective physics of some underlying quantum structure. But what equilibrium even means in a background independent context is a foundational open issue. In this talk, I will discuss a generalisation of Gibbs states for use in such contexts, while emphasising on the maximum entropy principle characterisation. The resulting setup is then applied in quantum gravity, by modelling a quantum spacetime as a many-body system of candidate quanta of geometry, and utilising their field theoretic formulation of group field theory (GFT). This leads to concrete examples of quantum gravitational generalised Gibbs states. I will then present non-perturbative thermofield double vacua, and their inequivalent thermal representations, as induced by these Gibbs states. An interesting class of thermal condensates are defined, which encode fluctuations in the underlying quantum geometry. These are subsequently applied in GFT cosmology to extract an effective FLRW universe at late times, with a bounce and accelerated expansion at early times.
May 12	Wed	Ana Lecuona (University of Glasgow)	Pure Maths Colloquium
14:00		Rational homology balls in low dimensional topology
		Google Meet
	Abstract: In this talk we will mainly focus on rational homology balls: their history, interest and prominence in nowadays low dimensional topology. We will start with the basic definitions and we will spend some time trying to understand the importance of these balls and how they relate to seemingly disjoint problems. We will end by discussing some recent results which will hopefully give a picture of the current state of the art. No prior knowledge of the topic will be assumed.
May 12	Wed	Kevin Wilson and Cameron Williams (Newcastle)	Statistics Seminar
14:00		A comparison of prior distribution aggregation methods
		Google Meet
	Abstract: When eliciting prior distributions from experts, it may be desirable to combine them into a single group prior. There are many methods of expert-elicited prior aggregation, which can roughly be categorised into two types. Mathematical aggregation methods combine prior distributions using a mathematical rule, while behavioural aggregation methods assist the group of experts to come to a consensus prior through discussion. As many commonly used aggregation methods have different requirements in the elicitation stage, there are few, if any, comparisons between them. Using a clinical trial into a novel diagnostic test for Motor Neuron Disease as a case study, we elicited a number of prior distributions from a group of experts. We then aggregated these prior distributions using a range of mathematical aggregation methods, including Equal Weights linear pooling, the Classical Method, and a Bayesian aggregation method. We also undertook an in-person behavioural aggregation with the experts, using the Sheffield Elicitation Framework, or SHELF. Using expert answers to seed questions, for which the elicitors know the true values, we compare and contrast the different aggregation methods and their performance. We also demonstrate how all considered aggregation methods outperform the individual experts.
May 12	Wed	George Moulantzikos
15:00		Cohomology and intersection theory
		online in Google Meet (please e-mail Evgeny for the link)
May 13	Thu	Dr Hugh Hudson (University of Glasgow and UC Berkeley)	SP2RC seminar
10:00		UK-SOSS: Carrington Events
		Zoom Link: https://zoom.us/j/95338171418
	Abstract: We often cite the Carrington flare (SOL1859-09-01) as an extreme flare/CME/geostorm event and a prototype "superflare." I discuss the original observations in the context of what we now know about solar and stellar flares. Although not an extreme event in the sense of being truly exceptional, it has become clear that the Carrington flare turned into a milestone in what we now call "multimessenger astronomy."
May 18	Tue	Srilakshmi Krishnamoorthy (I.I.S.E.R. Thiruvanthapuram)	Number Theory seminar
13:00		The Eisenstein elements of modular symbols of square-free level
		Google Meet
	Abstract: We present the explicit expression of the Eisenstein elements inside the space of modular symbols for Eisenstein series with integer coefficients for the congruence subgroups Γ0(N) of square- free level N. This answers a question of Merel. Our results are explicit versions of the Manin-Drinfeld theorem.
May 18	Tue	Joseph Martin and Callum Reader (Sheffield)	MiaowMiaow (2d category theory) seminar
14:00		'Duality Galore in Bimod and FMker' and 'Scalars and Traces in Closed Bicategories'
		Google Meet. Link will be emailed.
	Abstract: The seminar will run for 90 mins.
May 19	Wed	Birgit Richter (University of Hamburg)	Pure Maths Colloquium
14:00		Detecting and describing ramification for structured ring spectra
		Google Meet
	Abstract: This is a report on joint work with Eva Höning. For rings of integers in an extension of number fields there are classical methods for detecting ramification and for identifying ramification as being tame or wild. Noether's theorem characterizes tame ramification in terms of a normal basis and tame ramification can also be detected via the surjectivity of the norm map. We take the latter fact and use the Tate cohomology spectrum to detect wild ramification in the context of commutative ring spectra. I will discuss several examples in the context of topological K-theory and modular forms.
May 19	Wed	Alberto Cobos
15:00		Toric Fano varieties, reflexive polytopes and mirror symmetry
		online in Google Meet (please e-mail Evgeny for the link)
May 20	Thu	Kristopher Cooper (University of Glasgow, School of Physics & Astronomy (UK))	SP2RC/ESPOS seminar
10:00		Investigating small solar flares with NuSTAR
		Zoom (Meeting ID: 165 498 165)
	Abstract: Small, highly frequent flares are thought to contribute to heating the Sun’s atmosphere, particularly in active regions. This impulsive energy release would heat plasma >5 MK and accelerate electrons, producing weak thermal and non-thermal signatures that could be observed by a very sensitive X-ray telescope. No such solar telescope exists currently so we use the Nuclear Spectroscopic Telescope Array (NuSTAR), an astrophysical X-ray telescope, with focusing optics imaging spectroscopy providing a unique sensitivity for observing the Sun above 2.5 keV. In this seminar, I will present an overview of the discoveries from NuSTAR solar observations where decreasing solar activity between cycle 24 and 25 has allowed GOES sub-A class microflares to be observed regularly within, and small brightenings outside, active regions. In particular, I will describe several X-ray microflares from a recently emerged active region, AR12721, that were observed on 2018 September 9-10 with NuSTAR. In combination with SDO/AIA, I will discuss the temporal, spatial, and spectral evolution of these sub-A class microflares and show that temperatures up to 10 MK are reached. Using SDO/HMI, I also present evidence of photospheric magnetic flux cancellation/emergence at the footpoints in 8 NuSTAR microflares.
May 20	Thu	Vigeesh Gangadharan (Leibniz Institute for Solar Physics, Germany)	Plasma Dynamics Group
16:00		Internal gravity waves in the magnetized solar atmosphere
		https://meet.google.com/tzi-joyf-uci
	Abstract: Internal gravity waves (IGWs) are buoyancy-driven waves common in the Earth’s atmosphere and oceans. IGWs have also been observed in the Sun’s atmosphere and are thought to play an important role in the overall dynamics of the solar atmosphere. They supply bulk of the wave energy for the lower solar atmosphere, but their existence and role in the energy balance of the upper layer remains unclear. Using radiation-magnetohydrodynamic (R-MHD) simulations, we study naturally excited IGWs in realistic models of the solar atmosphere. In this talk, we discuss some of our recent results on the influence of the Sun's magnetic field on the propagation of IGWs and their energy transport. Our analysis suggests that the IGWs are generated independent of the mean magnetic property of the atmosphere. However, their propagation into higher layers is strongly affected by the presence and the topology of the magnetic field. We discuss how IGWs may play a significant role in the heating of the chromospheric layers in regions where horizontal fields are thought to be prevalent, like the internetwork region.
May 26	Wed	Du Pei (University of Harvard)	Pure Maths Colloquium
14:00		Hidden algebraic structures in geometry from fivebranes
		Google Meet
	Abstract: The existence of quantum field theories in higher dimensions predicts many hidden algebraic structures in geometry and topology. In this talk, I will survey some recent developments where such algebraic structures lead to new insights into 1) the quantization of moduli spaces of Higgs bundles, 2) the categorification of quantum invariants of 3-manifolds, and 3) novel types of TQFTs in four dimensions.
May 26	Wed	Bruno Barros (Lisbon)	Cosmology, Relativity and Gravitation
15:00		Dark energy interactions: phenomenology and observations
		Blackboard Collaborate
	Abstract: In this talk, I will thoroughly explore the phenomenology of dark energy couplings, by exposing two distinct models where dark energy interacts with dark matter. We will journey through three different cosmological phases, so as to study the main influence of the coupling on formation of structure processes. The background cosmology is analysed by resorting to numerical and dynamical system techniques. We will follow closely the linear behaviour of the matter perturbations and test their growth against redshift space distortions data. We also shed some light on the sensitivity of future missions to constrain the dark coupling. Finally, we are going to witness the collapse of matter overdensities by inspecting the physics of the spherical collapse, tracking the evolution of perturbations along the first stages of their nonlinear regime, and compute the number of bound structures formed.
May 27	Thu	Bradley W. Hindman (University of Colorado, Boulder (USA))	Plasma Dynamics Group
16:00		Do Coronal Loops Oscillate in Isolation?
		Google Meet
	Abstract: One of the most prominent features seen in images of the solar corona by EUV telescopes are the elegant arches of glowing plasma that trace magnetic field lines through the corona. Typically, these loops are preferentially illuminated segments of a larger structure comprised of an arcade of arched field lines. Such loops are often observed to undulate in response to nearby solar flares. A flurry of observational and theoretical effort has been devoted to the explanation and exploitation of these oscillations. The grand hope is that seismic techniques can be used as probes of the strength and structure of the corona’s magnetic field. The commonly accepted viewpoint is that each visible loop oscillates as an independent entity and acts as a separate wave cavity for MHD kink waves. Thus, the seismic analysis is conveniently reduced to a 1D wave problem with boundary conditions at the foot points of the loop in the photosphere. I will argue that for many events, this generally accepted model for the nature of the wave cavity is fundamentally wrong. In particular, the entire 3D magnetic arcade in which the bright loops reside participates in the oscillation. Thus, the true wave cavity is much larger than the individual loop and inherently multidimensional. I will present theoretical arguments to support this 3D viewpoint and discuss the implications and opportunities for seismology of the solar corona.
May 28	Fri	Fionnlagh Dover (SP2RC (UoS))	SP2RC seminar
13:00		Numerical MHD Investigation of Jets in the Solar Atmosphere
		Google meet link: https://meet.google.com/ciq-zovu-rzm
	Abstract: Solar spicules are one of the dominant dynamic phenomena of the lower solar atmosphere. Here, we show our results on modelling the propagation of such localised jets driven by a momentum pulse as the exciting force near photospheric heights. Using the MPI-AMRVAC code to perform 2D MHD simulations in an idealised stratified solar atmosphere, we investigate how key parameters (e.g., driver time, equilibrium magnetic field strength, velocity amplitude of driver and tilt with respect to the magnetic field) determine the morphology of these small-scale solar jets. A parametric study is carried out and using jet tracking software we analyse the jet properties (e.g., widths, apex heights, etc). We find that jet boundary deformation occurs naturally due to speeds involved in driving these jets within the range of spicule heights that could be then a possible alternative explanation for the appearance of transverse motions (both axisymmetric and non-axisymmetric deformations). By resolving structures up to 10 km, we also find unforeseen substructures inside the spicular jet beam. We propose observers to confirm this latter finding that may be challenging due to current spatial resolution limits.
Jun 3	Thu	Azaymi Litzi Siu-Tapia (Instituto de Astrofísica de Andalucía, IAA (ES))	SP2RC/ESPOS seminar
10:00		The solar atmosphere as observed through the Mg I b2 line at high spatial resolution
		Zoom (Meeting ID: 165 498 165)
	Abstract: The Mg I b2 line at 5173 Å forms over a large range of heights but its core, which forms under conditions of non-local thermodynamic equilibrium, is most sensitive to heights near the temperature minimum, a region of the solar atmosphere that has not been sufficiently explored. The next-generation solar observatories will have access to this spectral line and will allow for multi-line observations to study the different layers of the solar atmosphere simultaneously and with unprecedented polarimetric sensitivity. We will present a morphological classification of the intensity and circular polarization profiles of this spectral line at high-spatial-resolution, using observations from the Swedish 1-m Solar Telescope. We will also discuss the results of the weak field approximation applied to the Mg I b2 line, and their comparison with inversion results of the Fe I 6173 Å line to understand how the magnetic field changes with height in the solar atmosphere.
Jun 9	Wed	Noemi Frusciante (Lisbon)	Cosmology, Relativity and Gravitation
15:00		Probing modified gravity with cosmology and solutions to the Hubble tension
		Blackboard Collaborate
	Abstract: The late time cosmic acceleration is one of the most puzzling phenomena in modern cosmology. Its modeling within General Relativity (GR) through the cosmological constant (L) results in the LCDM scenario. Although the latter gives a precise description of the Universe, it is known that it still contains a number of unresolved problems. These lead researchers to look for modified gravity models, for example by including additional degrees of freedom. In this talk I will present the phenomenology and the cosmological bounds of theories consistent with the gravitational-wave event GW170817. In particular I will discuss models which solve the Hubble tension between Planck and local measurements and for which data show a statistically significant preference over LCDM.
Jun 17	Thu	Deborah Baker (Mullard Space Science Laboratory, University College London (UK))	SP2RC/ESPOS seminar
10:00		Magnetic Perturbations in a Sunspot Chromosphere Linked to Plasma Fractionation in the Corona
		Zoom (Meeting ID: 165 498 165)
	Abstract: Element abundance signatures have long been used as tracers of physical processes throughout astrophysics. Understanding the spatial and temporal variations in the composition of the solar corona provides insight into how matter and energy flow from the solar chromosphere out into the heliosphere as well as from the chromospheres of solar-type stars into their astrospheres. In this work, we investigate the spatial distribution of highly varying plasma composition around one of the largest sunspots of solar cycle 24. Observations of the photosphere, chromosphere, and corona are brought together with magnetic field modeling of the sunspot in order to probe the conditions that regulate the degree of plasma fractionation within loop populations of differing connectivities. We find that, in the coronalmagnetic field above the sunspot, variation in plasma composition is highly structured, with extremes in the level of fractionation among the distinct loop populations. Loops above the umbra contain unfractionated plasma, i.e. photospheric composition, while coronal loops rooted in the penumbra contain fractionated plasma, with the highest levels observed in the loops that connect within the active region. The distribution of the highly fractionated plasma appears to be correlated with the spatial locations at which intrinsic magnetic perturbations are identified in high spatial resolution spectropolarimetric observations of the solar chromosphere. Tracing field lines from regions of highly fractionated plasma in the corona to locations of magnetic perturbations detected in the chromosphere shows that they are magnetically linked. These results indicate a direct connection between sunspot chromospheric activity and observable changes in coronal plasma composition. We interpret our findings in the wider context of coronal heating and the ponderomotive force model of elemental fractionation.
Jun 17	Thu	Abdulrahman Albidah (Sheffield)	Plasma Dynamics Group
16:00		POD and DMD tutorial
		Google Meet
	Abstract: Modal decomposition, like POD and DMD, are incredible methodologies with a vast range of applicability. In our group, we have an open code for that in matlab. In today's talk, Abdulrahman will explain how those codes work.
Jun 24	Thu	Prof. Lucie Green (UCL, Mullard Space Science Laboratory)	SP2RC seminar
10:00		UK-SOSS: What can magnetic helicity tell us about the likelihood of an eruption from active regions?
		Zoom link: https://zoom.us/j/95338171418 Meeting ID 953 3817 1418
	Abstract: Understanding the physical processes that underly the occurrence of coronal mass ejections is a key area of research, whilst being able to forecast an ejection beforehand would provide significant benefits to space weather forecasting lead-times. In this talk, these two aims will be discussed in the context of a quantity known as magnetic helicity, in particular the so-called helicity proxy that can be determined from modelled active region magnetic field and which has shown potential in being able to indicate when an active region will produce eruptive activity. Results will be presented for NOAA active region 11158, that builds on the helicity proxy analysis already presented by Thalmann et al. (2019) to incorporate the observed evolution of the coronal field and the physical processes taking place in the time leading up to an eruption.
Jun 25	Fri	Dr Marco Stangalini (Italian Space Agency (ASI,Italy))	SP2RC seminar
13:00		Waves in the lower solar atmosphere through spectropolarimetry: first detection of torsional oscillations in the solar photosphere
		Google meet link: https://meet.google.com/ciq-zovu-rzm
	Abstract: MHD waves in the lower solar atmosphere were generally investigated through intensity and Doppler velocity data. However, modern high spatial and temporal resolution spectropolarimetry gives access to additional diagnostics, which can be helpful in the identification and the correct interpretation of the wave modes. Very recently, thanks to high-resolution spectropolarimetric observations in the lower solar atmosphere it was possible to detect for the first time anti-phase incompressible torsional oscillations in a magnetic pore. These waves have proven to be important in a range of physical systems due to their ability to transport non-thermal energy over long distances in a magnetised plasma. This property is of specific interest in solar physics where the extreme heating of the atmosphere of the Sun remains unexplained. Despite evidences in the upper atmosphere, they were not directly observed in the photosphere. The excitation of torsional waves in photospheric magnetic structures can significantly contribute to the energy transport in the solar atmosphere and the acceleration of the solar wind, especially if such signatures will be ubiquitously detected in even smaller structures with the forthcoming next generation of solar telescopes, like DKIST, EST and Solar Orbiter, which will significantly improve the spectropolarimetric accuracy and sensitivity. In this seminar, I will show and discuss these recent results and the new interesting possibilities enabled by high-resolution spectropolarimetry in the detection and identification of wave modes in solar magnetic structures.
Jul 2	Fri	Dr Manolis K. Georgoulis (RCAAM of the Academy of Athens )	SP2RC seminar
13:00		The Science of FLARECAST: Results, Open-Access Resources and Envisioned Future Trends in Solar Flare Forecasting
		https://meet.google.com/ciq-zovu-rzm
	Abstract: As an encompassing overview of the European Union FLARECAST project will be published shortly, I will attempt a critical description of the project’s key science results, involving the motivation, the methodology, the metadata and the performance verification tasks performed in its framework. The science of FLARECAST pointed to three objectives, all falling under its main goal to better understand the drivers of solar flare forecasting and to improve prediction. These objectives were, first, to find out which preflare properties of solar active regions, treated as flare predictors, work best for forecasting purposes; second, to identify promising new predictors; and third, to perform an explorative research on flare and eruption prediction that utilized numerical simulations and investigated the physical and statistical connection between flares and coronal mass ejections. Interesting, and potentially important, leads were found, that may well help spearhead future efforts. Given the project’s limited duration, some further desired tasks were ultimately left for the future. On a top level, we concluded that the stochastic nature of solar flares’ occurrence is so deeply rooted in the Sun’s fundamental magnetic activity that even a massive Big Data and machine learning effort such as FLARECAST could not decisively lift this barrier of stochasticity. Furthermore, FLARECAST adhered to the European Union’s open access policy and consistently planned to help avoid effort duplication in future forecast attempts by making openly available all data, codes, and infrastructure it created. Detailed guidance in retrieving these resources will also be presented.
Jul 23	Fri	Bodan Arsovski (Sheffield)	Number Theory seminar
14:00		p-adic representations and p-adic Hodge theory
		Google Meet
Sep 23	Thu	Rahul Yadav (Stockholm University, Sweden)	SP2RC/ESPOS seminar
10:00		Multiline Spectropolarimetric Observation of a C2-Class Solar Flare
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: We present high-resolution and multiline spectropolarimetric observations of a C2-class solar flare (SOL2019-05-06T08:47). The rise, peak, and decay phases of the flare were recorded continuously and simultaneously in the Ca II K, Ca II 8542 Å, and Fe I 6173 Å lines with the CRISP and CHROMIS instruments at the Swedish Solar Telescope (SST). At the flare footpoints, a non-LTE multiline inversion code (STiC) was employed to infer the temperature, magnetic field, line-of-sight (LOS) velocity, and microturbulent velocity. The temporal analysis of the inferred temperature at the flare footpoints shows that the flaring atmosphere from log τ500 ∼ −2.5 to −3.5 is heated up to 7 kK, whereas from log τ500 ∼ −3.5 to −5 the inferred temperature ranges between ∼7.5 kK and ∼11 kK. During the flare peak time, the LOS velocity shows both upflows (evaporation) and downflows (condensation) around the flare footpoints in the upper chromosphere and lower chromosphere, respectively. Moreover, the temporal analysis of the LOS magnetic field exhibits a maximum change of ∼600 G. After the flare, the LOS magnetic field decreases to the non-flaring value, exhibiting no permanent or step-wise change. The analysis of response functions to the temperature, LOS magnetic field, and velocity shows that the Ca II lines exhibit enhanced sensitivity to the deeper layers compared to the non-flaring atmosphere. We also estimated the radiative losses from the singly ionized Ca and Mg atoms using the semi-empirical model atmosphere inferred from the inversion of the CRISP and CHROMIS dataset. The obtained radiative losses range from 50 to 180 kW/m^2 near the flare footpoints. Our observations illustrate that even a less intense C-class flare can heat the deeper layers of the solar chromosphere, mainly at the flare footpoints, without affecting the photosphere.
Sep 29	Wed	Leanne Durkan (University College Dublin)	Cosmology, Relativity and Gravitation
15:00		Modelling Extreme Mass Ratio Inspirals for LISA
		Seminar Room B19, 301 Glossop Road
	Abstract: Extreme mass-ratio inspirals (EMRIs) are a key source of gravitational waves for the future space based detector, LISA. To model EMRI waveforms to the accuracy required for parameter estimation by LISA, we require black hole perturbation theory and gravitational self-force theory, where the perturbing quantity is the small mass ratio. In my talk I will provide an overview of how we model EMRIs, using the example of a Schwarzschild background and circular orbits. I will justify why we must calculate the metric perturbation to second-order in the small mass ratio, why we use the Lorenz gauge and why, to first-order, we can treat the smaller compact body as a point-like particle. I will present some recent results of the gravitational wave energy flux at future null infinity, discussing in more detail the contribution of the slow-time derivative of the first-order metric perturbation, which appears in the second-order source to the field equations. I will also briefly mention current research being explored to extend the calculation of the Lorenz gauge metric perturbation to eccentric orbits and to Kerr, required to develop physically realistic models for LISA.
Oct 6	Wed	Christiane Klein (Leipzig)	Cosmology, Relativity and Gravitation
15:00		Charged scalar fields inside charged black holes
		Blackboard Collaborate
	Abstract: The strong cosmic censorship conjecture states that black hole spacetimes cannot be continued beyond their inner horizon due to the divergence of local observables, such as the stress-energy tensor of a classical or quantum scalar field, at that horizon. In the case of a spherically symmetric, charged black hole, numerical and analytical studies indicate, that this conjecture is violated classically, even for charged scalar fields, but that the conjecture can be restored by quantum effects in the real scalar case. Here, we present a study on the behaviour of quantum charged scalar fields in a charged, non-rotating black hole. Apart from an extension of the results for real quantum fields, we focus on the charge current induced by this field. We derive an expression for the renormalized current in the Unruh vacuum. In addition, we demonstrate numerically, that the quantum scalar field can charge, instead of discharge, the black hole near the inner horizon.
Oct 7	Thu	Artem Koval (Astronomical Institute of the CAS)	SP2RC/ESPOS seminar
10:00		Shock-wave radio probing of solar wind sources in coronal magnetic fields
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: The Space Weather effects in the near-Earth environment as well as in atmospheres of other terrestrial planets arise by corpuscular radiation from the Sun, known as the solar wind. The solar magnetic fields govern the solar corona structure. Magnetic-field strength values in the solar wind sources - key information for modeling and forecasting the Space Weather climate - are derived from various solar space- and ground-based observations, but, so far not accounting for specific types of radio bursts. These are “fractured” type II radio bursts attributed to collisions of shock waves with coronal structures emitting the solar wind. Here, we report about radio observations of two “fractured” type II bursts to demonstrate a novel tool for probing of magnetic field variations in the solar wind sources. These results have direct impact on interpretations of this class of bursts and contribute to the current studies of the solar wind emitters.
Oct 7	Thu	Sergiy Shelyag (School of Information Technology, Deakin University, Australia)	Plasma Dynamics Group
12:00		Technicalities of MURaM solar photospheric models: how to use them and what to expect from them
		https://meet.google.com/crn-ivhm-mzr
	Abstract: In my presentation, I will provide a brief look into the details of how MURaM photospheric models are generated. I will review the fundamentals of numerical modelling of solar plasmas and discuss particular difficulties for such modelling and implemented solutions. Then, I will demonstrate the output of MURaM, show basic IDL scripts designed for reading the models and the processing techniques. Finally, I will describe technical details on why and how the MURaM models have to be converted to observables prior to attempts to compare them with the real observational data.
Oct 8	Fri	Bodan Arsovski (Sheffield)	Number Theory seminar
13:00		Limiting measures of supersingularities
		Google Meet
	Abstract: In 2001, Gouvêa and Buzzard noticed several interesting phenomena in the distributions of the p-adic slopes of weight k, level Γ_0(Np) eigenforms, the two main ones being that the slopes, in almost all cases, are integers; and that the slopes, in almost all cases, are no larger than (k-1)/(p+1), a much smaller bound than expected. In trying to explain the second phenomenon, Gouvêa made a conjecture that, after normalizing the slopes by dividing by k-1 so that they lie in the interval [0,1], their distributions tend to the uniform measure on [0,1/(p+1)]∪[p/(p+1),1] as k tends to infinity. In particular, Gouvêa's conjecture implies that the slopes are concentrated away from the middle interval (1/(p+1),p/(p+1)). This conjecture can be seen as the p-adic version of an interesting twist on the Sato–Tate conjecture: while the Sato–Tate conjecture asks about the distribution of the (real) slopes of a fixed modular form for varying primes, here one is interested in the distributions of the (p-adic) slopes of varying modular forms for a fixed prime. In this talk we discuss a proof that the slopes are indeed concentrated away from the middle interval (1/(p+1),p/(p+1)) when p>3 is Γ_0(N)-regular, which uses the p-adic local Langlands correspondence.
Oct 13	Wed	Alexander Smith (Saint Anselm College)	Cosmology, Relativity and Gravitation
13:30		Relational dynamics and quantum time dilation
		Blackboard Collaborate
	Abstract: The lesson of general relativity is background independence, which results in a Hamiltonian constraint. This presents a challenge for quantum gravity because the quantisation of this constraint demands that physical states of geometry and matter are frozen, leading to one aspect of the problem of time. We must then explain how the conventional notion of time evolution emerges, which motivates the need for a relational description of quantum dynamics. Using quantum clocks and covariant time observables, I will introduce a formulation of relational quantum dynamics that allows for a probabilistic notion of relativistic time dilation and a proper time / rest mass uncertainty relation. This framework will then be used to describe a quantum time dilation effect that occurs when a clock moves in a superposition of different relativistic momenta. I will argue that this time dilation effect may be observable with present-day technology and offers a new test of relativistic quantum mechanics.
Oct 14	Thu	Professor Mihalis Mathioudakis (Queen's University Belfast)	SP2RC seminar
10:00		UK-SOSS: From high-resolution observations of the Sun to the solar-stellar connection
		UK-SOSS Zoom Link: https://zoom.us/j/95338171418 Meeting ID: 953 3817 1418
	Abstract: Our nearest star has always been a unique source for our understanding of the universe in its many forms. The solar atmosphere and interior provide a working example where structures and dynamics can be studied over an enormous range of spatial and temporal scales. The seminar will begin with some global solar properties and phenomena, placing them in the context of stellar magnetic activity. We will then highlight some of the smallest features that can be resolved in the lower solar atmosphere and the physical parameters that can be extracted from them. We will comment on the high-resolution observations of the Sun and how they can help us tackle some of the challenges of stellar astrophysics.
Oct 15	Fri	Guoyin Chen (School of Astronomy and Space Science, Nanjing University)	SP2RC seminar
13:00		Coronal Loop Kink Oscillation Periods Derived with Realistic Density, Magnetic Field and Loop Geometry
		Join Zoom Meeting https://zoom.us/j/92001288271?pwd=S1FGWldWNGphUUZvZC9VNFZMWWZkUT09 Meeting ID: 920 0128 8271 Passcode: zQt2Df
	Abstract: The time domain analysis of coronal loop oscillations is an effective approach to study their physical properties, such as the magnetic field and density, which can also be derived from DEM analysis and magnetic field models independently. We take advantage of the aforementioned methods to do the following three main work: (1) the time domine analysis of coronal loop oscillations; (2) DEM diagnostics about temperature and density; (3) magnetic extrapolation to determine the realistic magnetic field distribution. These three parts are combined by the governing equation of coronal loop oscillations to show the consistency between the observed period and computed one. And we will show the impact of the loop geometry on the oscillation period.
Oct 15	Fri	Haluk Sengun (Sheffield)	Number Theory seminar
13:00		Periods of mod p Bianchi modular forms and Selmer groups
		Google Meet
	Abstract: The relationship between special values of L-functions of modular forms and Selmer group of modular p-adic Galois representations is a major theme in number theory. Given the developing mod p Langlands program, it is natural to ask whether there is some kind of mod p analogue of the above theme. Notice that mod p modular forms do not have associated L-functions! In this talk, I will report on ongoing work with Lewis Combes in which we formulate, and computationally test, a connection between Selmer groups of mod p Galois representations and mod p Bianchi modular forms. This is inspired by a speculation of Calegari and Venkatesh.
Oct 19	Tue	Robert Kurinczuk (Sheffield)
10:00		The local picture: Talk 1
		meet.google.com/bbv-xhgy-mie
Oct 20	Wed	Nicole Mideo (Toronto)	Mathematical Biology Seminar
13:00		Understanding variation in malaria infection dynamics
		https://york-ac-uk.zoom.us/j/93472504071
	Abstract: Infection outcomes are highly variable: some individuals suffer severe illness while others seem relatively unharmed by the same infection. Underlying this variation are numerous sources of heterogeneity, including parasite genetics, host genetics, and infectious dose, among others. Yet mechanistic explanations of differential infection outcomes remain elusive. Focusing on data from experimental malaria infections in lab mice, my research has been developing and refining mathematical models to reveal those mechanistic explanations. In this talk, I will describe what we have learned about the parasite traits, host traits, and their interactions that give rise to the observed variation in malaria infection dynamics and outcomes for hosts.
Oct 21	Thu	Paolo Pagano (Universita di Palermo)	Plasma Dynamics Group
16:00		What we know about wave heating modelling. Or maybe not.
		https://meet.google.com/mti-wvss-xbz
	Abstract: In this seminar, I will cover a number of results about wave heating models that emerged from our MHD simulations. Over the last few years, we have developed several models of coronal heating by phase-mixing of Alfvènic waves and, while some issues need more thorough investigation, some results seem to remain consistent across different models. I will mostly focus on the nature of the waves that can contribute to the coronal heating, on the structure of the boundary shell where the heating could happen, and on the amount of heating itself.
Oct 27	Wed	Ricardo Martinez-Garcia (South American Institute for Fundamental Research, Brazil)	Mathematical Biology Seminar
13:00		Beyond the law of mass action in ecology: the effect of range-residency on encounter statistics
		https://york-ac-uk.zoom.us/j/93472504071
	Abstract: For over 100 years, mathematical models in population ecology have relied on very strong and unrealistic assumptions about the way individuals move and get to interact with each other and with the environment. Specifically, they assume that individuals behave like the molecules of an ideal gas: following completely random trajectories through the entire area occupied by the population and only interacting with each other when their trajectories intersect. Under these assumptions, the encounter rates follow the law of mass action, and individual encounter events are uniformly distributed within the population range. However, mounting empirical evidence suggests that animals use space non-uniformly, occupy home ranges substantially smaller than the population range, and are often capable of nonlocal perception. I will discuss our recent efforts to develop a refined theory for ecological encounters grounded on empirically supported individual movement behavior [1, 2]. First, I will introduce the theoretical framework and derive novel analytical expressions for the encounter rates and the spatial distribution of encounters. Second, I will apply it to animal tracking data and discuss the ecological insights we obtain from such an analysis. I will conclude with a few remarks on future directions. References: [1] Martinez-Garcia, R., Fleming, C. H., Seppelt, R., Fagan, W. F., & Calabrese, J. M. (2020). How range residency and long-range perception change encounter rates. Journal of Theoretical Biology, 498, 110267. [2] Noonan, M. J., Martinez-Garcia, R., Davis, G. H., Crofoot, M. C., Kays, R., Hirsch, B. T., ... & Calabrese, J. M. (2021). Estimating encounter location distributions from animal tracking data, Methods in Ecology and Evolution, 12 (7), 1158-1173.
Oct 27	Wed	Alessandra Caraceni (Pisa)	Probability seminar
15:00		Polynomial mixing time for edge flips via growing random planar maps
		Google Meet
	Abstract: A long-standing problem proposed by David Aldous consists in giving a sharp upper bound for the mixing time of the so-called “triangulation walk”, a Markov chain defined on the set of all possible triangulations of the regular n-gon. A single step of the chain consists in performing a random edge flip, i.e. in choosing an (internal) edge of the triangulation uniformly at random and, with probability 1/2, replacing it with the other diagonal of the quadrilateral formed by the two triangles adjacent to the edge in question (with probability 1/2, the triangulation is left unchanged). While it has been shown that the relaxation time for the triangulation walk is polynomial in n and bounded below by a multiple of n^{3/2}, the conjectured sharpness of the lower bound remains firmly out of reach in spite of the apparent simplicity of the chain. For edge flip chains on different models -- such as planar maps, quadrangulations of the sphere, lattice triangulations and other geometric graphs -- even less is known. We shall discuss results concerning the mixing time of random edge flips on rooted quadrangulations of the sphere, partly obtained in joint work with Alexandre Stauffer. A “growth scheme” for quadrangulations which generates a uniform quadrangulation of the sphere by adding faces one at a time at appropriate random locations can be combined with careful combinatorial constructions to build probabilistic canonical paths in a relatively novel way. This method has immediate implications for a range of interesting edge-manipulating Markov chains on so-called Catalan structures, from “leaf translations” on plane trees to “edge rotations” on general planar maps. Moreover, we are able to apply it to flips on 2p-angulations and simple triangulation of the sphere, via newly developed “growth schemes” to appear in an upcoming paper.
Oct 29	Fri	Soós Szabolcs (SP2RC (UoS))	SP2RC seminar
13:00		On the differences in the periodic behaviour of magnetic helicity flux in flaring active regions with and without X-class events
		Google meet link: https://meet.google.com/ciq-zovu-rzm
	Abstract: Observational pre-cursors of large solar flares and eruptions offer advancement in the scientific understanding of the underlying physics, and provide a basis for future operational systems for forecasting. In this work, we study the evolution of the normalized emergence (EM), shearing (SH) and total (T) magnetic helicity flux components for 14 flaring and 14 non-flaring active regions (ARs) using the Spaceweather Helioseismic Magnetic Imager Active Region Patches (SHARP) vector magnetic field data. Each of the selected ARs contain a $\delta$-type spot. The three helicity components of all 28 ARs were analyzed using wavelet analysis. Localised peaks of the wavelet power spectrum were identified and statistically investigated in both the flaring and non-flaring AR cases. We find that: i) the peaks of the probability density functions of the EM/SH/T flux components appear in distinct bands; ii) the correlation of the period bands shows that the periodicity of the EM helicity flux component are distinct for the flaring and non-flaring ARs, while the periodicity of SH/T remain similar; iii) for the flaring ARs the distributions of the EM/SH/T peaks change after flares; and iv) when the EM periodicity does not contain harmonics, the ARs do not host a large energetic flare. Most importantly, v) significant power at long periods ($\sim$20 hour) in the T and EM components may serve as a pre-cursor for a large energetic flare, or at least an indication that the AR is likely to host such a flare.are.
Oct 29	Fri	Silvia Nagy (Queen Mary)	Cosmology, Relativity and Gravitation
16:00		Different approaches to gravity from Yang-Mills squared
		Seminar Room B19, 301 Glossop Road
	Abstract: The idea of writing various quantities in gravity as double copies of the analogous objects in Yang-Mills gauge theory has been gaining a lot of traction in recent years - I will give an overview of the numerous different formulations that have arisen from this drive. Then I will focus on 2 particular ones: the first is based on certain double copy replacement rules in the self-dual sector, and the second links with twistor theory. These have allowed for a recent expansion of the remit of the double copy in the context of symmetries and classical solutions. Finally, I will make some comments on a more ambitious question: is it possible to unify the various different formulations into a single framework?
Nov 2	Tue	Robert Kurinczuk (Sheffield)
10:00		The local picture: Talk 2
		meet.google.com/bbv-xhgy-mie
Nov 2	Tue	Callum Reader (Sheffield)	Category Theory
14:00		Scalars and Traces in Bicategories
		Hicks Seminar Room J11
Nov 3	Wed	Amy Hurford (Memorial University of Newfoundland and Labrador, Canada)	Mathematical Biology Seminar
13:00		Challenges and insights from modelling COVID-19 in a region where most cases are travel-related
		https://york-ac-uk.zoom.us/j/93472504071
	Abstract: Many research groups have mechanistically modelled COVID-19 dynamics using variations on Susceptible-Infected-Recovered compartmental models. In the Canadian province of Newfoundland and Labrador, this approach is challenging to apply due to a high proportion of cases that are travel-related. In this talk, I will discuss our approach to modelling COVID-19 for Newfoundland and Labrador, and how some of the unique features of the province may have affected COVID-19 epidemiology and public health policy.
Nov 3	Wed	Robert Kurinczuk (University of Sheffield)	Pure Maths Colloquium
14:00		Local Langlands in families for classical groups
		meet.google.com/qxa-rhcg-skx
	Abstract: The conjectural local Langlands correspondence connects representations of p-adic groups to certain representations of Galois groups of local fields called Langlands parameters. In recent joint work with Dat, Helm, and Moss, we have constructed moduli spaces of Langlands parameters over Z[1/p] and studied their geometry. We expect this geometry is reflected in the representation theory of the p-adic group. Our main conjecture “local Langlands in families” describes the GIT quotient of the moduli space of Langlands parameters in terms of the centre of the category of representations of the p-adic group generalising a theorem of Helm-Moss for GL(n). I will give an introduction to this picture and explain how after inverting the "non-banal primes" one can prove this conjecture for the local Langlands correspondence for classical groups of Arthur and others.
Nov 3	Wed	Ian Letter (Oxford)	Probability seminar
14:00		Hybrid zones and the effect of barriers.
		LT5
	Abstract: Hybrid zones are narrow regions in which two distinct types of individuals reproduce and produce offspring of mixed type. Some mathematical models conclude that hybrid zones of populations with asymmetric selection against heterozygotes evolve, when correctly rescaled, as mean curvature flow plus a constant flow. This conclusion rests on modelling the density of a particular allele as the solution of a partial differential equation in the euclidean space, proving the result in that deterministic setting and finally showing the presence of genetic drift does not disrupt the conclusion. In this talk, I will sketch the main ingredients to adapt this result to capture an effect one would see in a real-life population; the presence of barriers. Barriers refer to environmental obstacles that prevent individuals from invading certain zones. Mathematically this translates into studying the dynamics in a subset of the euclidean space with reflecting conditions on the boundary. We show that in a particular family of domains there is a phase transition; if the domain presents an opening bigger than an explicit constant there is an invasion of the fittest type, but if the opening is smaller than said constant then there is coexistence between the two types of individuals. As a consequence, we get that barriers can provide survival of the less fit homozygote, even if at the initial time the fittest homozygote dominates an unbounded region of the domain. We also mention how the presence of genetic drift (modelled by a Spatial-Lambda-Fleming Viot type process) may change these results. This is work under the supervision of Alison Etheridge.
Nov 4	Thu	Luca Giovannelli (Dipartimento di Fisica, Università degli Studi di Roma Tor Vergata) and Cristina Campi (Dipartimento di Matematica, Università di Genova)	SP2RC/ESPOS seminar
10:00		Forecasting solar flares with a new topological parameter and a supervised machine-learning method
	Abstract: Solar flares originate from active regions (ARs) hosting complex and strong bipolar magnetic fluxes. Forecasting the probability of an AR to flare and defining reliable precursors of intense flares, i.e., X- or M-class flares, are extremely challenging tasks in the space weather field. In this talk, we focus on two metrics as flare precursors, the unsigned flux R*, tested on MDI/SOHO data and calibrated for higher spatial resolution SDO/HMI maps, and a novel topological parameter D representing the complexity of a solar active region. The parameter D is based on the automatic recognition of magnetic polarity inversion lines (PILs) in identified SDO/HMI ARs and is able to evaluate their magnetic topological complexity. We use both a heuristic approach and a supervised machine-learning method to validate the effectiveness of these metrics to predict the occurrence of X- or M-class flares in a given solar AR during the following 24 hr period. Our feature ranking analysis shows that both parameters play a significant role in prediction performances. Moreover, the analysis demonstrates that the new topological parameter D is the only one, among 173 overall predictors, that is systematically ranked within the top 10 positions. Reference: Cicogna et al., Flare-forecasting Algorithms Based on High-gradient Polarity Inversion Lines in Active Regions, ApJ, 915, id.38, 2021
Nov 4	Thu	André V. G. Cavalieri (Instituto Tecnológico de Aeronáutica)	Plasma Dynamics Group
16:00		Extraction and modelling of coherent structures in turbulent flows
		https://meet.google.com/jcc-erwn-fva
	Abstract: Detailed measurements or numerical simulations of turbulent flows reveal the existence of coherent large-scale structures, which are relevant for turbulence properties such as wall friction, heat transfer or sound radiation. Recent years have seen the emergence of modal decomposition techniques, which, when applied to turbulent flows, allow an extraction of coherent structures in a quantitative manner. Such structures have properties related to the linearised Navier-Stokes system, and may be modelled as the most amplified responses to applied forcing; this provides a rationale for understanding coherent structures as dominant waves obtained by the linearisation of the flow equations. In this presentation we will review modal decomposition of turbulent flows focusing on spectral proper orthogonal decomposition (SPOD), and linearised models using the resolvent operator. We will explore the connection between SPOD and resolvent modes in some canonical flows such as turbulent jets and channels. Finally, we will discuss how to include non-linearity in dynamical models of coherent structures, showing recent results for turbulence estimators and reduced-order models.
Nov 9	Tue	Haluk Sengun (Sheffield)
10:00		The global picture: Talk 1.
		meet.google.com/bbv-xhgy-mie
Nov 10	Wed	Rachel Warnock (Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany)	Mathematical Biology Seminar
13:00		A phylogenetic approach to unifying models in life and earth sciences
		https://york-ac-uk.zoom.us/j/93472504071
	Abstract: The fossilised birth-death (FBD) process provides a modelling framework that explicitly combines the diversification and fossil sampling processes. The model can be applied to infer dated trees, based on the analysis of phylogenetic (morphological or molecular) character data. It can also be used to infer key macroevolutionary parameters (origination, extinction and fossil recovery rates), even in the total absence of phylogenetic character data. Here, I will discuss my work into the application of the FBD model to recover metrics commonly used in quantitative paleobiology (origination, extinction, species richness) based on analyses of stratigraphic ranges or fossil occurrence data. The FBD model provides a mechanistic and flexible framework that has several key advantages compared to alternative methods, creating many opportunities for process-based inference in paleobiology.
Nov 10	Wed	Ananyo Dan (University of Sheffield)	Pure Maths Colloquium
14:00		McKay correspondence for isolated Q-Gorenstein singularities
		meet.google.com/qxa-rhcg-skx
	Abstract: The McKay correspondence is a (natural) correspondence between the (non-trivial) irreducible representations of a finite subgroup G of $SL(2,\mathbb{C})$ and the irreducible components of the exceptional divisor of a minimal resolution of the associated quotient singularity $\mathbb{C}^2//G$. A geometric construction for this correspondence was given by González-Sprinberg and Verdier, who showed that the two sets also correspond bijectively to the set of indecomposable reflexive modules on the quotient singularity. This was generalized to higher dimensional quotient singularities (i.e., quotient of $\mathbb{C}^n$ by a finite subgroup of $SL(n,\mathbb{C})$) by Ito-Reid, where the above sets were substituted by certain smaller subsets. It was further generalized to more general quotient singularities by Bridgeland-King-Reid, Iyama-Wemyss and others, using the language of derived categories. In this talk, I will survey past results and discuss what happens for the isolated Q-Gorenstein singularities case (not necessarily a quotient singularity). If time permits, I will discuss applications to Matrix factorization. This is joint work in progress with J. F. de Bobadilla and A. Romano-Velazquez.
Nov 10	Wed	Eugene Lim (King's College)	Cosmology, Relativity and Gravitation
15:00		Gravitational Waves from Exotic Compact Objects
		Blackboard Collaborate
	Abstract: If dark matter is made out of light bosonic fields, then they can collapse to form highly compact self-gravitating objects collectively known as exotic compact objects (ECOs). Since they are compact, they can merge to either form a more massive ECO, or a black hole, producing gravitational waves which can be probed by GW detectors. In this talk, I will discuss the physics of such objects and their expected signatures from a hypothetical merger scenario. I will talk about the technical challenges that are needed to be overcome before we can make sufficiently precise predictions that can then be used to search for them.
Nov 11	Thu	Prof. Sandra Chapman (University of Warwick)	SP2RC seminar
10:00		UK-SOSS: Space weather climate on solar cycle time-scales
		Zoom link: https://zoom.us/j/95338171418
	Abstract: Space weather and solar terrestrial physics observations are increasingly becoming a data analytics challenge and there are common approaches with other fields such as earth climate observations. Whilst focussing on specific applications, this talk aims to present generic methodology for inhomogeneous ‘real world’ data. Over the last 5 cycles we have high-quality in-situ solar wind parameters and ground-based geomagnetic indices. Climate is the distribution of weather, and we will examine how the distributions of these parameters and indices vary within and between solar cycles. Over the last 14 cycles we have geomagnetic indices such as the aa index which are poorly resolved in amplitude but nevertheless contain information on the likelihood of occurrence of extreme space weather events, and we discuss how this can be quantified, setting the Carrington event in the context of extreme events that have occurred over the last 150 years. Each solar cycle is of unique duration, and we show how the Hilbert transform of daily sunspot number can be used to map each cycle onto a uniform time-base or ‘sun clock’. We can then use this mapping to quantify how activity in space weather relevant parameters, and in particular the likelihood of super-storms, is modulated by the solar cycle. This reveals the phases in the solar cycle where there is a clear ‘switch on’ and ‘switch off’ of activity and these are in principle predictable. Sun clocks for both the Schwabe and Hale cycles will be discussed.
Nov 12	Fri	Michael K Griffiths (Research IT, University of Sheffield)	SP2RC seminar
13:00		Computational MHD for solar physics with Graphical Processing Units
		https://meet.google.com/ciq-zovu-rzm
	Abstract: The talk will review the development of MHD codes for GPU platforms and will focus on the development of a GPU version of the Sheffield Advanced Code. After a discussion of code validation we report on the application of the code to a computational study of solar global oscillations. The solar p modes are generated by global resonant oscillations and turbulent motions just beneath the photosphere. The resulting propagation of this wave energy into the solar atmosphere may be used as a diagnostic tool to predict some of the physical characteristics of the suns atmospheric layers. We report on a results of hydrodynamic and MHD simulations for different regions of the solar atmosphere. An extended with a sinusoidal profile across the base of the computational model was used to recreate atmospheric motions generated by global resonant oscillations. The results indicate a shift in frequency arising from interference between the driven waves and refections from the transition layer. Results for the MHD models exhibit a periodic behaviour comparable with observational data.
Nov 12	Fri	Hiraku Atobe (Hokkaido University)	Number Theory seminar
13:00		Local newforms for GL(n)
		Google Meet
	Abstract: In 1981, Jacquet--Piatetskii-Shapiro--Shalika established the theory of local newforms for irreducible generic representations of general linear groups over p-adic fields. In this talk, we extend their results to all irreducible representations. To do this, we introduce a new family of compact open subgroups indexed by certain tuples of non-negative integers. For the proof, we define local Rankin--Selberg integrals for Speh representations. This is a joint work with Satoshi Kondo and Seidai Yasuda.
Nov 16	Tue	Haluk Sengun (Sheffield)
10:00		The global picture: Talk 2.
		meet.google.com/bbv-xhgy-mie
Nov 17	Wed	Yamir Moreno (Universidad de Zaragoza, Spain)	Mathematical Biology Seminar
13:00		A data-driven perspective for the mathematical modeling of the COVID-19 pandemic
		https://www.google.com/url?q=https://york-ac-uk.zoom.us/j/93472504071&sa=D&source=calendar&ust=1633960477276127&usg=AOvVaw3SK1fTyzInt1SrhtMTHTcs
	Abstract: The Coronavirus disease 2019 (COVID-19) has forced an unprecedented response from health authorities worldwide and the World Health Organization. Despite the adoption of drastic measures, the pandemic is still ongoing worldwide, and recursive surges of infections are observed in many countries. Even with vaccination campaigns currently rolling out, specific pharmaceutical interventions need to be adopted to reduce the pressure on healthcare systems. Here we show results that correspond to different stages of the pandemic using data-driven modeling. Specifically, we present simulations using data-driven models tailored to mobility data from China, Spain, and the U.S. The models are used to estimate the effectiveness of customary public interventions on the spread of COVID-19 in these locations as well as to calculate herd immunity thresholds of realistic populations and vaccine coverage needed to protect them. Our main findings highlight that having a coordinated response system is key for the containment of the spread of COVID19 and its possible eradication at the lowest possible cost.
Nov 17	Wed	Silvia Pla García (Valencia)	Cosmology, Relativity and Gravitation
15:00		Quantum Field Theory in FLRW universes: vacuum choices and renormalization
		Hicks LT9
	Abstract: In this talk I will review two of the main issues in the theory of quantum fields in curved space-times, with special attention to FLRW universes and charged scalar fields. One is the ambiguity in the choice of a preferred vacuum state. The second is the explicit evaluation of the vacuum expectation value of composite operators of the quantum fields (e.g., the stress energy tensor), which requires the application of renormalization techniques. I will focus on the adiabatic regularization method. Then, I will discuss its connection with other renormalization techniques (Hadamard renormalization, De Witt–Schwinger method). Finally, I will illustrate the importance of all previous considerations with a simple physical example.
Nov 18	Thu	Ross Pallister (Solar and Space Physics group, Northumbria University, UK)	SP2RC/ESPOS seminar
10:00		Test-particle simulations at tearing coronal null-point current sheets
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: Magnetic reconnection is widely accepted to be a major contributor to nonthermal particle acceleration in the solar atmosphere. We investigate particle acceleration in two evolving field geometries: first in an isolated tearing current sheet, then in a full-scale coronal jet. Both geometries involve 3D reconnection with at least one magnetic null point. A test-particle approach is employed, using electromagnetic fields from magnetohydrodynamic (MHD) simulations of these geometries. Using this method, we examine the trajectories of high-energy protons and electrons injected near reconnecting null points and how the directionality of their acceleration differs. We will discuss what the ejection and impact patterns of heliosphere and photosphere-incident particles respectively can tell us about the location, size and shape of field structures that are formed in tearing current sheets during null-point reconnection in the solar corona. We will also consider how we may observe the simulated differences between proton and electron impact patterns.
Nov 18	Thu	Beatrice Popescu-Braileanu (Katholieke Universitet Leuven)	Plasma Dynamics Group
16:00		Damping of the small scales due to partial ionization effects in the solar chromosphere
		Google Meet
	Abstract: The chromosphere is a partially ionized layer of the solar atmosphere, the transition between the photosphere where the gas motion is determined by the gas pressure and the corona dominated by the magnetic field. Partial ionization effects are usually modeled in the single-fluid approach through the ambipolar term in a generalized Ohm's law or in a purely two-fluid model of neutral and charged particles. We study the effect of partial ionization for 2D wave propagation in a gravitationally stratified, magnetized atmosphere with properties similar to the solar chromosphere in the single-fluid approach with ambipolar effect. We adopt an oblique uniform magnetic field in the plane of propagation with strength suitable for a quiet sun region. We use numerical simulations where we continuously drive fast waves at the bottom of the atmosphere. The collisional coupling between ions and neutrals decreases with the decrease of the density and the ambipolar effect becomes important. Fast waves excited at the base of the atmosphere reach the equipartition layer and reflect or transmit as slow waves. While the waves propagate through the atmosphere and the density drops, the waves steepen into shocks. The main effect of ambipolar diffusion is damping of the waves. We find that for the parameters chosen, the ambipolar diffusion affects the fast wave before it is reflected, with damping being more pronounced for waves which are launched in a direction perpendicular to the magnetic field. Slow waves are less affected by ambipolar effects. The damping increases for shorter periods and larger magnetic field strengths. Small scales produced by the nonlinear effects and the superposition of different types of waves created at the equipartition height are efficiently damped by ambipolar diffusion. Magnetic energy can be converted into internal energy through the dissipation of the electric current produced by the drift between ions and neutrals. In the two-fluid model the damping is related to the decoupling between charges and neutrals. We observed that waves in neutrals and plasma, initially coupled at the upper photosphere, become uncoupled at higher heights in the chromosphere and the waves are damped. In simulations of the Rayleigh-Taylor instability ion-neutral collision frequency is the primary determining factor in development or damping of small-scale structures. Kinetic energy can be converted into internal energy through the frictional heating produced by the drift between ions and neutrals.
Nov 19	Fri	Vaidehee Thatte (King's College London)	Number Theory seminar
13:00		Arbitrary Valuation Rings and Wild Ramification
		Google Meet
	Abstract: Classical ramification theory deals with complete discrete valuation fields k((X)) with perfect residue fields k. Invariants such as the Swan conductor capture important information about extensions of these fields. Many fascinating complications arise when we allow non-discrete valuations and imperfect residue fields k. Particularly in positive residue characteristic, we encounter the mysterious phenomenon of the defect (or ramification deficiency). The occurrence of a non-trivial defect is one of the main obstacles to long-standing problems, such as obtaining resolution of singularities in positive characteristic. Degree p extensions of valuation fields are building blocks of the general case. In this talk, we will present a generalization of ramification invariants for such extensions and discuss how this leads to a better understanding of the defect. If time permits, we will briefly discuss their connection with some recent work (joint with K. Kato) on upper ramification groups.
Nov 23	Tue	Haluk Sengun (Sheffield)
10:00		The global picture: Talk 3
		meet.google.com/bbv-xhgy-mie
Nov 23	Tue	Simon Willerton (Sheffield)	Category Theory
14:00		Optimal Transport and Enriched Categories
		Hicks Seminar Room J11
	Abstract: I will describe an initial foray into looking at how category theory fits within the field of optimization. The dual of the standard optimal transport problem admits a duality within itself which is intimately related to an adjunction arising from a profunctor. I will look at the centre of this adjunction in some detail and relate it to other adjunctions cropping up in other areas.
Nov 24	Wed	Oscar Randal-Williams (University of Cambridge)	Pure Maths Colloquium
14:00		Homeomorphisms of R^d
		meet.google.com/qxa-rhcg-skx
	Abstract: The group Top(d) of homeomorphisms of d-dimensional Euclidean space is a basic object in geometric topology, with its quotient Top(d)/O(d) by the subgroup of linear isometries completely controlling the difference between smooth and topological manifolds in all dimensions (except 4). I will explain some of the classical methods for studying the topology of this group, and report on some recent advances.
Nov 24	Wed	Julio Arrechea (IAA, Granada)	Cosmology, Relativity and Gravitation
15:00		All cats are grey in the dark: semiclassical relativistic stars
		Blackboard Collaborate
	Abstract: Quantum vacuum polarization violates energy conditions in the spacetime external to a compact star. As such an object is made to approach the black hole limit, semiclassical corrections become capable of producing new equilibrium end-states in stellar evolution. The semiclassical contribution is modelled by a massless quantum scalar field in the Boulware vacuum state, and its renormalized stress-energy tensor is firstly approached by an analytic Polyakov approximation. This already reveals a crucial difference with respect to classical stellar equilibrium: We find families of solutions that exhibit bounded pressures and mass up to a central core of Planckian radius. A minimal deformation of the Polyakov approximation inside this central core is sufficient to produce regular ultracompact configurations that surpass the Buchdahl compactness bound. We review the main features of these semiclassical relativistic stars.
Nov 26	Fri	Haluk Sengun (Sheffield)
10:00		The global picture: Talk 4
		meet.google.com/bbv-xhgy-mie
Nov 30	Tue	Narasimha Kumar (Indian Institute of Technology Hyderabad)	Number Theory seminar
10:00
		Google Meet
Nov 30	Tue	Joseph Martin (Sheffield)	Category Theory
14:00		Duality in Monoidal Bicategories
		Hicks Seminar Room J11
Dec 1	Wed	Vishwesha Guttal (Indian Institute of Science, India)	Mathematical Biology Seminar
13:00		TBC
		https://york-ac-uk.zoom.us/j/93472504071
	Abstract: TBC
Dec 2	Thu	Abhinav Prasad (Indian Institute of Technology (BHU), India)	SP2RC/ESPOS seminar
10:00		Role of Heating-Cooling Misbalance on the Phase Shift of Propagating Slow Waves in Non-adiabatic Solar Coronal Loops
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: Invoking the effects of thermal conductivity, compressive, viscosity, radiative losses, and heating-cooling misbalance, we derive the new general dispersion relation for the propagating slow MHD waves in the solar corona and solve it to determine the phase shifts of density and temperature perturbations along with their dependence on the equilibrium parameters of the plasma such as the background density and temperature. We also derive a new generalised mathematical expression for the polytropic index using the linear MHD model and find that in the presence of thermal conduction alone it remains close to its classical value for all the considered equilibrium density and temperature observed in typical coronal loops. Under the considered heating and cooling models, we find that the expected polytropic index can be matched with the observed value of 1.1 ± 0.02 in typical coronal loops if the thermal conductivity is enhanced by an order of magnitude compared to its classical value. We also explore the role of different heating functions for typical coronal parameters and find that although the polytropic indices remain close to 5/3, the phase difference between density and temperature perturbations is highly dependent on the form of heating function.
Dec 2	Thu	Matthew Lennard (Sheffield)	Plasma Dynamics Group
16:00		Recovering flows in a highly magnetic environment using deep learning.
		Google Meet
	Abstract: The magnetohydrodynamics (MHD) model for plasmas describes many complex features of the solar atmosphere. High quality simulations can utilise the equations of MHD to reproduce many complex features including the totality of the birth and death of active regions (AR). Forecasting the formation of ARs still provides a challenging problem due to the lack of high quality observational data and new methods—I aim to show that machine learning (ML) approach provides a grand opportunity for observational solar physics and test the capability of ML and deep learning (DL).
Dec 3	Fri	Hanneke Wiersema (Cambridge)	Number Theory seminar
13:00
		Google Meet
Dec 7	Tue	Haluk Sengun (Sheffield)
10:00		The global picture: Talk 5
		meet.google.com/bbv-xhgy-mie
Dec 8	Wed	Jan Grabowski (University of Lancaster)	Pure Maths Colloquium
14:00		Mutation through a tropical lens
		Hicks Seminar Room J11
	Abstract: The idea of mutating an object in some family into another has spread across algebra, geometry and combinatorics in the past decade. Some instances have been studied for a long time but the idea has gained new life following the introduction of cluster algebras at the turn of the century. In this talk, I will talk about a framework under development with my collaborators, that uses a “tropical lens” to find and formalise the similarities between the different notions of mutation and which is leading to new understanding of these phenomena.
Dec 8	Wed	Takis Konstantopoulos (Liverpool)	Probability seminar
15:00		Longest and heaviest paths in directed random graph
		Google Meet
	Abstract: In this talk, I will give an overview of results regarding the behaviour of longest paths in Barak-Erdos graphs as well as weighted versions of them, examining their connections to particle systems such as the infinite bin model and to regenerative techniques.
Dec 9	Thu	Professor Eduard Kontar (University of Glasgow)	SP2RC seminar
10:00		UK-SOSS: New look at the Sun at radio-frequencies
		Zoom link: https://zoom.us/j/95338171418
	Abstract: Observations of the Sun at radio-frequencies provides unique look at a variety of solar processes: from solar activity to the solar corona turbulence studies. Over the last few years, a unique set of solar radio observations with unprecedented temporal and frequency resolutions using the Low Frequency Array (LOFAR), Solar Parker Probe and RPW/Solar Orbiter opened new opportunities for detailed studies of the variety of solar processes in the outer solar corona. The new observations at sub-second scales are often intriguing and puzzling, requiring new models and re-thinking of the current models. In the talk, I will highlight these new observations and exciting opportunities with the Square Kilometre Array which is under construction.
Dec 10	Fri	Professor Spiros Patsourakos (University of Ioannina)	SP2RC seminar
13:00		An Introduction to solar flares and Coronal Mass Ejections
		https://meet.google.com/ciq-zovu-rzm
	Abstract: The Sun is anything but quiet, and hosts a plethora of dynamic phenomena covering a wide range of spatio-temporal scales and energetics. The high-end of the energy distribution of dynamic solar phenomena is populated by solar flares and Coronal Mass Ejections (CMEs), which are astrophysical templates of intense plasma heating, radiation mass expulsion and particle acceleration, key drivers of intense space-weather conditions in the heliosphere, and a Pandora's box for our understanding of the environment around exoplanets orbiting Sun-like stars. With this seminar we will supply an introduction to solar flare and CMEs, and juxtapose their basic properties with existing theories and models.
Dec 10	Fri	Sadiah Zahoor (Sheffield)	Number Theory seminar
13:00
		Google Meet
Dec 14	Tue	Tobias Berger (Sheffield)
10:00		Kudla-Millson Theory: Talk 1
		meet.google.com/bbv-xhgy-mie
Dec 15	Wed	Oliver Lorscheid (IMPA and University of Groeningen)	Pure Maths Colloquium
14:00		The moduli space of matroids
		meet.google.com/qxa-rhcg-skx
	Abstract: Matroids are combinatorial gadgets that reflect properties of linear algebra in situations where this latter theory is not available. This analogy prescribes that the moduli space of matroids should be a Grassmannian over a suitable base object, which cannot be a field or a ring; in consequence usual algebraic geometry does not provide a suitable framework. In joint work with Matt Baker, we use algebraic geometry over F1, the so-called field with one element, to construct such moduli spaces. As an application, we streamline various results of matroid theory and find simplified proofs of classical theorems, such as the fact that a matroid is regular if and only if it is binary and orientable. We will dedicate the first half of this talk to an introduction of matroids and their generalizations. Then we will outline how to use F1-geometry to construct the moduli space of matroids. In a last part, we will explain why this theory is useful to simplify classical results in matroid theory.
Dec 15	Wed	Özenç Güngör (Case Western)	Cosmology, Relativity and Gravitation
15:00		A classical, non-singular bounce and its stability analysis
		Hicks LT9
	Abstract: Bouncing cosmological models offer a viable alternative to Big-Bang cosmology and have gained recent attention. In a bouncing cosmology, the universe is initially contracting towards a minimum size before expanding. Such cosmological models are geodesically complete by construction and offer simple solutions to problems such as the Horizon problem. I will present a model that realizes such a cosmology and discuss its analytical and numerical properties. I will then focus more on cosmological perturbations in a positively curved universe and discuss the stability of said perturbations for the model in question.
Dec 16	Thu	Vishal Upendran (Inter-University Center for Astronomy and Astrophysics (IUCAA), India)	SP2RC/ESPOS seminar
10:00		On the formation of solar wind & switchbacks, and quiet Sun heating
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: Abstract: The solar coronal heating in quiet Sun (QS) and coronal holes (CH), including solar wind formation, are intimately tied by magnetic field dynamics. Thus, a detailed comparative study of these regions is needed to understand the underlying physical processes. CHs are known to have subdued intensity and larger blueshifts in the corona. This work investigates the similarities and differences between CHs and QS in the chromosphere using the Mg II h & k, C II lines, and transition region using Si IV line, for regions with identical absolute magnetic flux density (|B|). We find CHs to have subdued intensity in all the lines, with the difference increasing with line formation height and |B|. The chromospheric lines show excess upflows and downflows in CH, while Si IV shows excess upflows (downflows) in CHs (QS), where the flows increase with |B|. We further demonstrate that the upflows (downflows) in Si IV are correlated with both upflows and downflows (only downflows) in the chromospheric lines. CHs (QS) show larger Si IV upflows (downflows) for similar flows in the chromosphere, suggesting a common origin to these flows. These observations may be explained due to impulsive heating via interchange (closed-loop) reconnection in CHs (QS), resulting in bidirectional flows at different heights, due to differences in magnetic field topologies. Finally, the kinked field lines from interchange reconnection may be carried away as magnetic field rotations and observed as switchbacks. Thus, our results suggest a unified picture of solar wind emergence, coronal heating, and near-Sun switchback formation. References: — “On the formation of solar wind & switchbacks, and quiet Sun heating”: Vishal Upendran and Durgesh Tripathi 2021, ApJ (accepted) — “Properties of the C II 1334 Å Line in Coronal Hole and Quiet Sun as Observed by IRIS”: Vishal Upendran and Durgesh Tripathi 2021, ApJ, 922, 112
Dec 17	Fri	Tobias Berger (Sheffield)
13:00		Kudla-Millson theory: Talk 2
		meet.google.com/bbv-xhgy-mie
Jan 13	Thu	Prof James McLaughlin (Northumbria University)	SP2RC seminar
10:00		UK-SOSS: Oscillatory Reconnection: wave-generation, quasi-periodic pulsations, time-dependent reconnection and seismological tool
		Zoom link: https://zoom.us/j/95338171418
	Abstract: Oscillatory Reconnection – a relaxation mechanism with periodic changes in connectivity – has been proposed as a potential physical mechanism underpinning several periodic phenomena in the solar atmosphere, including quasi-periodic pulsations (QPPs). At its heart, Oscillatory Reconnection is a time-dependent reconnection process and the dynamic release of stored magnetic energy is central to multiple fields of study (including solar physics, astrophysics, fusion, laboratory-based plasma, computational MHD and space weather). This talk will review the state-of-the-art in this area, and we reveal a relationship between the equilibrium magnetic field strength, decay rate and period, which opens the tantalising possibility of utilising Oscillatory Reconnection as a seismological tool. Reference: McLaughlin et al. (2018, Space Science Reviews, 214, 45) + Zimovets, McLaughlin, et al. (2021, Space Science Reviews, 217, 66) + Karampelas, McLaughlin, et al. (2022, Astrophysical Journal, accepted)
Jan 20	Thu	Vigeesh Gangadharan (Leibniz Institute for Solar Physics (KIS), Germany)	SP2RC/ESPOS seminar
10:00		Internal gravity waves in the magnetized solar atmosphere
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: Internal gravity waves (IGWs) are buoyancy-driven waves common in the Earth’s atmosphere and oceans. IGWs have also been observed in the Sun’s atmosphere and are thought to play an important role in the overall dynamics of the solar atmosphere. They supply bulk of the wave energy for the lower solar atmosphere, but their existence and role in the energy balance of the upper layer remains unclear. Using radiation-magnetohydrodynamic (R-MHD) simulations, we study naturally excited IGWs in realistic models of the solar atmosphere. In this talk, we discuss some of our recent results on the influence of the Sun’s magnetic field on the propagation of IGWs and their energy transport. Our analysis suggests that the IGWs are generated independent of the mean magnetic property of the atmosphere. However, their propagation into higher layers is strongly affected by the presence and the topology of the magnetic field. We discuss how IGWs may play a significant role in the heating of the chromospheric layers in regions where horizontal fields are thought to be prevalent, like the internetwork region.
Feb 2	Wed	David Benisty (Cambridge)	Cosmology, Relativity and Gravitation
15:00		Lorentzian Quintessential Inflation
		Seminar Room B19, 301 Glossop Road
	Abstract: From the assumption that the slow roll parameter $\epsilon$ has a Lorentzian form as a function of the e-folds number N, a successful model of a quintessential inflation is obtained. The form corresponds to the vacuum energy both in the inflationary and in the dark energy epochs. The form satisfies the condition to climb from small values of $\epsilon$ to 1 at the end of the inflationary epoch. In the late universe $\epsilon$ becomes small again and this leads to the Dark Energy epoch. The observables that the models predict fits with the latest Planck data: r ∼ 10−3 , ns ≈ 0.965. Naturally a large dimensionless factor that exponentially amplifies the inflationary scale and exponentially suppresses the dark energy scale appears, producing a sort of cosmological seesaw mechanism. We find the corresponding scalar Quintessential Inflationary potential with two flat regions - one inflationary and one as a dark energy with slow roll behavior.
Feb 7	Mon	Jeongseok Oh (Imperial College)	The Sheffield Geometry and Physics Seminar
14:00		Virtual cycles on projective completions and quantum Lefschetz formula
		Hicks Seminar Room J11
	Abstract: For a compact quasi-smooth derived scheme M with (-1)-shifted cotangent bundle N, there are at least two ways to localise the virtual cycle of N to M via torus and cosection localisations, introduced by Jiang-Thomas. We produce virtual cycles on both the projective completion and projectivisation of N and show the ones on the former push down to Jiang-Thomas cycles and the one on the latter computes the difference. Using the idea we study the difference between quintic and formal quintic Gromov-Witten invariants.
Feb 7	Mon	Qaasim Shaafi (Imperial College)	The Sheffield Geometry and Physics Seminar
15:30		Gromov-Witten invariants of Blow-Ups
		Hicks Seminar Room J11
	Abstract: Gromov-Witten invariants play an essential role in mirror symmetry and enumerative geometry. Despite this, there are few effective tools for computing Gromov-Witten invariants of blow-ups. Blow-ups of X can be rewritten as subvarieties of Grassmann bundles over X. In joint work with Tom Coates and Wendelin Lutz, we exploit this fact and extend the abelian/non-abelian correspondence, a modern tool in Gromov-Witten theory. Combining these two steps allows us to get at the genus 0 invariants of a large class of blow-ups.
Feb 9	Wed	David Stefanyszyn (Cambridge)	Cosmology, Relativity and Gravitation
15:00		Bootstrapping primordial fluctuations
		Hicks LT4
	Abstract: Our understanding of observables in AdS space and Minkowski space is well developed. We can construct boundary observables in AdS space, and the S-matrix in Minkowski space, using fundamental physical principles such as symmetries, locality and unitarity while avoiding the numerous redundancies associated with local Lagrangians. Our understanding of observables in dS space is however significantly less well developed even though dS space is an integral part of our best descriptions of the early and late universe. In this talk I will present recent progress on our efforts to bootstrap cosmological correlation functions in dS space. I will mostly concentrate on inflationary correlators and explain how we can construct them directly using symmetries, locality and unitarity without having to work with specific models. I will illustrate the power of these bootstrap methods by showing how gravitational three-point functions are heavily constrained by these physical principles despite the complications of the corresponding Lagrangian descriptions.
Feb 10	Thu	Prof Thomas Neukirch (University of St Andrews)	SP2RC seminar
10:00		UK-SOSS: Bringing Balance to the Force: Equilibrium Models in Solar Physics
		Zoom link: https://zoom.us/j/95338171418 Meeting ID 953 3817 1418
	Abstract: Equilibrium models have a variety of useful applications in solar physics, despite the fact that the Sun is highly dynamical. At a fundamental level it is often advisable to start the study of a complex system by finding its steady states. These states can then, for example, be used as a basis for investigating waves and instabilities. Furthermore, the response of the equilibria to the variation of system parameters or boundary conditions can help to explore and predict aspects of the nonlinear behaviour of the system. However, in this talk I will mainly focus on a more practical aspect, namely the use of equilibrium models in the extrapolation of photospheric magnetic field measurements into the solar corona. While potential and force-free magnetic field models are still the most widely used equilibrium solutions for this task, over the past few years some extrapolation methods have employed magnetohydrostatic solutions. I plan to discuss some of the approaches used, with an emphasis on analytical methods.
Feb 10	Thu	Samuel Skirvin (University of Sheffield)	Plasma Dynamics Group
16:00		Properties of MHD waves in non-uniform equilibria
		Google Meet
	Abstract: In this talk I will give an overview of the research I have undertaken throughout my PhD journey. I will introduce a numerical eigensolver that is capable of finding the permissible wave solutions in any symmetrically non-uniform equilibrium relevant to the solar atmosphere, in both a Cartesian and cylindrical geometry. Results of the numerical approach are compared with known analytical solutions which are then extended to investigate a number of non-uniform case studies including (i) non-uniform plasma density in a magnetic slab (ii) non-uniform plasma flow in a coronal slab (iii) non-uniform plasma density in a magnetic flux tube (iv) non-uniform plasma flow in a coronal flux tube (v) linear and non-linear rotational plasma flow in a magnetic flux tube. For a number of case studies, both 2D and 3D visualisations of the resulting propagating MHD modes are shown. Implications of the results for observations and seismological purposes are discussed.
Feb 23	Wed	Justin Vines (Albert Einstein Institute Potsdam; UCLA)	Cosmology, Relativity and Gravitation
15:00		Scattering waves and/or particles off spinning black holes
		Blackboard Collaborate
	Abstract: We will explore some questions, and some (historical and recent) beginnings of answers to them, concerning the scattering of classical and/or quantum waves/fields (massless/massive; spin-0, spin-1/2, ...) off of a spinning black hole, i.e., in a background Kerr spacetime --- and the relationships of such processes to the scattering (and bound states) of various particle-like objects around black holes.
Feb 24	Thu	Leigh Orf	Plasma Dynamics Group
16:00		Simulation, visualization, and analysis of the world's most powerful thunderstorms
		Google Meet
	Abstract: Supercell thunderstorms are recognized as the one of the earth's most powerful atmospheric phenomena, producing heavy rain, hail, and tornadoes that sometimes result in catastrophic devastation and loss of life. Accurately predicting supercell behavior in order to alert the public remains a top priority for federal forecasters, and much work remains to be done to achieve this goal. Part of the difficulty of forecasting the behavior of these storms stems from our poor understanding of processes that occur within supercells that result in violent tornadoes. In this talk, I will first provide a brief background that includes the mathematical equations and numerical model used in the study, and describe my own specific code development involving I/O and lossy floating point compression. I will then present results from tornado-resolving large eddy supercell thunderstorm simulations conducted on some of the world's most powerful research supercomputers, focusing on processes that are associated with tornado formation and maintenance. I will also present recent research that focuses on the tops of the thunderstorms (what is visible to orbiting meteorological satellites) exploring the behavior of simulated cloud-top features that are associated with the most severe thunderstorms.
Mar 2	Wed	Dr David Kuridze (Aberystwyth University)	SP2RC seminar
13:00		Spectropolarimetry and solar magnetic field diagnostics
		Hicks G07 / Google Meet: https://meet.google.com/tmi-zjmx-rjo
	Abstract: The magnetic field is key to the dynamics, evolution, and heating of the solar atmosphere, yet direct measurements are rare and highly uncertain. In this seminar I will discuss about the techniques and challenges of measuring the magnetic field in the corona. I will also present the results from my work where we reported on the unique observations of the flaring coronal loops at the solar limb using high resolution imaging spectropolarimetry from the Swedish 1-meter Solar Telescope. The vantage position, orientation and nature of the chromospheric material that filled the observed flare loops allowed us to determine their magnetic field with unprecedented accuracy.
Mar 3	Thu	Szabolcs Soós (Eötvös Loránd University (ELTE), Hungary)	SP2RC/ESPOS seminar
10:00		On the Differences in the Periodic Behavior of Magnetic Helicity Flux in Flaring Active Regions
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: Observational precursors of large solar flares provide a basis for future operational systems for forecasting. We studied the evolution of the normalized emergence (EM), shearing (SH), and total (T) magnetic helicity flux components for 14 flaring (with at least one X-class flare) and 14 nonflaring (10 hr) do not change. (iv) When the EM periodicity does not contain harmonics, the ARs do not host a large energetic flare. (v) Finally, significant power at long periods (∼20 hr) in the T and EM components may serve as a precursor for large energetic flares.
Mar 3	Thu	William Elbæk Mistegård (Centre for Quantum Mathematics)	The Sheffield Geometry and Physics Seminar
10:00		The Automorphism Equivariant Hitchin Index
		Hicks Seminar Room J11
	Abstract: The moduli space of Higgs bundles on a compact Riemann surface was introduced by Hitchin in his study of the self-duality equations on a Riemann surface. This is a quasi-projective hyper-Kähler variety, which supports an algebraic torus-action and a torus-equivariant line bundle generating the Picard group. This line bundle is called the determinant line bundle of cohomology, or determinant line bundle for short. Given an automorphism of the Riemann surface, there is an induced lift to the determinant line bundle. We define and study the automorphism equivariant Hitchin index (AEHI). This the trace of the derived action on the torus-weight spaces of the cohomology of the determinant line bundle. Our study is motivated by topological quantum field theory and complex Chern-Simons theory via non-abelian Hodge theory, which identifies the moduli space of Higgs bundles with the moduli space of flat complex connections on the Riemann surface. We prove that the AEHI is a topological invariant of the three-manifold obtained as the mapping torus of the automorphism of the Riemann surface and we provide an explicit formula for the AEHI in terms of: cohomological pairings of the Atiyah-Bott generators on the moduli space of parabolic bundles on the quotient Riemann surface (i.e. the orbit space of the automorphism), cohomological pairings on symmetric powers of the quotient Riemann surface and Seifert invariants of the mapping torus. These results provides new links between algebraic geometry and quantum topology, and our topological invariant can be seen as a generalization of the Witten-Reshetikhin-Turaev quantum invariant of the mapping torus. This is joint work with J.E. Andersen and T. Hausel.
Mar 3	Thu	Kento Osuga (Warsaw)	The Sheffield Geometry and Physics Seminar
11:30		Refinement of Quantum Curves
		Hicks Seminar Room J11
	Abstract: Topological recursion is a recursive formalism that takes an algebraic curve as the initial data, and computes a variety of invariants such as Kontsevich-Witten intersection numbers or knot invariants. Another interesting application of topological recursion is a quantisation of algebraic curves which are often called quantum curves. For degree two curves, topological recursion admits a suitable 1-parameter refinement so-called refined topological recursion. In this talk I will address properties of refined topological recursion and construct explicit form of refined quantum curves for genus zero curves. If time permits, I will also discuss about a somewhat unexpected relation between topological recursion and BPS structures in the refined setting.
Mar 9	Wed	Vesna Stojanoska (University of Illinois Urbana-Champaign)	Pure Maths Colloquium
15:00		Duality for some Galois groups in stable homotopy theory
		meet.google.com/qxa-rhcg-skx
	Abstract: In classical algebra, the integer primes p help decompose objects as well as problems into their p-primary parts, which may be easier to study. The same is true in homotopy theory, but the situation is more interesting since for each integer prime p, there are infinitely many nested homotopical primes. For each of those homotopical primes, there is an (unramified) Galois group that governs the local story and encodes the symmetries of chromatic homotopy theory. These Galois groups turn out to be particularly nice profinite groups, known as compact p-adic analytic. Such groups and their fascinating duality properties within algebra were studied by Lazard. I will try to explain a newer result, which shows that their homotopical duality properties are even better, giving powerful implications for the chromatic Galois extensions that they govern.
Mar 9	Wed	Susanne Schander (Perimeter Institute )	Cosmology, Relativity and Gravitation
15:00		Backreaction in Quantum Cosmology
		Blackboard Collaborate
	Abstract: Several approaches to quantum gravity suggest that the big bang singularity is resolved and is often replaced by a big bounce. This raises the question of whether there are phenomenological consequences of such a scenario. As the physics involved in particular concerns the Planck era before inflation, one expects that quantum backreaction between the homogeneous and inhomogeneous degrees of freedom cannot be neglected in this regime. After a brief introduction to these concepts and the current status of the phenomenology involved, we review space adiabatic perturbation theory (SAPT) which was invented by Panati, Spohn and Teufel as an extension of the well known Born-Oppenheimer approach (BOA) for quantum mechanical systems with backreaction. We explain why BOA is insufficient for quantum cosmology and why an extension of SAPT to quantum field theory is non-trivial. Finally, we apply SAPT to quantum backreaction in cosmology, list which challenges had to be overcome and present the current status of our calculations.
Mar 10	Thu		Category Theory
15:00		Categorical Systems Theory Reading Group
		Hicks Seminar Room J11
	Abstract: This week we'll be reading sections 2.1, 2.2, 2.3 and 2.4. Find the book here: http://davidjaz.com/Papers/DynamicalBook.pdf
Mar 10	Thu	Abdulaziz Alharbi (Sheffield)	Plasma Dynamics Group
16:00		Waves in Partially Ionised Multi-Fluid Solar Atmospheric Plasmas
		https://meet.google.com/mfm-pqyu-mgx
	Abstract: The solar atmospheric plasma is a complex environment, where the plasma changes with height from being controlled by pressure forces to a regime where dynamics is driven by magnetic forces, but also where the plasma changes from being partially ionised to fully ionised. In this talk, I will give an overview of the research I have undertaken throughout my PhD studies on this topic where I discuss results on waves and their properties in strongly and weakly partially ionised plasma using a multi-fluid framework.
Mar 14	Mon	Murad Alim (Hamburg)	The Sheffield Geometry and Physics Seminar
14:00		Non-perturbative quantum geometry, resurgence and BPS structures
		Hicks Seminar Room J11
	Abstract: BPS invariants of certain physical theories correspond to Donaldson-Thomas (DT) invariants of an associated Calabi-Yau geometry. BPS structures refer to the data of the DT invariants together with their wall-crossing structure. On the same Calabi-Yau geometry another set of invariants are the Gromov-Witten (GW) invariants. These are organized in the GW potential, which is an asymptotic series in a formal parameter and can be obtained from topological string theory. A further asymptotic series in two parameters is obtained from refined topological string theory which contains the Nekrasov-Shatashvili (NS) limit when one of the two parameters is sent to zero. I will discuss in the case of the resolved conifold how all these asymptotic series lead to difference equations which admit analytic solutions in the expansion parameters. A detailed study of Borel resummation allows one to identify these solutions as Borel sums in a distinguished region in parameter space. The Stokes jumps between different Borel sums encode the BPS invariants of the underlying geometry and are captured in turn by another set of difference equations. I will further show how the Borel analysis of the NS limit connects to the exact WKB study of quantum curves. This is based on joint works with Lotte Hollands, Arpan Saha, Iván Tulli and Jörg Teschner.
Mar 14	Mon	Dimitri Zvonkine (Laboratoire Mathématiques de Versailles)	The Sheffield Geometry and Physics Seminar
15:30		Gromov-Witten invariants of complete intersections
		Hicks Seminar Room J11
	Abstract: We show that there is an effective way to compute all Gromov-Witten (GW) invariants of all complete intersections. The main tool is Jun Li's degeneration formula: it allows one to express GW invariants of a complete intersection from GW invariants of simpler complete intersections. The main difficulty is that, in general, the degeneration formula does not apply to primitive cohomology insertions. To circumvent this difficulty we introduce simple nodal GW invariants. These invariants do not involve primitive cohomology classes, but instead make use of imposed nodal degenerations of the source curve. The algorithm for computing GW invariants relies on two main statements: (i) simple nodal GW invariants can be computed by the degeneration formula, (ii) simple nodal GW invariants determine all GW invariants of a complete intersection. The first statement is geometric; the second uses the invariance of GW invariants under monodromy and some representation theory. This is joint work with Hulya Arguz, Pierrick Bousseau and Rahul Pandharipande.
Mar 16	Wed	Hossein Movasati (IMPA)	Pure Maths Colloquium
14:00		Periods of families of curves in threefolds
		meet.google.com/qxa-rhcg-skx
	Abstract: Clemens' conjecture states that the the number of rational curve in a generic quintic threefold is finite. If it is false we prove that certain periods of rational curves in such a quintic threefold must vanish. Our method is based on a generalization of a proof of Max Noether's theorem using infinitesimal variation of Hodge structures and its reformulation in terms of integrals and Gauss-Manin connection.
Mar 16	Wed	Andrew Wade (Durham)	Probability seminar
15:00		Deposition, diffusion, and nucleation on an interval
		Hicks LT9
	Abstract: I will talk about an interacting particle model motivated by nanoscale growth of ultra-thin films. Particles are deposited (according to a space-time Poisson process) on an interval substrate and perform Brownian motions until any two meet, when they nucleate to form a static island, which acts as an absorbing barrier to subsequent particles. This is a continuum version of a lattice model studie in the applied literature. We are interested in the induced interval-splitting process. In particular, we show that the long-time evolution converges to a Markovian interval-splitting process, which we describe. The density that appears in this description is derived from an exit problem for planar Brownian motion from a right-angled triangle, extending work of Smith and Watson. The splitting density has a compact Fourier series expansion but, apparently, no simple closed form. This talk is based on joint work with Nicholas Georgiou (Durham): https://arxiv.org/abs/2010.00671
Mar 17	Thu	Juan Camilo Guevara Gomez (Rosseland Centre for Solar Physics, University of Oslo, Norway)	SP2RC/ESPOS seminar
10:00		Small-scale MHD waves in the solar chromosphere with ALMA
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: Magnetohydrodynamic (MHD) waves are thought to be one of the key mechanisms for transferring energy and momentum through the Sun’s atmosphere, hence maintaining the temperature profile of the outer atmospheric layers. Here, we have studied small-scale chromospheric bright features, exhibiting oscillations in brightness temperature, size, and horizontal velocity, in Bands 3 (∼3 mm) and 6 (∼1.2 mm) of 2 seconds cadence solar observations with ALMA, as well as in associated synthetic lines from a Bifrost simulation, degraded to match the ALMA’s spatial and temporal resolutions. In total, 486 and 235 features were analysed in the observations and simulations, respectively. Periods of the oscillations and phase angles between the perturbations in any of the two parameters were characterised by means of wavelet analysis. As a result, median periods were obtained for the oscillations on the order of 90 s (Band 3) and 64 s (Band 6) for brightness temperature, 82 s (Band 3) and 56 s (Band 6) for size and, 65 s (Band 3) and 52 s (Band 6) for horizontal velocity. Phase relations between the high-frequency oscillations in brightness temperature and size suggest the presence of fast and slow MHD sausage modes in the small magnetic structures. In addition, the high-frequency fluctuations in transverse displacement are likely Alfvénic and can be representative of MHD kink mode. Furthermore, we have compared the outcomes between the two ALMA frequency bands as they are considered to be formed at distinct heights in the solar chromosphere and have used the simulations to discuss the context of the observational results. Finally, this study confirms the diagnostic potential of solar ALMA observations with very good cadence and resolution, as well as their essential role as complementary with respect to other diagnostics.
Mar 18	Fri	Dr Mausumi Dikpati (NCAR, Boulder, Colorado)	SP2RC seminar
13:00		Solar Rossby waves and their implications in space weather
		Google Meet
	Abstract: Abstract: Rossby waves are a class of inertial waves, occurring in thin layers within fluid regions of stars and planets due to the variation in Coriolis forces with latitude.The discovery of Rossby waves (Rossby, 1939) in the Earth's atmosphere led to great advances in the ability to forecast our planet's weather patterns. It is the combination of mean west to east atmospheric flow and (finite amplitude) Rossby waves in the atmosphere that create “jet streams” at midlatitudes. Understanding their interaction and the resulting longitudinal structure allows for accurate prediction of how synoptic weather patterns evolve and propagate to the east. In effect the “jet stream” steers our Earth's weather from location to location in midlatitudes. In the past several years observational evidence has indicated that there are also Rossby waves in the Sun. Although Rossby waves have been detected in the Sun's photosphere and corona, they most likely originate in layers where the vertical extent and radial motions are much less than the horizontal extent and motions. Solar tachocline is such a layer where Rossby waves can be generated in the Sun, and because of predominantly horizontal motions of supergranules in the sub-photospheric layer, that layer can also be a generation layer for solar Rossby waves. Rossby waves differ from their Earth's counterparts by being strongly modified by the magnetic fields in the Sun. After discussing the basics of solar Rossby waves, we will present a few recent simulations of nonlinear interactions between Rossby waves and magnetic fields in solar tachocline. We will show that “tachocline nonlinear oscillations” (TNOs) occur, very much like nonlinear Orr mechanism in fluid dynamics. TNOs have periods similar to those observed in the solar atmosphere— enhanced periods of solar activity, or “seasons”—occurring at intervals between six months and two years. These seasonal/subseasonal activity bursts produce the strongest eruptive space weather events. Thus, a key to forecasting the timing, amplitude, and location of future activity bursts, and hence space weather events, could lie in our ability to simulate the longitudinal patterns produced by the interactions of Rossby waves and magnetic fields.
Mar 23	Wed	Nikita Nikolaev (University of Sheffield)	Pure Maths Colloquium
14:00		Moduli Spaces of Connections and Abelianisation
		Hicks Seminar Room J11
	Abstract: Complex singular differential equations play a major role far beyond pure mathematics: classical equations like Airy, Bessel, and Schrödinger equations are just some famous examples that appear in physics and engineering. As geometers, we prefer to study their geometric generalisations called meromorphic connections on holomorphic vector bundles over Riemann surfaces (a.k.a. "differential equations on steroids"). There are many excellent reasons to do this: one is that their moduli spaces (i.e., spaces of equivalence classes) have an incredibly rich geometry that links with a vast variety of subjects from (to name just a few) integrable systems and Poisson geometry, to quantum algebras and representation theory, to Gromov-Witten theory and quantum field theory. Moduli spaces of connections are exceptionally captivating objects, "a gift to geometry that keeps on giving" as some of us would say. In broad and as accessible terms as possible, I will present a little bit of this really fascinating story to give you a sense or a glimpse of the subject’s richness. At the end, I will mention a word or two about a new geometric method (called abelianisation) to analyse higher-rank connections (i.e., higher-order differential equations) by placing them in correspondence with much simpler objects: rank-one connections (i.e., first-order differential equations) but over a geometrically more complicated Riemann surface.
Mar 23	Wed	Antonella Palmese (UC Berkeley)	Cosmology, Relativity and Gravitation
15:00		Probing the Universe’s expansion and the origin of compact object binaries with multi-messenger astronomy
		Blackboard Collaborate
	Abstract: The synergy between gravitational wave (GW) experiments, such as LIGO/Virgo, and optical surveys, such as the Dark Energy Survey (DES), is most prominent in the discovery of electromagnetic counterparts to GW events and the application of the standard siren method, which has already enabled several measurements of the Hubble Constant. Our DES follow-up observations of the first binary neutron star merger detected by LIGO/Virgo enabled the discovery of the first optical counterpart to a GW event and the first standard siren measuement, while also providing information about the origin of the binary. We have later extended the standard siren analysis to compact object binary merger events without electromagnetic counterparts using galaxy catalogs, for which I will present the latest results. These measurements are a promising tool to shed light on the Hubble constant tension in the coming years. In the last part of the talk, I will present some interesting possibilities for the formation of the most massive binary black hole mergers detected so far which are related to galaxies’ central black holes, in particular those in dwarf galaxies and Active Galactic Nuclei.
Mar 24	Thu	Fatima Kahil (Max Planck Institute)	Plasma Dynamics Group
16:00		On the scientific capabilities of SO/PHI
		Google Meet
	Abstract: The Polarimetric and Helioseismic Imager (PHI) is one of the six remote sensing instruments on board the Solar Orbiter Satellite (SO). It is a spectropolarimetric imager which provides maps of the photospheric magnetic field with a spatial resolution of 200 km at perihelion (0.3 AU). In this talk, I will introduce the SO/PHI instrument and show its proven capabilities tested during the commissioning and cruise phase of the Solar Orbiter. Cross-calibration of the SO/PHI data products with other NEO satellites like SDO will be presented as well. Intercalibration of the SO/PHI high resolution magnetograms with the EUV images of the Extreme Ultraviolet Imager (EUI) on-board SO allowed for studying the magnetic component of the small-scale EUV brightenings detected by EUI and termed campfires. I will present the results of this study and show how the next higher resolution SO/PHI data taken near perihelion at 0.3 AU from the Sun will help improve our understanding of the magnetic origin of these campfires
Mar 28	Mon	Angelica Simonetti (Cambridge)	The Sheffield Geometry and Physics Seminar
14:00		Z/2Z-smoothings of cusp singularities
		Hicks Seminar Room J11
	Abstract: Cusp singularities and their quotients by a suitable action of Z/2Z are among the surface singularities which appear at the boundary of the compactification of the moduli space of surfaces of general type due to Kollar, Shepherd-Barron and Alexeev. Since only those singularities that admit a smoothing family occur at the boundary of this moduli space, it is useful to find nice conditions under which they happen to be smoothable. We will describe a sufficient condition for a cusp singularity admitting a Z/2Z action to be equivariantly smoothable. In particular we will see it involves the existence of certain Looijenga (or anticanonical) pairs (Y,D) that admit an involution fixed point free away from D and that reverses the orientation of D.
Mar 28	Mon	Qingyuan Jiang (Edinburgh)	The Sheffield Geometry and Physics Seminar
15:30		Derived projectivizations of complexes
		Hicks Seminar Room J11
	Abstract: In this talk, we will discuss the counterpart of Grothendieck's projectivization construction in the realm of derived algebraic geometry. (1) We will first discuss the motivations and definitions of derived projectivizations and study their fundamental properties. (2) We will then focus on complexes of perfect-amplitude contained in [0,1]. In this case, the derived projectivizations enjoy special pleasant properties. For example, they satisfy the generalized Serre's theorem and the derived version of Beilinson's relations, and there are structural decompositions for their derived categories. (3) Finally, we will discuss some applications of this framework, including: (3-i) applications to classical situations, such as derived categories of certain reducible schemes and irreducible singular schemes. (3-ii) applications to Hecke correspondence moduli, focusing on the cases of surfaces. (3-iii) applications to moduli of pairs and moduli of extensions, focusing on the cases of curves, surfaces, and threefolds. If time allows, we might also discuss the generalizations of these results to the cases of derived Grassmannians and some other types of derived Quot schemes.
Mar 31	Thu	Susanna Parenti (Institut d'Astrophysique Spatiale (IAS), Université Paris-Saclay, CNRS, France)	SP2RC/ESPOS seminar
10:00		Validation of a wave heated 3D MHD coronal-wind model using Polarized Brightness and EUV observations
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: The 3D MHD global modeling is a powerful tool to test all the possible candidate physical processes responsible for the formation and evolution of the corona and heliosphere. To fully understand the possible role of each of these mechanisms, we need a validation process where the output from the simulations is quantitatively compared to the observational data. In this work, we present the results from our validation process applied to the wave turbulence driven 3D MHD corona-wind model WindPredict-AW. At this stage of the model development, we focus the work to the coronal regime in quiescent condition. We analyze three simulations results, which differ by the boundary values. We use the 3D distributions of density and temperature, output from the simulations at the time of around the first Parker Solar Probe perihelion (during minimum of the solar activity), to synthesize both extreme ultraviolet (EUV) and white light polarized (WL pB) images to reproduce the observed solar corona. For these tests, we selected AIA 193 A, 211 A and 171 A EUV emissions, MLSO K-Cor and LASCO C2 pB images obtained the 6 and 7 November 2018. We then make quantitative comparisons of the disk and off limb corona. We show that our model is able to produce synthetic images comparable to those of the observed corona.
Apr 6	Wed	Antonio Ferreiro (Dublin City University)	Cosmology, Relativity and Gravitation
15:00		Particle production in expanding universes
		Blackboard Collaborate
	Abstract: The spontaneous production of particles due to a gravitational field is one of the cornerstones of the theory of quantum fields in curved spacetime. This effect has an important role in our current understanding of the early phases of our Universe. I will introduce this phenomenon and point out the difficulties that arise when computing physical magnitudes, e.g. the stress-energy tensor. Finally, I will show the connection between this effect and the generation of matter during the reheating phase in the inflationary scenario.
Apr 25	Mon	Naoki Koseki (Edinburgh)	The Sheffield Geometry and Physics Seminar
14:00		Cohomological chi-independence for Gopakumar-Vafa invariants
		Hicks Seminar Room J11
	Abstract: Recently, Maulik and Toda gave a mathematical definition of the Gopakumar-Vafa(GV) invariants, which are the virtual counts of curves inside a Calabi-Yau 3-fold. GV invariants are conjecturally equivalent to other curve counting theories such as Gromov-Witten invariants (GV=GW conjecture). One of the mysterious features of GV invariants is a chi-independence conjecture, which is expected from GV=GW conjecture. In my recent work with Tasuki Kinjo (Tokyo), we proved the chi-independence of GV invariants for a certain class of non-compact Calabi-Yau 3-dolds, called local curves. I will explain our result and other recent developments of the theory.
Apr 25	Mon	Nadir Fasola (Sheffield)	The Sheffield Geometry and Physics Seminar
15:30		Surface defects in Vafa-Witten theory and flags of sheaves on the projective plane
		Hicks Seminar Room J11
	Abstract: Nested Hilbert schemes of points and curves on smooth projective surfaces encode interesting information about enumerative problems and physical theories. Their virtual fundamental classes have been shown to recover both the virtual classes of Seiberg-Witten and reduced stable pair theories, while their obstruction theories can be used to obtain information about Vafa-Witten and reduced Donaldson-Thomas invariants. Motivated by a D-brane construction arising in supersymmetric String Theory, I’ll study the representation theory of an enhancement of the ADHM quiver. This, in a particular case, models nested Hilbert schemes of points on the affine plane or, more generally, flags of framed torsion-free sheaves on the projective plane. The partition function of the theory determined by such a quiver naturally computes generating functions of virtual invariants of moduli spaces of stable representations, which, in turn, are conjectured to carry some information about the cohomology of character varieties via a work of Hausel, Letellier and Rodriguez-Villegas.
Apr 27	Wed	Ieke Moerdijk	Topology Reading Group
10:00		Models for $E_n$ Operads
		Hicks Seminar Room J11
Apr 27	Wed	Wushi Goldring (University of Stockholm)	Pure Maths Colloquium
14:00		Propagating algebraicity of automorphic representations via functoriality
		meet.google.com/qxa-rhcg-skx
	Abstract: Automorphic representations are some of the richest and most mysterious mathematical objects discovered to-date. They simultaneously generalize (i) infinite-dimensional representations of real Lie groups, (ii) modular forms and (iii) the Hecke characters of class field theory. As such, automorphic representations incorporate representation theory, analysis and arithmetic. In the late 1960's, Robert Langlands laid out a program to unravel much of the seemingly hidden structure of automorphic representations. To begin to understand the Langlands program, it is useful -- at least at first -- to distinguish two kinds of conjectures: Roughly, Langlands' Functoriality Principle can be seen as intrinsic to automorphic representations -- revealing a myriad of relations between different automorphic representations of different groups. By contrast, the extrinsic Langlands correspondence explains how certain automorphic representations should be related to Galois theory and algebraic geometry. Every automorphic representation has associated numerical invariants called Hecke eigenvalues -- these are complex numbers. One of the most interesting aspects of the Langlands program is that some automorphic representations have Hecke eigenvalues which are algebraic numbers, while for others they are transcendental. At this time, we seem to lack a conceptual understanding for why this dichotomy exists. While the Langlands correspondence suggests that certain automorphic representations should have algebraic Hecke eigenvalues, it remains unclear -- even at the level of conjectures -- wherein lies the watershed line between algebraic and transcendental. I will spend most of my talk introducing automorphic representations, their Hecke eigenvalues, functoriality and the correspondence. The end goal of my talk is then to explain what can be said about the algebraicity of Hecke eigenvalues by combining (1) Previously known cases of algebraicity and (2) Langlands functoriality. On the one hand, I will explain why the algebraicity of Hecke eigenvalues does propagate from some cases to others via functoriality -- this gives new theorems and conjectures on algebraicity of Hecke eigenvalues. On the other hand, I will explain why most cases -- including Maass forms -- are not reducible to known ones via functoriality.
Apr 27	Wed	Wenkai Xu (Oxford)	Probability seminar
15:00		Stein's Method on Testing Goodness-of-fit for Exponential Random Graph Models
		Hicks LT9
	Abstract: In this talk, I will introduce a novel nonparametric goodness-of-fit testing procedure for exchangeable exponential random graph models (ERGMs) when a single network realisation is observed. The test determines how likely it is that the observation is generated from a target unnormalised ERGM density. The test statistics are derived from a kernel Stein discrepancy, a divergence constructed via Stein’s method using functions in a reproducing kernel Hilbert space, combined with a discrete Stein operator for ERGMs. Theoretical properties for the testing procedure for a class of ERGMs will be discussed; simulation studies and real network applications will be presented.
Apr 27	Wed	Adrián del Rio (Penn State)	Cosmology, Relativity and Gravitation
15:00		Electric-Magnetic duality anomaly induced by gravitational waves
		Blackboard Collaborate
	Abstract: Since the discovery in 1969 of the anomalous non-conservation of the chiral fermion current in QED, it is known that classical symmetries of field theories may fail to survive the quantization, leading to what is known as quantum anomalies. In this talk I will introduce a new example in the context of quantum electrodynamics and gravity. I will first show that the classical electric-magnetic symmetry of Maxwell theory breaks down quantum-mechanically in curved spacetimes. Then I will show that solutions of Einstein's equations can trigger this effect if and only if they admit a flux of gravitational radiation with net circular polarization. I will argue that typical scenarios where this occurs include binary black holes that break spacetime mirror symmetries, as for instance in precessing systems. The emergence of this anomaly physically implies that some astrophysical systems can spontaneously generate a flux of photons from the quantum vacuum with net helicity. This is not predicted by the Hawking effect and could have interesting implications.
Apr 28	Thu	Ieke Moerdijk	Topology Reading Group
16:00		Models for $E_n$ Operads
		Hicks Seminar Room J11
May 3	Tue	Domenic Germano (Melbourne)	Mathematical Biology Seminar
11:00		A realistic model of simple epithelia, and modelling boundaries of epithelial tissues
		Hicks G07
	Abstract: Simple epithelial tissues occur in various structures throughout the body, such as the endothelium, mesothelium, linings of the lungs, saliva and thyroid glands, and gastrointestinal tract. Despite the prevalence of simple epithelial tissues, the maintenance of tissue and organ structures during dynamic homeostasis is often not well understood. In order for a system to be stable, cell renewal, cell migration and cell death must be finely balanced. Moreover, a tissue’s shape must remain relatively unchanged. Furthermore, for the mathematical biologist, there is a choice to make, regarding appropriate boundaries and how they should be modelled, as not all models result in the same outcome. This talk will contain two parts. In the first part, we will present a novel 3D, multilayer, cell-centre model of simple epithelial tissues. In this model, cell movement is governed by the minimisation of a bending potential across the epithelium, cell-cell adhesion, and viscous effects. Using this model, we will show how the tissue is capable of maintaining a consistent structure while undergoing self renewal. During the second part, we will address the issue of making suitable modelling choices with relation to tissue boundaries. We will present three key models and discuss the advantages and disadvantages of each model, as well as some model applications.
May 4	Wed	Ieke Moerdijk	Topology Reading Group
10:00		Models for $E_n$ Operads
		Hicks Seminar Room J11
May 4	Wed	Marcel Ortgiese (Bath)	Probability seminar
16:00		Voter models on subcritical inhomogeneous random graphs.
		Hicks LT9
	Abstract: The voter model is a classical interacting particle system modelling how consensus is formed across a network. We analyse the time to consensus for the voter model when the underlying graph is a subcritical scale-free random graph. Moreover, we generalise the model to include a `temperature' parameter. The interplay between the temperature and the structure of the random graph leads to a very rich phase diagram, where in the different phases different parts of the underlying geometry dominate the time to consensus. Our proofs rely on the well-known duality to coalescing random walks and a detailed understanding of the structure of the random graphs in terms of a thinned Galton-Watson forest.
May 4	Wed	Lissa de Souza Campos (Pavia)	Cosmology, Relativity and Gravitation
16:00		Sensible dynamics on Static Spacetimes
		Blackboard Collaborate
	Abstract: I will consider a free, scalar, massive quantum field theory on static spacetimes with a timelike boundary. Invoking the works of Ishibashi and Wald, Sturm-Liouville theory and concepts from algebraic quantum field theory, I will outline the steps to take for the explicit construction of physically-sensible two-point functions admitting generalized Robin boundary conditions. Each boundary condition determines an inequivalent dynamics, but they are all equivalently physically-sensible. I will comment on an ongoing investigation aimed at highlighting an extra ambiguity regarding the choice of boundary conditions at an irregular singularity: there might be not just one or a one-parametric family of, but rather infinite admissible boundary conditions to be taken into account.
May 5	Thu	Ieke Moerdijk	Topology Reading Group
16:00		Models for $E_n$ Operads
		Hicks Seminar Room J11
May 9	Mon	Martijn Kool (Utrecht)	The Sheffield Geometry and Physics Seminar
14:00		Counting surfaces on Calabi-Yau fourfolds
		Hicks Seminar Room J11
	Abstract: I will introduce invariants for counting surfaces on Calabi-Yau fourfolds. In a family, they are deformation invariant along Hodge loci. If non-zero, the variational Hodge conjecture for the family under consideration holds. Time permitting, I will discuss DT/PT wall-crossing and relations to Nekrasov's Magnificent Four. Joint work with Y. Bae and H. Park.
May 9	Mon	Balázs Szendrői (Oxford)	The Sheffield Geometry and Physics Seminar
15:30		ADE singularities, Quot schemes and generating functions
		Hicks Seminar Room J11
	Abstract: Starting with an ADE singularity C^2/Gamma for Gamma a finite subgroup of SL(2,C), one can build various moduli spaces of geometric and representation-theoretic interest as Nakajima quiver varieties. These spaces depend in particular on a stability parameter; quiver varieties at both generic and non-generic stability are of geometric interest. We will explain some of these connections, focusing in particular on generating functions of Euler characteristics at different points in stability space. Based on joint papers and projects with Craw, Gammelgaard, Gyenge, and Nemethi.
May 11	Wed	Ieke Moerdijk	Topology Reading Group
10:00		Models for $E_n$ Operads
		Hicks Seminar Room J11
May 11	Wed	Sven Raum (University of Stockholm)	Pure Maths Colloquium
13:30		Simple operator algebras associated with groups and group-like structures
		meet.google.com/qxa-rhcg-skx
	Abstract: One of the original motivations of Murray and von Neumann introducing operator algebras was to study the unitary representation theory of groups. This naturally leads to the question of studying building blocks of representation theory, that is simple operator algebras associated with groups. From a modern point of view, not only groups but also other group-like structures such as groupoids should be investigated. This talk introduces the audience to group and groupoid operator algebras and tells the story of how our point of view on their simplicity changed dramatically over the past 10 years. At the end of the talk, I will present some recent results on simple groupoid C*-algebras that were obtained in joint work with Kennedy, Kim, Li and Ursu.
May 11	Wed	Sunny Vagnozzi (Cambridge)	Cosmology, Relativity and Gravitation
16:00		Searching for dark energy off the beaten track
		Blackboard Collaborate
	Abstract: Most of the efforts in searching for dark energy (DE) have focused on its gravitational signatures, and in particular on its equation of state. However, there is a lot to be learned by getting off the beaten track. I will first focus on non-gravitational interactions of (screened) DE with visible matter, leading to the possibility of “direct detection of dark energy”, analogous to direct detection of dark matter: I will argue that such interactions can and potentially may already have been detected in experiments such as XENON1T, while discussing some of their complementary cosmological and astrophysical signatures. I will then discuss early- and late-time consistency tests of LCDM, and how these may shed light on (early and late) DE, particularly in relation to the Hubble tension, presenting two such tests based on the early ISW effect and the ages of the oldest astrophysical objects in the Universe. If time allows, I will present new ways of probing more general ultralight particles (which may be related to either dark matter or DE), using black hole shadows and planetary objects such as asteroids.
May 12	Thu	Ieke Moerdijk	Topology Reading Group
16:00		Models for $E_n$ Operads
		Hicks Seminar Room J11
May 18	Wed	Ieke Moerdijk	Topology Reading Group
10:00		Models for $E_n$ Operads
		Hicks Seminar Room J11
May 18	Wed	Shahn Majid (Queen Mary University of London)	Pure Maths Colloquium
14:00		Quantum Riemannian geometry of the $A_n$ graph, jets and geodesics
		meet.google.com/qxa-rhcg-skx
	Abstract: We describe recent results in quantum or noncommutative Riemannian geometry based on bimodule connections. Here the coordinate algebra can be any unital algebra A equipped with a differential structure expressed as a bimodule Omega^1 of 1-forms as part of a differential graded algebra with A in degree 0. The simplest case is A the commutative algebra of functions on the vertices of a directed graph with Omega^1 spanned by the arrows. We show in this framework that the intrinsic quantum Riemannian geometry of the A_n graph o-o-…-o of n vertices is necessarily q-deformed with q^{2(n+1)}=1. It's q-> 1 limit is the intrinsic quantum Riemannian geometry of the natural numbers viewed as a half-line graph. We then discuss more generally how solutions of the Yang-Baxter or braid relations arise naturally from noncommutative differential geometry and relate both to quantum jet bundles and to the notion of a quantum geodesic.
May 18	Wed	Francesco Sartini (ENS Lyon)	Cosmology, Relativity and Gravitation
15:00		Hidden symmetries in black holes
		Blackboard Collaborate
	Abstract: The spacetime in the interior of a black hole can be described by a homogeneous line element, for which the Einstein–Hilbert action reduces to a one-dimensional mechanical model. We have shown that this model exhibits a symmetry under the (2+1)-dimensional Poincaré group. The existence of this symmetry unravels new aspects of symmetry for black holes and opens the way toward a rigorous group quantization of the interior, which in turn provides a powerful tool to discriminate between different regularization schemes. Remarkably, the physical ISO(2,1) symmetry can be seen as a broken infinite-dimensional symmetry. This is done by reinterpreting the action for the model as a geometric action for the BMS3 group, where the configuration space variables are elements of the algebra bms3 and the equations of motion transform as coadjoint vectors.
May 19	Thu	Prof Robert Walsh (University of Central Lancashire)	SP2RC seminar
10:00		It is rocket science! Coronal physics research highlights from sounding rocket instrumentation
		Zoom link: https://zoom.us/j/95338171418 Meeting ID 953 3817 1418
	Abstract: For over 40 years NASA’s Sounding Rocket Program has provided vital scientific, technical, and educational contributions to space science and is still one of the most robust, versatile, and cost-effective ways to undertake innovative space-based research. Sounding rockets carry scientific instruments into space along a parabolic trajectory. Their overall time in space is brief (typically approx. 15 minutes from launch to landing), and at lower vehicle speeds for a well-placed scientific experiment. The cost factor makes sounding rockets an attractive alternative as they do not need expensive boosters or extended telemetry and tracking coverage since they never achieve orbit. This cost effectiveness continues as the sounding rocket program takes advantage of a high degree of commonality and in many cases, only the experiment (provided by the science team) is changed. In almost all astronomy, planetary, solar, and microgravity missions, the payloads are recovered which means the costs of the experiment and sub-systems are spread out over many possible repeated missions. Of course, the limited factor of only a few minutes of true space-based data resulting such a rocket flight must also be taken into account, The solar physics community has benefited greatly over many years from sounding rocket missions for both the calibration of in-operation satellite instrumentation as well as the development of high performance imagers and spectrometers to examine the corona in remarkable ways. This talk will examine some of these missions, outlining what it is like to part of such a “ successful rocket team” (and how to act when things don’t go according to plan!). In particular, the presentation will focus on results from the unique datasets obtained by the Marshall X-ray Imaging Spectrometer and the High Resolution Coronal Imager, both of which are scheduled to fly again in 2023 and 2024 respectively.
May 19	Thu	Ieke Moerdijk	Topology Reading Group
16:00		Models for $E_n$ Operads
		Hicks Seminar Room J11
May 23	Mon	Francesca Carocci (EPFL)	The Sheffield Geometry and Physics Seminar
14:00		BPS invariant from non Archimedean integrals
		Hicks Seminar Room J11
	Abstract: We consider moduli spaces M(ß,χ) of one-dimensional semistable sheaves on del Pezzo and K3 surfaces supported on ample curve classes. Working over a non-archimedean local field F, we define a natural measure on the F-points of such moduli spaces. We prove that the integral of a certain naturally defined gerbe on M(ß,χ) with respect to this measure is independent of the Euler characteristic. Analogous statements hold for (meromorphic or not) Higgs bundles. Recent results of Maulik-Shen and Kinjo-Coseki imply that these integrals compute the BPS invariants for the del Pezzo case and for Higgs bundles. This is a joint work with Giulio Orecchia and Dimitri Wyss.
May 23	Mon	Lotte Hollands (Heriott-Watt University)	The Sheffield Geometry and Physics Seminar
15:30		Resurgence, partition functions and BPS states for N=2 theories
		Hicks Seminar Room J11
	Abstract: Recently, there have been various exciting developments in the interplay between BPS structures, topological string partition functions and exact WKB analysis. In this talk I will report on this from the perspective of four-dimensional N=2 field theory and its lift to five dimensions. I will try to explain how the non-perturbative open and closed partition functions for these theories may be obtained from the exact WKB analysis applied to the associated differential/ difference equations, and how these partition functions encode their BPS states. This talk is based on 2109.14699, 2203.08249 and work in progress.
May 25	Wed	Umut Varolgunes (Bogazici University)	Pure Maths Colloquium
14:00		Local-to-global methods in relative symplectic cohomology
		meet.google.com/qxa-rhcg-skx
	Abstract: In my thesis, I introduced a Floer theoretic invariant for compact subsets of symplectic manifolds called relative symplectic cohomology. This invariant has already proved to be very useful in symplectic rigidity questions and also opened the way to a fruitful reinterpretation of mirror symmetry. Most of these applications rely on an analogue of Mayer-Vietoris property from topology that holds for relative symplectic cohomology under well-understood geometric assumptions. I will briefly introduce the invariant, discuss the Mayer-Vietoris property and present some computations relevant to mirror symmetry. I will try to make the talk accessible to a more diverse audience by mainly sticking to dimension two, where a symplectic form is nothing but an area form.
May 25	Wed	Dan Graves	ShEAF: postgraduate pure maths seminar
16:00		From Algebraic Topology to Terrapin Station in three easy steps
		Hicks Seminar Room J11
May 26	Thu	Samuel Grant (Queen's University Belfast, United Kingdom)	SP2RC/ESPOS seminar
10:00		The Propagation of Coherent Waves Across Multiple Solar Magnetic Pores
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: Solar pores have long been documented as efficient magnetic conduits for propagating magnetohydrodynamic wave energy from the photosphere into the outer regions of the solar atmosphere. Observations of pores often contain isolated and/or unconnected structures, which prevents the statistical examination of wave activity inter- play as a function of atmospheric height. Here, using high resolution observations acquired by the Dunn Solar Telescope, we examine photospheric and chromospheric wave signatures stemming from a unique collection of magnetic pores originating from the same decaying sunspot. A common driver for waves in each pore is detected, allowing for an unprecedented study of each wave guide using novel methods, to gain insight into their underlying attributes, with a view to next-gen solar observatories.
May 27	Fri	Dr Jiajia Liu (Queen's University Belfast)	SP2RC seminar
13:00		Solar Coronal Jets and the Solar Cycle
		Google Meet
	Abstract: From geysers and atmospheric jet streams on the Earth to spicules and coronal jets in the solar atmosphere, and astronomical jets from accretion disks, elongated eruptive events exist at a tremendous range of scales in the universe. Unlike their chromospheric counterparts, spicules, which have been widely suggested to be related to the global oscillation of the Sun, solar coronal jets have been mostly studied as localised events. In this talk, I will briefly summarise a series of our work on coronal jets from the aspects of their energy partition and rotational motion, before presenting our recent adventure of exploring the potential link between solar coronal jets and the solar cycle, based on a large dataset built from more than 1200 coronal jets automatically detected from the SDO observations in the past 10 years.
Jun 1	Wed	Dan Fretwell (University of South Wales)	Pure Maths Colloquium
14:00		Quaternary Lattices, Modular Forms and Elliptic Curves.
		Hicks Seminar Room J11
	Abstract: A common theme in modern Number Theory is to find interesting discrete objects coming from very different places, but whose arithmetic properties are intimately connected. In this talk we will (hopefully) see a surprising example of this, connecting the first and third objects in the title (using the second to bridge the gap). Time permitting, we will sketch the proof, motivated by a hidden 1.5th object (Clifford algebras). (Based on joint work with E. Assaf, C. Ingalls, A. Logan, S. Secord and J. Voight)
Jun 6	Mon	Christian Böhning (Warwick)	The Sheffield Geometry and Physics Seminar
14:00		Skew matrices of linear forms, matrix factorisations and intermediate Jacobians of cubic threefolds
		Hicks Seminar Room J11
	Abstract: I will report on some ongoing joint work with Hans-Christian von Bothmer (Hamburg) and Lukas Buhr (Mainz). Results due to Druel and Beauville show that the blowup of the intermediate Jacobian of a smooth cubic threefold X in the Fano surface of lines can be identified with a moduli space of semistable sheaves of Chern classes c_1=0, c_2=2, c_3=0 on X. We identify this space with a space of matrix factorisations. This has the advantage that this description naturally generalises to singular and even reducible cubic threefolds. In this way, given a degeneration of X to a reducible cubic threefold X_0, we obtain an associated degeneration of the above moduli spaces of semistable sheaves.
Jun 6	Mon	Navid Nabijou (Cambridge)	The Sheffield Geometry and Physics Seminar
15:30		Roots and Logs in the Enumerative Forest
		Hicks Seminar Room J11
	Abstract: Logarithmic and orbifold structures provide two independent ways to model curves in a variety tangent to a divisor. Simple examples demonstrate that the resulting systems of invariants differ, but a more structural explanation of this defect has remained elusive. I will discuss joint work with Luca Battistella and Dhruv Ranganathan, in which we identify "birational invariance" as the key property distinguishing the two theories. Our proof hinges on a technique – rank reduction – for reducing questions about normal crossings divisors to questions about smooth divisors, where the situation is much better understood. Connections to local curve counting will also be discussed. No prior knowledge of Gromov-Witten theory will be assumed.
Jun 8	Wed	Bachir Bekka (Université de Rennes 1)	Pure Maths Colloquium
14:00		The spectral gap property for group actions
		meet.google.com/qxa-rhcg-skx
	Abstract: A measure preserving action of a group G on a measure space X gives rise to a unitary representation of G on the Hilbert space $L^2(X)$. This action may or may not have the spectral gap property which is a very strong form of ergodicity. For instance, groups with Kazhdan's property (T) always have this property. We will survey the importance of the spectral gap property in various problems arising in graph theory, dynamical systems or operator algebras. In the case where X is a homogeneous space arising from an algebraic group, we will show that the absence of the spectral gap property is often related to amenability.
Jun 8	Wed	Sivakumar Namasivayam (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Vacuum polarization on three-dimensional anti-de Sitter space-time with Robin boundary conditions
		Hicks LT4
	Abstract: Quantum field theory in curved space-time is a theory of quantum fields propagating on a background classical curved space-time. We study a quantum scalar field, with general mass and coupling, on a background three dimensional anti-de Sitter space-time (adS3) with a view to determining the vacuum and thermal expectation values of the square of the scalar field, $\langle\Phi^2\rangle$, known as the vacuum polarisation (VP). Anti-de Sitter space-time is a maximally symmetric solution to Einstein’s field equations with a constant negative curvature which plays a pivotal role in the Ads-CFT (conformal field theory) correspondence. However the presence of a time-like boundary at spatial infinity means that information can be lost to the boundary in finite time, meaning that adS is not a globally hyperbolic space-time. Thus, we need to impose appropriate boundary conditions in order to have a well-posed quantum field theory. Applying Dirichlet, Neumann and Robin boundary conditions at the spacetime boundary, we have found that the vacuum expectation values of the VP with either Neumann or Dirichlet boundary conditions are constant and respect the maximum symmetry of the background spacetime. This is not seen with Robin boundary conditions however, which depend on the spacetime location. We have also found that both the vacuum and thermal expectation values of the VP, for all Robin parameters (except Dirichlet), converge to the Neumann value at the spacetime boundary whereas the Dirichlet expectation values have a different limit.
Jun 15	Wed	Lisa Mickel (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Entanglement entropy of a thermalized black hole in group field theory
		Hicks LT4
	Abstract: Finding a description of black holes in theories of quantum gravity is a common challenge, where one of the topics of interest is to derive the entropy of a black hole. In this talk we will work in the framework of coloured group field theories (GFTs). In previous work, coloured GFT states with a suitable topology were introduced to obtain a foliation for the Schwarzschild black hole and calculate the entanglement entropy across a (horizon) surface. We extend this construction by thermalizing the interior and exterior of the black hole using the framework of thermofield dynamics before constructing the state. The state we consider is obtained from a so-called seed state with the appropriate topology that is then consecutively refined in a topology preserving manner. Since this is work in progress, I will conclude with some final remarks on possible challenges that we might face during the computation of the entanglement entropy.
Jun 17	Fri	Emilia Kilpua (University of Helsinki)	SP2RC seminar
13:00		Solar wind and coronal mass ejections
		Google Meet
	Abstract: This seminar will focus on discussing the ionised stream of plasma - the solar wind - that flows continuously from the Sun through interplanetary space. First the basic concepts and physics of the solar wind will be presented as well as of the transient coronal mass ejections (CMEs) that are regularly launched from the Sun. The seminar will continue with the outlook on recent modelling and observational efforts to study and forecast the solar wind and CMEs, with the EUropean Heliospheric FOrecasting Information Asset (EUHFORIA).
Jun 22	Wed	Andrea Calcinari (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Towards anisotropic cosmology in group field theory
		Hicks LT4
	Abstract: In cosmological group field theory models for quantum gravity coupled to a massless scalar field, the total volume follows the classical Friedmann dynamics of a flat FLRW Universe at low energies while resolving the Big Bang singularity at high energies. An open question is how to generalise these results to other homogeneous cosmologies. In this talk I will show the first steps taken towards studying Bianchi models in group field theory, based on the introduction of a new anisotropy observable analogous to the β variables in Misner’s parametrisation. In a model based on coupling three Peter-Weyl modes, we find that in an expanding Universe β initially behaves like its classical analogue before “decaying”, showing a previously studied isotropisation. I will conclude with some potential future developments about defining relational dynamics in group field theory without the need of matter, just like one can do in a classical setting thanks to the anisotropy degrees of freedom.
Jun 23	Thu	Peter Hunana (Instituto de Astrofísica de Canarias (IAC))	SP2RC/ESPOS seminar
10:00		Generalized Fluid Models of the Braginskii-type
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: Several generalizations of the well-known fluid model of Braginskii (Rev. of Plasma Phys., 1965) are considered. We use the Landau collisional operator and the moment method of Grad. We focus on the 21-moment model that is analogous to the Braginskii model, and we also consider a 22-moment model. Both models are formulated for general multi-species plasmas with arbitrary masses and temperatures, where all the fluid moments are described by their evolution equations. The 21-moment model contains two “heat flux vectors” (3rd and 5th-order moments) and two “viscosity-tensors” (2nd and 4th-order moments). The Braginskii model is then obtained as a particular case of a one ion-electron plasma with similar temperatures, with de-coupled heat fluxes and viscosity-tensors expressed in a quasi-static approximation. We provide all the numerical values of the Braginskii model in a fully analytic form (together with the 4th and 5th-order moments). For multi-species plasmas, the model makes calculation of transport coefficients straightforward. Formulation in fluid moments (instead of Hermite moments) is also suitable for implementation into existing numerical codes. It is emphasized that it is the quasi-static approximation which makes some Braginskii coefficients divergent in a weakly-collisional regime. Importantly, we show that the heat fluxes and viscosity-tensors are coupled even linearly and that the fully contracted (scalar) perturbations of the 4th-order moment, which are accounted for in the 22-moment model, modify the energy exchange rates.
Jun 30	Thu	Hanneke Wiersema (Cambridge)	Number Theory seminar
11:00		Modularity in the partial weight one case
		Google Meet
	Abstract: The strong form of Serre's conjecture states that a two-dimensional mod p representation of the absolute Galois group of Q arises from a modular form of a specific weight, level and character. Serre considered modular forms of weight at least 2, but in 1992 Edixhoven refined this conjecture to include weight one modular forms. In this talk we explore analogues of Edixhoven's refinement for Galois representations of totally real fields, extending recent work of Diamond–Sasaki. In particular, we show how modularity of partial weight one Hilbert modular forms can be related to modularity of Hilbert modular forms with regular weights, and vice versa.
Jun 30	Thu	Tzu-Jan Li (Paris)	Number Theory seminar
13:00		On endomorphism algebras of Gelfand--Graev representations
		Google Meet
	Abstract: Helm and Moss have recently studied a problem on "local Langlands correspondence in families" for the p-adic general linear groups, through which they have also obtained an invariant-theoretical description of integral endomorphism algebras of Gelfand--Graev representations of finite general linear groups. In this talk, we shall generalise Helm--Moss's result on endomorphism algebras of Gelfand--Graev representations to the case of any reductive groups having connected center. Instead of using Helm--Moss's p-adic approach, we will use the Brauer theory of modular representations to relate the endomorphism algebra in question with the desired invariant-theoretical description. This talk is mainly based on the work [1] in collaboration with Jack Shotton.
Jun 30	Thu	Chris Williams (Nottingham)	Number Theory seminar
14:30		p-adic L-functions for GL(3)
		Google Meet
	Abstract: Let \pi be a p-ordinary cohomological cuspidal automorphic representation of GL(n,A_Q). A conjecture of Coates--Perrin-Riou predicts that the (twisted) critical values of its L-function L(\pi x\chi,s), for Dirichlet characters \chi of p-power conductor, satisfy systematic congruence properties modulo powers of p, captured in the existence of a p-adic L-function. For n = 1,2 this conjecture has been known for decades, but for n > 2 it is known only in special cases, e.g. symmetric squares of modular forms; and in all previously known cases, \pi is a functorial transfer via a proper subgroup of GL(n). In this talk, I will explain what a p-adic L-function is, state the conjecture more precisely, and then describe recent joint work with David Loeffler, in which we prove this conjecture for n=3 (without any transfer or self-duality assumptions).
Jul 1	Fri	Belucz Bernadett (SP2RC (UoS))	SP2RC seminar
13:00		MHD Instabilities of Extended Solar Cycle in a Shallow-water Tachocline Model
		Google Meet
	Abstract: The wings of sunspot butterfly diagram, combined observations of EUV brightpoints, faculae, filaments, ephemeral active regions or coronal green line emissions demonstrate extended wings to much higher latitudes up to 60 degrees, which is known as the Extended Solar Cycle (ESC). This pattern shows a strong overlap between cycles. We represent these extended and overlapped wings by oppositely-directed double magnetic bands. We compute the unstable eigenmodes for MHD Rossby waves, study the interaction between the low-latitude bands and the high-latitude bands and properties of these energetically active Rossby waves as these band-pairs migrate to the equator.
Jul 7	Thu	Lakshmi Pradeep Chitta (Max Planck Institute for Solar System Research (MPS), Germany)	SP2RC/ESPOS seminar
10:00		Solar coronal heating from small-scale magnetic braids
	Abstract: Relaxation of braided coronal magnetic fields through reconnection is thought to be a source of energy to heat plasma in active region coronal loops. However, observations of active region coronal heating associated with untangling of magnetic braids remain sparse. One reason for this paucity could be the lack of coronal observations with sufficiently high spatial and temporal resolution to capture this process in action. Using new high spatial resolution (250–270 km on the Sun) and high cadence (3–10 s) observations from the Extreme Ultraviolet Imager (EUI) on board Solar Orbiter we observed untangling of small-scale coronal braids in different active regions. The untangling is associated with impulsive heating of the gas in these braided loops. We assess that coronal magnetic braids overlying cooler chromospheric filamentary structures are perhaps more common. Furthermore, our observations show signatures of both spatially coherent and intermittent coronal heating during relaxation of magnetic braids. Our study reveals the operation of both more gentle and explosive modes of magnetic reconnection in the solar corona. In this talk, we present these new EUI observations and discuss the implications for magnetic braiding associated coronal heating.
Jul 8	Fri	Steven A. Wrathmall (Durham University)	SP2RC seminar
13:00		Developing atomic line filters for improved space-weather forecasting
		Join Zoom Meeting https://us06web.zoom.us/j/84656397591
	Abstract: Major solar flare events pose a serious risk to our critical infrastructures (power networks telecommunications, navigation etc) if they interact with Earth's magnetosphere and cause geomagnetic storms. The Quantum Light and Matter group at Durham University is a part of the SAMNET network [1] to develop early warning systems for such events. At the heart of the solar telescopes are atomic line filters. Our group has worked extensively on the modelling and construction of these narrow band filters [2,3,4]. The aim of this talk is to present our recent work on developing filters to support improved space weather forecasting. 1. R. Erdélyi, M. B. Korsós, X. Huang et al., “The Solar Activity Monitor Network - SAMNet,” J. Space Weather. Space Clim. 12, 2 (2022). 2. James Keaveney, Charles S. Adams, Ifan G. Hughes, ElecSus: Extension to arbitrary geometry magneto-optics, Computer Physics Communications, Volume 224, 2018, Pages 311-324, 3. James Keaveney, Steven A. Wrathmall, Charles S. Adams, and Ifan G. Hughes, "Optimized ultra-narrow atomic bandpass filters via magneto-optic rotation in an unconstrained geometry," Opt. Lett. 43, 4272-4275 (2018) 4. Fraser D. Logue, Jack D. Briscoe, Danielle Pizzey, Steven A. Wrathmall, and Ifan G. Hughes, "Better magneto-optical filters with cascaded vapor cells," Opt. Lett. 47, 2975-2978 (2022)
Jul 28	Thu	Roberta Duarte (São Paulo (USP))	Plasma Dynamics Group
16:00		The First AI Simulation of a Black Hole
		Google Meet
	Abstract: In this pilot study, we investigate the use of a deep learning (DL) model to temporally evolve the dynamics of gas accreting onto a black hole in the form of a radiatively inefficient accretion flow (RIAF). We have trained a machine to forecast such a spatiotemporally chaotic system -- i.e. black hole weather forecasting -- using a convolutional neural network (CNN) and a training dataset which consists of numerical solutions of the hydrodynamical equations, for a range of initial conditions. We find that deep neural networks seem to learn well black hole accretion physics and evolve the accretion flow orders of magnitude faster than traditional numerical solvers, while maintaining a reasonable accuracy for a long time. For instance, CNNs predict well the temporal evolution of a RIAF over a long duration of 8e4 GM/c³ which corresponds to 80 dynamical times at r = 100 GM/c². The DL model is able to evolve flows from initial conditions not present in the training dataset with good accuracy. Our approach thus seems to generalize well. Once trained, the DL model evolves a turbulent RIAF on a single GPU four orders of magnitude faster than usual fluid dynamics integrators running in parallel on 200 CPU cores. We speculate that a data-driven machine learning approach should be very promising for accelerating not only fluid dynamics simulations, but also general relativistic magnetohydrodynamic ones.
Aug 25	Thu	Rodrigo Miranda (Brasilia, Brazil)	Plasma Dynamics Group
16:00		Complexity of intermittent magnetic field turbulence within reconnection exhausts in the solar wind at 1 AU
		Google Meet
	Abstract: We apply the Jensen-Shannon (J-S) complexity-entropy index to magnetic field data of four reconnection exhausts detected in the solar wind at 1 AU. Three events are related to the passage of an interplanetary coronal mass ejection, and one event is related to a rope-rope magnetic reconnection event. The interplanetary magnetic field is projected into the LMN coordinates by applying the hybrid minimum variance analysis. The J-S index indicates that the three components of the magnetic field display entropy and complexity values similar to stochastic fluctuations. However, we show that a high degree of intermittency within the inertial subrange is related to a lower degree of entropy and a higher degree of complexity. We also show that, for all four events, the L component of the magnetic field displays lower entropy and higher complexity than the M and N components. These results suggest that coherent structures can be responsible for decreasing entropy and increasing complexity within reconnection exhausts in the interplanetary magnetic-field turbulence.
Aug 26	Fri	Pasupulati Sunil Kumar (IISER Thiruvananthapuram)	Number Theory seminar
14:00		On the existence of Euclidean ideal class in quartic, cubic and quadratic extensions.
		Google Meet
	Abstract: Abstract. In 1979, Lenstra introduced the definition of the Euclidean ideal which is a generalization of Euclidean domain. Definition 1. Let R be a Dedekind domain and I be the set of non zero integral ideals of R. If C is an ideal of R, then it is called Euclidean if there exists a function Ψ : I → N, such that for every I ∈ I and x ∈ I^−1C - C there exist a y ∈ C such that Ψ ((x − y)IC^−1) < Ψ(I). Lenstra established that for a number field K with rank(O^x K ) ≥ 1, the number ring OK contains a Euclidean ideal if and only if the class group ClK is cyclic, provided GRH holds. Several authors worked towards removing the assumption of GRH. In this talk, I prove the existence of the Euclidean ideal class in abelian quartic fields. As a corollary, I will prove that a certain class biquadratic field with class number two has a Euclidean ideal class. I also discuss the existence of a Euclidean ideal class in certain cubic and quadratic extensions. This is joint work with Srilakshmi Krishnamoorthy.
Aug 29	Mon	Paulo Godolphim (Universidad de Chile)	Mathematical Biology Seminar
10:00		Vertex model micro-mechanical validation in fish embryo morphogenesis
		Hicks LT4
	Abstract: The vertex model is one of the most used physical models to describe confluent tissues. Many works show the vertex model gives excellent qualitative and quantitative descriptions of different in vitro and in vivo experiments. Nevertheless, systematic validation of the model is yet barely explored. Our initial assumption is that only finding the optimal parameters that correctly describe/mimic the evolution of an (experimental) tissue is necessary but not sufficient to consider a model as an accurate description. We propose that a more restrictive condition must be matched. If a model is a good description, then the same set of parameters must be able to describe at the same time the whole tissue and also any sub-part of the tissue. We call this stricter approach Micromechanics, where one executes vertex-by-vertex independent simulations to find the optimal parameters for each vertex. If the optimal parameters are homogeneous, then the model is considered valid. If not, this indicates we need to modify the model to ensure homogeneity in the parameters alongside the tissue. We are working with experimental in vivo data of the EVL cell layer in the epiboly process (time ~11h to 22h) of an Annual Killifish embryo, where simulated vertices' positions are compared with those obtained using fluorescent microscopy. Our results show that the model tested has inhomogeneous parameters, indicating that it is not a valid description for our data. Our conclusions are still preliminary, however, we believe that this characteristic can be corrected by introducing a non-homogeneous viscosity term in the tissue energy functional.
Sep 13	Tue	Solomon Friedberg (Boston College)	Number Theory seminar
14:00		Towards a New Shimura Lift
		Hicks Seminar Room J11
	Abstract: The classical Shimura correspondence lifts automorphic representations on the double cover of $SL_2$ (corresponding to classical half-integral weight forms) to automorphic representations on $PGL_2$. Though efforts have been made for many years to generalize this map to higher rank groups and higher degree covers, our knowledge is limited. In this talk I present joint work with Omer Offen that points to a new Shimura lift for automorphic representations on the triple cover of $SL_3$ -- we establish the Fundamental Lemma for a relative trace formula. Moreover, this project will characterize the image of the lift by means of a period involving a theta function on $SO_8$, confirming a 2001 conjecture of Bump, Friedberg and Ginzburg.
Sep 22	Thu	Andres A. Ramos (Instituto de Astrofisica de Canarias (IAC), Spain)	Plasma Dynamics Group
16:00		Methods in Machine Learning for solar spectroscopy
		https://meet.google.com/tan-kjfo-wfv
	Abstract: Solar spectropolarimetry is entering the realm of big data. Current and future telescopes will produce data at a rate that will make it hard to store in a single machine and even harder to operate on the data. Thankfully, in the last decade, machine learning has experienced an enormous advance, thanks to the open possibility of training very deep and complex neural networks. In this contribution I show options to explore to deal with the big data problem and also how deep learning can be used to efficiently solve difficult problems in Solar Physics. I will focus on how differentiable programming (aka deep learning) is helping us to have access to velocity fields in the solar atmosphere, correct for the atmospheric degradation of spectropolarimetric data and carry out fast 3D inversions of the Stokes parameters to get physical information of the solar atmosphere.
Sep 28	Wed	Steffen Gielen (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Unitarity and clock dependence in quantum cosmology
		Hicks LT10
	Abstract: General relativity gives us the freedom to choose different time coordinates to describe evolution, but also says that only relational notions of evolution (such as "what is the value of quantity A when quantity B takes the value $b_0$"?) are meaningful, i.e., possibly related to observation. When we quantise, this leads to various basic technical and conceptual questions known under the heading of the "problem of time": depending on the viewpoint we seem to have either no dynamics at all or too many, potentially inequivalent, ways of defining time evolution in quantum theory. The standard quantum-mechanical demand of unitary time evolution becomes ambiguous in the general-relativistic context, as it may refer to different notions of time. Here I will discuss some of these issues in a simple cosmological model, where three inequivalent quantum theories can be defined. Demanding unitarity in these simple theories leads to quite radically different "predictions" for the resulting cosmology, illustrating the problem of time.
Oct 4	Tue	Robert Kurinczuk (Sheffield)	Number Theory seminar
13:00		The integral Bernstein centre
		Hicks Seminar Room J11
Oct 5	Wed	Haluk Sengun (Sheffield)	Pure Maths Colloquium
14:00		Theta correspondence via $C^*$-algebras
		Hicks Seminar Room J11
	Abstract: Theta correspondence is a major theme in the theory of automorphic forms and in representation theory. In a nutshell, the correspondence sets up a bijection between certain sets of smooth admissible irreps of a pair of reductive groups G,H which sit as each others' centralizers in a larger symplectic group. In joint work with Bram Mesland (Leiden), we showed that the theta correspondence, in many cases, can be interpreted within the framework of Rieffel's induction theory for representations of C*-algebras. This interpretation reveals some new fundamental features: the theta correspondence is functorial and is continuous with respect to weak containment. In the talk, I will explain our approach and time permitting, will discuss some further applications. Many of the results I will discuss can be found in the preprint arXiv:2207.13484.
Oct 5	Wed	Robert Santacruz (New Brunswick)	Cosmology, Relativity and Gravitation
15:00		Do black holes emit matter?
		Hicks LT10
	Abstract: It is known that the classical mathematical description of black holes contains some undesired properties, such as the singularity. In this seminar, I will explain how to construct an effective LQG model of black hole collapse that: i) avoids the singularity and divergent observables; ii) follows a bounce resulting in an outgoing shock wave; iii) determines the lifetime of these objects to be proportional to the mass squared; iv) provides a conformal diagram that strongly modifies the “information loss” picture.
Oct 6	Thu	Markus Szymik (Sheffield)	Topology Seminar
16:00		Work in progress on knots and primes
		F38
	Abstract: Analogies between low-dimensional topology and number theory have been suggested for over a century. One thing I am interested in at the moment is seeing how we can use the algebra of racks and quandles to classify such objects and understand their symmetries. In this talk, I will briefly introduce this algebra, sketch my work in progress, and indicate some possible future directions if time permits.
Oct 6	Thu	Inaki Esnaola (Sheffield)	Plasma Dynamics Group
16:00		On measures of dependence between solar wind parameters and fluxes of relativistic electrons at GEO
		https://meet.google.com/qxy-tmxa-jbi
	Abstract: The identification of the external parameters that govern complex systems is a central problem in the analysis of system dynamics. Data-driven approaches often rely on classical measures of dependence to identify the input parameters, such as linear correlation, error reduction ratio, mutual information, and maximal correlation. All of the above, with the exception of linear correlation, capture nonlinear dependencies in the dynamical system but lack scalability and require non-trivial parameter selection to tune the analysis. While measures of dependence provide quantitative estimates of the dependence between the variables in the data, only maximal correlation describes the structure of the dependence in terms of the best linear regressor under quadratic penalty. We review the properties of different measures and provide operational insight into the estimates provided by different measures. We use the nonlinear dependence measures to study what solar wind parameters govern the evolution of fluxes of electrons in the energy range 1.8-3.5 MeV at the geostationary orbit. Data from Los Alamos National Laboratory (LANL) geosynchronous energetic particle instrument Energetic Sensor for Particles (ESP) [Reeves et al. 2011] is used in this investigation. The results obtained are discussed in relation to the relative importance of the solar wind density and the solar wind velocity as control parameters for fluxes of relativistic electrons at GEO.
Oct 12	Wed	Andre Henriques (University of Oxford)	Pure Maths Colloquium
14:00		2d QFTs as objects of mathematics
		Hicks Seminar Room J11
	Abstract: One dimensional quantum field theory, also known as quantum mechanics, has been completely understood since the first half of the 20th century, thanks to groundbreaking work of John von Neumann. Two dimensional quantum field theory (2d QFT), on the other hand, has been axiomatised in a variety of different ways, and is still very much work in progress. An important conjecture known as the Segal-Stolz-Teichner conjecture, predicts that the space of all supersymmetric 2d QFTs has the homotopy type of elliptic cohomology. This conjecture is currently far out of reach. But its consequences are being explored by physicists, and they are finding ample computational evidence for it. Still, it noteworthy that this conjecture has not even reached the stage of precise mathematical conjecture, because of lack of a suitable precise definition of 2d QFT. A much simpler variant of the Segal-Stolz-Teichner conjecture (still completely out of reach), predicts that the space of all 2d QFTs –not supersymmetric– is contractible. I will present some speculations around this latter conjecture, and use them to make some physical predictions.
Oct 13	Thu	Daniel Graves (Leeds)	Topology Seminar
16:00		A talk on the PROBlem of PROducing PROPer indexing categories for categories of monoids
		Hicks Seminar Room J11
	Abstract: PROPs are "product and permutation categories". They encode structure borne by objects in a symmetric monoidal category. In this talk I will discuss how the PROP that indexes the structure of a monoid in a symmetric monoidal category is closely related to the theory of crossed simplicial groups. I will then report on recent work (and work in progress) which generalizes this in two ways. I will discuss, firstly, how we can extend known results in the symmetric case to cover monoids with extra structure and, secondly, how we can translate all the results to the setting of braided monoidal categories.
Oct 14	Fri	Dr Noémi Zsámberger (Sheffield)	SP2RC/ESPOS seminar
13:00		MHD wave propagation in asymmetric solar waveguides
		Hicks Building G34a and https://meet.google.com/ciq-zovu-rzm
	Abstract: The analytical and numerical modelling of the behaviour of magnetohydrodynamic (MHD) waves in various magnetic geometries is a constantly evolving, active area of research within the field of solar magneto-seismology. This presentation focuses on MHD wave propagation and instabilities in a family of asymmetric Cartesian waveguide models. Thanks to the introduction of various sources of asymmetry (background density, magnetic field or flow speed), this generalisation of classical (symmetric) slab geometries allows us to refine our models of several features in the richly structured solar atmosphere. Including background asymmetry in these configurations influences the phase speeds and cut-off frequencies of the eigenmodes, and, in the case of flow asymmetry, it can also change the threshold for the onset of the Kelvin-Helmholtz instability. The asymmetric nature of the models also allows us to develop solar magneto-seismologic tools and provide efficient methods for obtaining further information about the solar plasma (e.g. magnetic bright points).
Oct 14	Fri	Chad Briddon (Nottingham)	Cosmology, Relativity and Gravitation
14:00		Using SELCIE to investigate screened scalar field models sourced by complex systems
		Hicks LT6
	Abstract: The mechanism that produces the dark energy driving the expansion of the universe remains a mystery. One popular proposal is to have a scalar field play the role of dark energy. Such a field would have, at least, indirect coupling to matter and so result in a new fundamental force which could be used as a probe to detect these fields. However, no such 'fifth force' has been detected so far, placing strong constraints on models of this type. The 'chameleon' is a scalar field that couples to matter but due to its nonlinear effective potential it possesses a screening mechanism which allows it to evade detection in high density regions such as our solar system, while still having a measurable effect on cosmological scales. The difficulty of this and similar models is that the nonlinear equations lack known analytic solutions except in highly symmetric cases. To this end we have developed a Python package named SELCIE (Screening Equations Linearly Constructed and Iteratively Evaluated) which allows the user to construct systems with arbitrary density profiles and solve for the resulting chameleon field profile. It accomplishes this by using the gmsh and FEniCS software packages. This software has already been used to investigate which properties of NFW halos maximise the likelihood of detecting fifth forces generated by the chameleon field. Using this tool, we have been investigating how the chameleon fifth forces in vacuum chamber experiments depend on the shape of the source used.
Oct 17	Mon	Laura Wadkin (Newcastle)	Mathematical Biology Seminar
14:00		Modelling the spread of tree diseases and invasive pests
		Hicks LT6
Oct 18	Tue	Maleeha Khawaja (Sheffield)	Number Theory seminar
13:00		The Fermat equation over real biquadratic fields
		Hicks Seminar Room J11
	Abstract: We will take a look at an overview of the so called modular approach to Diophantine equations. We will particularly focus on the obstacles that arise when applying this approach to the Fermat equation over real biquadratic fields, using Q(sqrt2, sqrt3) as an illustrating example.
Oct 19	Wed	Vlad Bavula (University of Sheffield)	Pure Maths Colloquium
14:00		Holonomic modules and 1-generation in the Jacobian Conjecture
		Hicks Seminar Room J11
	Abstract: In three different areas of Mathematics (Commutative Algebra, Algebra of differential operators, and Poisson algebras) there are three long standing open conjectures that turned out to be equivalent: the Jacobian Conjecture, the Dixmier Conjecture, and the Poisson Conjecture. These are questions about whether certain homomorphisms which are "almost automorphisms" are in fact automorphisms. We show that the Jacobian Conjecture, the Dixmier Conjecture, and the Poisson Conjecture are questions about holonomic modules for the Weyl algebra $A_n$. Using this approach we show that the images of the Jacobian maps, endomorphisms of the Weyl algebra $A_n$ and the Poisson endomorphisms are large in the sense that further strengthening of the results on largeness would be either to prove the conjectures or produce counter examples (the conjectures hold if and only if the images coincide with the algebras). A short direct algebraic (without reduction to prime characteristic) proof is given of equivalence of the Jacobian and the Poisson Conjectures (this gives a new short proof of equivalence of the Jacobian, Poisson and Dixmier Conjectures).
Oct 19	Wed	Anna Tokareva (Imperial College London)	Cosmology, Relativity and Gravitation
15:00		Gravitational wave production after non-local $R^2$ inflation
		Hicks LT10
	Abstract: Gravity can be embedded into a renormalizable theory by means of adding quadratic in curvature terms. However, this at first leads to the presence of the Weyl ghost. It is possible to get rid of this ghost if the locality assumption is weakened and the propagator of the graviton is represented by an entire function of the d'Alembertian operator without new poles and zeros. Models of this type admit a cosmological solution describing the $R^2$, or Starobinsky, inflation. We study graviton production after inflation in this model and show that it is negligible despite the presence of the higher derivative operators which could potentially cause instabilities.
Oct 20	Thu	Arun Mangalam (Indian Institute of Astrophysics, Bangalore)	Plasma Dynamics Group
13:00		Twisted magnetic flux tubes and its stability
		Google Meet
	Abstract: We construct a magnetohydrostatic (MHS) equilibrium model of a vertical axisymmetric flux tube with a twisted magnetic field that expands as it spans from the photosphere to the transition region in a stratified solar atmosphere under the influence of solar gravity. Using a self-similar formulation and a quadratic flux function for the poloidal current and gas pressure, expressed as a second-order polynomial of the flux function for the magnetic shape function, we solve the Grad-Shafranov equation (GSE) semi-analytically. Incorporating the appropriate boundary conditions we have built a closed field configuration of the flux tube. Using the input parameter space which is consistent with the observations, we calculate the magnetic and thermodynamic structure of the flux tube. We also study the stability analysis of the flux tube configuration using the variational method to find the minima of the constrained energy to obtain the region of stability for the flux tube models. We find that the estimated configurations are in reasonable agreement with the observations for magnetic bright points (MBPs). The obtained closed field model can be used for the construction of a realistic structure like a magnetic canopy.
Oct 20	Thu	Joshua Jackson (Sheffield)
14:00		A tasting menu in non-reductive GIT
		Hicks Seminar Room J11
	Abstract: Non-reductive GIT is a new generalisation of Mumford's classical GIT, that allows quotienting algebraic varieties by actions of non-reductive groups. I will explain how it works, and indicate the range of applications it has seen so far.
Oct 24	Mon	Prerna Singh (SheffieldSheffield)	Mathematical Biology Seminar
14:00
		Hicks LT6
Oct 26	Wed	Celine Maistret (University of Bristol)	Pure Maths Colloquium
14:00		The Birch and Swinnerton-Dyer conjecture and the Parity conjecture
		Hicks Seminar Room J11
	Abstract: The Birch and Swinnerton-Dyer conjecture (BSD) plays a pivotal role in the study of elliptic curves by allowing us to solve their equations systematically. In this talk, I will first define elliptic curves and present the conjecture. Then I will explain how BSD beautifully blends key arithmetic information of the curve into a surprising formula and will introduce the Parity conjecture. I’ll discuss a few results on the Parity conjecture in collaboration with V. Dokchitser and H. Green.
Oct 26	Wed	Elliot Nash (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Chiral Connection Formulations, Reality Conditions and Cosmology
		Hicks LT10
	Abstract: Many attempts have been made to reformulate GR in terms of different mathematical objects. One such attempt was made by J.Plebanski in the 1970's which involved rewriting GR as a theory of connections and differential forms, taking advantage of a certain geometric duality. This work has been developed over time, leading to so-called "chiral connection" reformulations (Krasnov 2011). They reformulate GR as a diffeomorphism invariant gauge theory with structure group SO(3,C). These theories are of complex fields and have manifestly complex valued actions. Extra conditions - Reality Conditions - are needed to select solutions that correspond to real Lorentzian GR. Even in highly symmetric cosmological models the reality conditions can interact with the dynamical theory in a highly non-trivial way and need to be treated carefully. The role of the reality conditions in the classical theory must be well understood so that we can understand the role they play in the quantum theory.
Oct 27	Thu	Paul Mitchener (Sheffield)	Topology Seminar
16:00		Assembly Maps
		Hicks Seminar Room J11
	Abstract: An assembly map is a universal approximation of a homotopy-invariant functor by a generalised homology. In this talk, we introduce the concept and examine examples. When we have an assembly map, we have an associated generalised Novikov conjecture, stating that the map is injective when applied to the classifying space of a group. The plan is to show a general technique coming from coarse geometry to prove injectivity of the assembly map for certain classes of groups.
Oct 28	Fri	Ho Leung Fong (Sheffield)	Galois Cohomology Learning Seminar
10:00		Profinite groups, Part I
		Hicks Seminar Room J11
Oct 28	Fri	Dr. Lijuan Liu (School of Atmospheric Sciences, Sun Yat-Sen University )	SP2RC/ESPOS seminar
13:00		The increase of the photospheric horizontal magnetic field in major solar flares
		Google meet link: https://meet.google.com/ciq-zovu-rzm
	Abstract: The rapid increase of the horizontal magnetic field (Bh) around the flaring polarity inversion line is the most prominent photospheric field change during flares. It is considered to be caused by the contraction of flare loops, the details behind which is still not fully understood. Here we investigate the Bh increase in 35 major flares using HMI high-cadence vector magnetograms. We find that the Bh increase is always accompanied by the increase of field inclination. It usually initiates near the flare ribbons, showing a step-like change in between the ribbons. In particular, its evolution in the early flare phase shows a close spatiotemporal correlation to flare ribbons. We further find that the Bh increase tends to have similar intensity in confined and eruptive flares but a larger spatial extent in eruptive flares in a statistical sense. Its intensity and timescale have inverse and positive correlations to the initial ribbon separations, respectively. The results altogether are well consistent with a recent proposed scenario that suggests that the reconnection-driven contraction of flare loops enhances the photospheric Bh according to the ideal induction equation, providing statistical evidence of the reconnection-driven origin for the Bh increase for the first time.
Oct 31	Mon	Cara Brook (Chicago)	Mathematical Biology Seminar
14:00
		Online
Nov 1	Tue	Nadir Matringe (Paris)	Number Theory seminar
13:00		Symmetric periods for automorphic forms on unipotent groups
		Hicks Seminar Room J11
	Abstract: Let G be an algebraic group defined over a number field k with ring of adeles A, and let $\sigma$ be a k-involuiton of G. Studying the nonvanishing of (possible regularizations of) the period integral $p:\phi \mapsto \int_{G^\sigma(k)\backslash G^\sigma(A)} \phi(h)dh$ on topologically irreducible submodules of $L^2(G(k)\backslash G(A))$ is a very popular topic when G is reductive. Here I will focus on the case where G is unipotent, and explain that p does not vanish on such a submodule $\Pi$ if and only if $\Pi^\vee=\Pi^\sigma$.
Nov 2	Wed	Eleonore Faber (University of Leeds)	Pure Maths Colloquium
14:00		From the magic square of rotations and reflections to the McKay correspondence
		Hicks Seminar Room J11
	Abstract: This story starts with rotations in Euclidean 3-space: the finite subgroups of SO(3) are either cyclic or dihedral or one of the symmetry groups of the Platonic solids. In the 19th century, Felix Klein investigated the orbit spaces of those groups and their double covers, the so-called binary polyhedral groups. This investigation is at the origin of singularity theory. Quite surprisingly, in 1979, John McKay found a direct (though then mysterious) relationship between the resolution of the singularities of the orbit spaces and the representation theory of the finite group one starts from. This "McKay correspondence" is manifested, in particular, by the ubiquitious Coxeter-Dynkin diagrams. The McKay correspondence marks essentially the beginning of "Noncommutative singularity theory", the use of representation theory of not necessarily commutative algebras to understand the geometry of singularities, a subject area that has exploded during the last two decades in particular because of its role in the mathematical formulation of string theory in Physics. In this talk I will survey the beautiful classical mathematics at the origin of this story and then give a sampling of recent results (joint with Ragnar-Olaf Buchweitz, Colin Ingalls, Simon May, and Marco Talarico) and work still to be done.
Nov 2	Wed	Guilherme Franzmann (Stockholm )	Cosmology, Relativity and Gravitation
15:00		Is our Universe geometrical after all?
		Hicks LT10
	Abstract: After decades, we still lack a proper understanding of the quantum nature of gravity. Nonetheless, we have already seen many theoretical hints that gravity does not easily fit in the quantum mechanical framework. In this talk, I will discuss the issues associated with gravitating vacuum energy and take that as empirical evidence of the breakdown of QFT in the presence of gravity. Then, I will argue for a radical alternative where space(-time) is completely emergent from quantum mechanics alone, defined for finite-dimensional Hilbert spaces. After briefly reviewing how spacetime can be emergent, I will sketch a new research program that establishes experimental signatures to test the emergent nature of spacetime.
Nov 2	Wed	Joseph Martin	MiaowMiaow (2d category theory) seminar
15:00		Duals for Monoidal Bicategories
		Hicks Seminar Room J11
	Abstract: The goal of this series is to understand duals at all levels in a monoidal bicategory, but we'll cover a bunch of things along the way such as monoidal categories, bicategories and enriched categories, and there'll be lots of examples throughout. You don't need a strong background in category theory to come along.
Nov 3	Thu	Piyali Chatterjee ((Indian Institute of Astrophysics, IIA, India) )	SP2RC/ESPOS seminar
10:00		Insights into the solar spicule forest from simulations and laboratory experiments
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: Spicular jets are highly elongated chromospheric plasma features that are believed to transport momentum to the solar wind and non-thermal energy to heat the atmosphere. At any given time, it is estimated that about 3 million spicules are present on the Sun. We find an intriguing parallel between the simulated spicular forest in a solar-like atmosphere and the numerous jets of polymeric fluid in the laboratory when both are subjected to harmonic forcing. In our radiative (both 2D and 3D) MHD simulations with sub-surface convection, the solar surface oscillations are excited similarly to those harmonic vibrations. A forest of spicules are formed in our simulations with heights ranging between 6 and 25 Mm, bearing substantially closer resemblance to clusters of jets observed in the solar atmosphere. Taken together, the numerical simulations of the Sun and the laboratory fluid dynamics experiments provide insights into the mechanism underlying the ubiquity of jets. The insight provided by the polymeric fluid experiments when combined with the commonalities with the numerical solar MHD simulations is that four basic ingredients are sufficient to assemble a forest of spicules on the Sun by non-linear wave development.
Nov 3	Thu	Andrea Brini (Sheffield)
14:00		Curve counting on surfaces and topological strings
		Hicks Seminar Room J11
	Abstract: I will describe some correspondences relating different types of enumerative invariants associated to a pair (X,D), with X a complex projective surface and D a singular anticanonical divisor in it. These include the log Gromov-Witten invariants of the pair, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi-Yau threefolds, the Donaldson-Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar-Vafa-type invariants. A lot of my personal motivation to believe in the correspondences comes from dualities in physics, but the talk won't require any knowledge of string theory, and nobody will get hurt as a result. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants. Based on past & present work with Bousseau, van Garrel, Nabijou, and our very own Yannik
Nov 3	Thu	Simon Willerton (Sheffield)	Topology Seminar
16:00		Metric spaces, enriched categories and convexity
		Hicks Seminar Room J11
	Abstract: The notion of convexity of sets can be captured in a category theoretic way using a what is known as a monad which associates to a space the finite formal convex combinations of elements. Various authors have looked at such convexity monads on categories of metric spaces. It became clear to me that the work of Fritz-Perrone on this could be naturally expressed if you considered metric spaces as enriched categories, that is categories enriched over a category non-negative real numbers. In this talk I'll explain this point of view and how notions of concave and convex maps naturally arise when you think higher-categorically. The work is motivated by an attempt to combine two categorical approaches to thermodynamics, one from Lawvere involving enriched categories and one from Baez-Lynch-Moeller involving convexity; I might mention some aspects of that if time permits.
Nov 3	Thu	Max McMurdo (Sheffield)	Plasma Dynamics Group
16:00		Phase mixing in partially ionised plasmas
		Google Meet
	Abstract: Effective plasma heating requires short transversal scales. Phase mixing is one of the most promising mechanisms for explaining the heating of the upper solar atmosphere by producing small transversal scales in the presence of large transversal gradients in the Alfvén speed, here we take that to mean a gradient in the equilibrium magnetic field. Such transversal gradients in the equilibrium magnetic field are abundant in the solar atmosphere. Using a single fluid approximation of a partially ionised chromospheric plasma we study the effectiveness of the damping of phase mixed shear Alfvén waves and investigate the effect of varying the ionisation degree on the dissipation of waves. Our results show that the dissipation length of shear Alfvén waves strongly depends on the ionisation degree of the plasma, but more importantly, in a partially ionised plasma the damping length of shear Alfvén waves is several orders of magnitude shorter than in the case a fully ionised plasma, providing further evidence that phase mixing is a large contributor to heating the solar corona. The effectiveness of phase mixing is investigated for various ionisation degrees, ranging from fully neutral to fully ionised plasmas.
Nov 4	Fri	Ho Leung Fong (Sheffield)	Galois Cohomology Learning Seminar
10:00		Profinite groups, Part II
		Hicks Seminar Room J11
Nov 4	Fri	Joseph Martin	MiaowMiaow (2d category theory) seminar
13:00		Duals for Monoidal Bicategories
		Hicks Seminar Room J11
	Abstract: The goal of this series is to understand duals at all levels in a monoidal bicategory, but we'll cover a bunch of things along the way such as monoidal categories, bicategories and enriched categories, and there'll be lots of examples throughout. You don't need a strong background in category theory to come along.
Nov 7	Mon	Tom Bridgeland (Sheffield)
13:00		Introduction to stability conditions
		Hicks Seminar Room J11
	Abstract: This is a service talk for Jon Woolf's seminar on Thursday. I will start by talking about triangulated categories and t-structures. Then I will give the definition of a stability condition on a triangulated category and discuss the space of all such structures on a fixed category.
Nov 9	Wed	Joseph Martin	MiaowMiaow (2d category theory) seminar
15:00		Duals for Monoidal Bicategories
		Hicks Seminar Room J11
	Abstract: The goal of this series is to understand duals at all levels in a monoidal bicategory, but we'll cover a bunch of things along the way such as monoidal categories, bicategories and enriched categories, and there'll be lots of examples throughout. You don't need a strong background in category theory to come along.
Nov 10	Thu	Jon Woolf (Liverpool)
14:00		Stability conditions with massless objects
		Hicks Seminar Room J11
	Abstract: The Bridgeland stability space of a triangulated category is a non-compact complex manifold with a wall-and-chamber structure capturing interesting aspects of the category’s structure. I will describe joint work with Broomhead, Pauksztello and Ploog in which we partially compactify the stability space by allowing `degenerate’ stability conditions with massless objects. One reason this is interesting is that the added boundary points are closely related to the walls. I will illustrate this connection in low-dimensional examples arising from quivers with two vertices.
Nov 11	Fri	Constantinos Papachristoforou (Sheffield)	Galois Cohomology Learning Seminar
10:00		Cohomology of profinite groups, Part I
		Hicks Seminar Room J11
Nov 11	Fri	Shreeyesh Biswal (SP2RC (UoS))	SP2RC/ESPOS seminar
13:00		Could MPILs help forecast solar flares?
		Hicks Building G34a / Google Meet: https://meet.google.com/tmi-zjmx-rjo
	Abstract: Solar flares are intense eruptions of radiation from the solar surface and they are closely associated with Coronal Mass Ejections (CMEs) that are known to inflict radio and magnetic disturbances on the Earth. Recent studies on the forecasting of solar flares involving the 3D extrapolation of the pre-flare magnetic configuration have identified a particular height range between the photosphere and the lower solar corona where the flare onset prediction time can be maximised. This novel concept of an ‘optimal height range’ has been developed by studying the variation of predictors as a function of height above the photosphere and time before the eruption of a flare. Recent studies have even established that the weighted horizontal gradient of the line of sight component of the magnetic field, i.e. the ‘WGM morphological parameter’ and ‘Magnetic Helicity’ are good predictors. We have applied the concept of optimal height to a set of four predictors related to Magnetic Polarity Inversion Lines (MPILs); namely (i) the maximum length of MPILs, (ii) the total length of MPILs, (iii) the total absolute magnetic flux and (iv) R-value. We discuss the need for such predictors and our preliminary observations by assessing their behaviour as a function of height (above the photosphere) and time (before the flare) for a select few Active Regions.
Nov 11	Fri	Joseph Martin	MiaowMiaow (2d category theory) seminar
13:00		Duals for Monoidal Bicategories
		Hicks Seminar Room J11
	Abstract: The goal of this series is to understand duals at all levels in a monoidal bicategory, but we'll cover a bunch of things along the way such as monoidal categories, bicategories and enriched categories, and there'll be lots of examples throughout. You don't need a strong background in category theory to come along.
Nov 15	Tue	Ciaran Schembri (Dartmouth)	Number Theory seminar
13:00
		Hicks Seminar Room J11
Nov 16	Wed	Dan Ciubotaru (University of Oxford)	Pure Maths Colloquium
14:00		Unipotent conjugacy classes and group representations
		Hicks Seminar Room J11
	Abstract: One of the first theorems that we prove in the complex representation theory of a finite group is that the number of irreducible representations (up to isomorphism) equals the number of conjugacy classes in the group. For example, for the group of permutations of the set {1,2,...,n}, the conjugacy classes are parametrised by partitions of n (the cycle decomposition) and so are the complex irreducible representations (via Young's construction from the 1890s). But this is not a natural bijection, just like there is not a natural isomorphism between a finite vector space and its dual in general. However, for certain classes of groups, that come with extra structure (like the ones appearing in Lie theory), one expects natural relations between the irreducible representations of the group, on one hand, and conjugacy classes in a *dual* group, on the other. This happens for example, when the group in question is a finite reflection crystallographic group, or a connected algebraic group over a finite or local field. In these correspondences, a particularly interesting role is played by the unipotent conjugacy classes in the dual group. I will give a survey of some of these connections and then emphasise the case of (infinite-dimensional) representations of reductive algebraic groups (like the general linear group of n by n matrices) with coefficients in a local field, where I'll explain what the unipotent classes tell us about the growth of characters and the parametrisation of such representations. The new results in the talk are joint with Lucas Mason-Brown and Emile Okada.
Nov 16	Wed	Joseph Martin	MiaowMiaow (2d category theory) seminar
15:00		Duals for Monoidal Bicategories
		Hicks Seminar Room J11
	Abstract: The goal of this series is to understand duals at all levels in a monoidal bicategory, but we'll cover a bunch of things along the way such as monoidal categories, bicategories and enriched categories, and there'll be lots of examples throughout. You don't need a strong background in category theory to come along.
Nov 17	Thu	Patrick Kennedy-Hunt (Cambridge)
14:00		The logarithmic Hilbert scheme
		Hicks Seminar Room J11
	Abstract: The Hilbert scheme of a projective variety X is the moduli space of closed subschemes of X. In this talk we will discuss a version of the Hilbert scheme for a pair (X,D) with D a (reasonable) divisor on X. This logarithmic Hilbert scheme is a special case of the logarithmic Quot scheme. As motivation, note hard algebraic geometry problems can be studied by degenerating to simpler situations. Logarithmic geometry provides a suite of tools to study such degenerations. For example, these techniques have been applied to study (logarithmic) GromovWitten theory and more recently (logarithmic) Donaldson-Thomas theory. The logarithmic Hilbert scheme of curves on a threefold is the moduli space studied in logarithmic Donaldson-Thomas theory. A long-term hope is to study other moduli spaces of coherent sheaves with techniques from logarithmic geometry.
Nov 17	Thu	Sarah Whitehouse (Sheffield)	Topology Seminar
16:00		Homotopy theory of spectral sequences
		Hicks Seminar Room J11
	Abstract: I'll discuss recent joint work with Muriel Livernet. We consider the homotopy theory of the category of spectral sequences with the class of weak equivalences given by those morphisms inducing a quasi-isomorphism at a certain fixed page. We show that this admits a structure close to that of a category of fibrant objects in the sense of Brown and in particular the structure of a partial Brown category with fibrant objects. We use this to compare with related structures on the categories of multicomplexes and filtered complexes.
Nov 17	Thu	Luiz A. C. A. Schiavo (Sao Paulo State)	Plasma Dynamics Group
16:00		Statistical methods for analyzing turbulent flows
		Google Meet
	Abstract: Turbulent flows are represented by complex multi-scale phenomena and chaotic motions. Despite its complexity, we can find some more elementary components referred to as coherent or quasi-coherent structures. These structures are challenging to define precisely and are usually identified by flow visualization, conditional sampling techniques, or other methodologies. In the past decades, different methodologies were extensively applied for better understanding and modeling the chaotic motion of turbulent flows. This presentation will review classical and modern statistical tools for extracting information from turbulent flows. First, some classical tools to quantify the state of turbulence will be presented, such as two-point correlation, multidimensional correlation maps, space-time correlations, and turbulence anisotropy maps. Finally, we will discuss modern flow decomposition methods such as orthogonal decomposition (POD), spectral proper orthogonal decomposition (SPOD), and momentum potential theory, focusing on how those methods can help us to analyze coherent structures and build reduced-order models.
Nov 18	Fri	Constantinos Papachristoforou (Sheffield)	Galois Cohomology Learning Seminar
10:00		Cohomology of profinite groups, Part II
		Hicks Seminar Room J11
Nov 18	Fri	Joseph Martin	MiaowMiaow (2d category theory) seminar
13:00		Duals for Monoidal Bicategories
		Hicks Seminar Room J11
	Abstract: The goal of this series is to understand duals at all levels in a monoidal bicategory, but we'll cover a bunch of things along the way such as monoidal categories, bicategories and enriched categories, and there'll be lots of examples throughout. You don't need a strong background in category theory to come along.
Nov 21	Mon	Christopher Revell (Manchester)	Mathematical Biology Seminar
14:00		Couple stresses and discrete potentials in the vertex model of cellular monolayers
		Hicks LT6
Nov 22	Tue	Peiyi Cui (University of East Anglia)	Number Theory seminar
13:00
		Hicks Seminar Room J11
Nov 23	Wed	Luis Garcia (University College London)	Pure Maths Colloquium
14:00		Modular symbols, linking numbers and the Euler class
		Hicks Seminar Room J11
	Abstract: Modular symbols are a fundamental tool for the computation of the homology of certain linear groups. It has been observed that, surprisingly, they also control the relations among certain trigonometric and elliptic functions. After introducing modular symbols and their elementary properties I will explain why this is the case and give some arithmetic applications.
Nov 23	Wed	Sébastien Gomé (PMMH - CNRS, ESPCI Paris)	Fluid Dynamics Seminar
14:00		Transition to turbulence in planar shear flows
	Abstract: In planar shear flows, the route to turbulence is paved by co-exising laminar and turbulent structures. At high enough Reynolds numbers, these transitional structures spontaneously emerge as regular patterns. Once the Reynolds number is reduced, turbulent zones become sparser and either decay to the absorbing laminar state or propagate. Using a rare-event method inspired from stochastic processes, we measure a super-exponential evolution of the mean decay or propagation times with Reynolds number, which we connect to extreme value distributions. Laminar-turbulent patterns are associated to a strong mean flow along laminar-turbulent interfaces. Via a spectral energy analysis, we determine the mechanisms by which this mean flow is fuelled, and confirm its importance in selecting a pattern wavelength. When the large-scale circulation is numerically suppressed, the transition scenario is modified and resembles the initial analogy with Directed Percolation formulated by Pomeau.
Nov 23	Wed	Silvia Pla Garcia (King's College London)	Cosmology, Relativity and Gravitation
15:00		Ultraviolet regularity, CPT, and the big bang quantum vacuum
		Hicks LT 10
	Abstract: In this talk, I will explain how to construct CPT-invariant quantum states in a radiation dominated-universe. I will show the boundary conditions that these states must satisfy to become ultraviolet regular [Hadamard]. Finally, I will propose some examples and briefly discuss one of the physical motivations of this analysis: the two-sheeted universe with time-reversal symmetry.
Nov 25	Fri	Peijin Zhang (Bulgaria Academy of Sciences)	SP2RC/ESPOS seminar
13:00		Low-frequency radio view of the Sun
		Google Meet: https://meet.google.com/tmi-zjmx-rjo
	Abstract: Low-frequency radio observation provides a unique viewing point for solar and spaceweather studies, including the inspection of solar energetic particles and the diagnostics for background plasmas. Solar radio bursts are generated from high energy particles pacing through the solar atmosphere and inner heliosphere interacting with the background plasma. The Low-frequency array (LOFAR) is a radio telescope composed of massive numbers of antennas spreading all over Europe, it is currently the largest radio telescope in the frequency range of 10-240MHz. In this talk, I present the recent proceedings in solar and spaceweather radio observations with LOFAR's high resolution and sensitivity, including the imaging and spectroscopy of solar radio bursts, using bright quasar to perform sounding detection for the inner-heliosphere, and imaging of the quiet Sun.
Nov 28	Mon	Jessica Crawshaw (Oxford)	Mathematical Biology Seminar
14:00		The role of hierarchical Bayesian inference in understanding macular degeneration treatment strategies
		Hicks LT6
	Abstract: Age-related macular degeneration (AMD) is a leading cause of central blindness worldwide. Wet AMD is characterised by choroidal neovascularization (CNV), for which there is currently no definitive cure for AMD. Intraocular injections of anti-angiogenic drugs is the clinical gold standard for disease management, slowing the progression of vision loss. However, the fluid dynamics within the eye leads to relatively rapid drug elimination, resulting in the need for regular intraocular injections. Age-related macular degeneration (AMD) is a disease which slowly destroys ones’ central vision, with a huge impact on quality of life. It is the leading cause of central blindness in the working-aged population worldwide. Wet AMD is characterised by the pathological proliferation of the retinal vasculature triggered by an unhealthy abundance of vascular endothelial growth factor (VEGF). These newly formed blood vessels are immature and leaky, allowing fluids to seep into the retina, damaging the local photoreceptors (critical light sensing cells). Currently, there is no cure for AMD. As such, intraocular injections of anti-VEGF drugs to reduce the abundance of retinal VEGF is the clinical gold standard for AMD disease management, slowing the progression of vision loss. However, injections into the eye are unpleasant (to say the least), and the fluid dynamics within the eye leads to relatively rapid drug elimination, resulting in the need for regular intraocular injections. In this talk, we will present, and analyse, a pharmacokinetic/pharmacodynamic (PK/PD) model of a popular anti-VEGF drug: Ranibizumab. This model has been developed to improve our understanding of the ocular pharmacology of Ranibizumab, and to provide a robust prediction of Ranibizumab retention in the eye. Results from this PK/PD model are compared to published experimental (cynomolgus monkey) and clinical (human) data. We present a hierarchical Bayesian inference strategy to determine clinically relevant parameter distributions and an understanding of disease progression. Using this hierarchical strategy, we provide an insight into the large clinically observed inter-patient variability in drug retention, and thus disease progression, for each patient. Finally, this model establishes the initial basis for a computational framework we are developing to mathematically compare the ocular PK/PD of Ranibizumab with other clinical anti-VEGF drugs in the treatment of AMD.
Nov 29	Tue	Alice Pozzi (Imperial College London)	Number Theory seminar
13:00
		Hicks Seminar Room J11
Dec 1	Thu	Rob Silversmith (Warwick)
00:00		Cross-ratios and perfect matchings
		Hicks Seminar Room J11
	Abstract: Given a bipartite graph G (subject to a constraint), the "cross-ratio degree" of G is a non-negative integer invariant of G, defined via a simple counting problem in algebraic geometry. I will discuss some natural contexts in which cross-ratio degrees arise. I will then present a perhaps-surprising upper bound on cross-ratio degrees in terms of counting perfect matchings — the proof involves Gromov-Witten theory. Finally, I will discuss the tropical side of the story.
Dec 1	Thu	Quentin Noraz (Rosseland Centre for Solar Physics, University of Oslo, Norway)	SP2RC/ESPOS seminar
10:00		New insights about the past, present and future of solar magnetism
	Abstract: The magnetic field of solar-type stars is generated and sustained through an internal dynamo process. This process is mostly determined by the combined action of turbulent convective motions and differential rotation. It can sometimes lead to magnetic cyclic variabilities, like the 11-years solar cycle. Evidence of magnetic cycles have been detected for other solar-type stars as well, ranging from a few years to a few tens of years. How are these cycles controlled? Observations and stellar evolution models show that solar-like stars spin-down during their main-sequence. In parallel, numerical simulations of these stars show that different regimes of differential rotation can be reach and are characterized with the Rossby number. In particular, anti-solar differential rotation (fast poles, slow equator) may exist for high Rossby numbers (slow rotators), which grows when the rotation spins-down. If this regime appears during the main sequence, we may wonder how the dynamo process will be impacted, especially if our Sun is in such a transition. In particular, can slowly rotating stars have magnetic cycles? We performed a numerical multi-D parametric study with the STELEM and ASH codes to understand the magnetic field generation of solar-type stars under various differential rotation regimes. We particularly focused on the energy transfers powering these stellar dynamos, and on the existence of magnetic cycles for different stages of the main sequence. We find that short cycles are favoured for small Rossby numbers (fast rotators), and long cycles for intermediate (solar-like) Rossby numbers. We further assess that energy transfers can reach up to 3% of the stellar luminosity to sustains these dynamos, and ultimately powering surface eruptive events. Finally, we find that anti-solar rotating stars (high Rossby numbers) can only sustain magnetic cycles for specific dynamo processes. This led us to develop a theoretical criterion to select anti-solar candidates with the perspective to bring new constraints on our models, stellar evolution, and more particularly on the future of the Sun.
Dec 1	Thu	Ieke Moerdijk (Sheffield)	Topology Seminar
16:00		The complete graph operad
		Hicks Seminar Room J11
	Abstract: The complete graph operad is an E_n-operad, completely combinatorial in nature, and apparently occupying a central position in the world of E_n-operads. This in spite of the fact that up to now there seems to be no (correct) proof in the literature that this operad actually is E_n. I'll discuss some aspects of this operad that I didn't get to in my crash course last spring, but I will try to make the talk independent of what was discussed in that course.
Dec 2	Fri	Andrew Fisher (Sheffield)	Galois Cohomology Learning Seminar
10:00		Cohomological dimension, Part I
		Hicks Seminar Room J11
Dec 2	Fri	Aishawnnya Sharma (Department of Physics Bahona College, India)	SP2RC/ESPOS seminar
13:00		Dynamics of Sunspot Waves in the Solar Atmosphere
		Hicks Building G34a / Google Meet: https://meet.google.com/tmi-zjmx-rjo
	Abstract: Waves play an important role in the heating of the upper atmosphere of the Sun. Different features observed over sunspots at different atmospheric heights host a variety of waves, such as the 5-minutes photospheric oscillations, the 3-minute chromospheric oscillations, umbral flashes and waves, running penumbral waves (RPWs), and propagating coronal waves. Although these oscillations and waves have been studied for decades, we are still far from understanding the physics behind their origin and the possible coupling among them. In this talk, the speaker will talk on multiwavelength imaging observations that will provide pieces of evidence on the nature and extent of the coupling among different sunspot waves observed in the different layers of the solar atmosphere.
Dec 5	Mon	Thomas Hiscock (Aberdeen)	Mathematical Biology Seminar
14:00		Mathematical models of tetrapod joint patterning: how does a finger get its knuckles?
		Hicks LT6
	Abstract: Repeating joints are a hallmark feature of tetrapod digits, allowing our fingers to bend, and enabling a diversity of limb functions across species (e.g., walking, grasping, flying). Whilst many relevant genes and cell behaviours have been identified, it remains unclear how these key players co-ordinately control the location, number, and orientation (i.e., the patterning) of joints within each digit. In this talk, I will describe our ongoing efforts to understand joint patterning by building mathematical models of digit development. I will describe some of the insights and hypotheses that these mathematical models have inspired, together with experimental data that is helping to refine our models.
Dec 6	Tue	Rachel Newton (King's College London)	Number Theory seminar
13:00
		Hicks Seminar Room J11
Dec 7	Wed	Guillaume Conchon-Kerjan (Bath)	Probability seminar
15:00		Scaling limit of a branching process in a varying environment
		F41
	Abstract: A branching process in varying environment is a Galton-Watson tree whose offspring distribution can change at each generation. The evolution of the size of successive generations has drawn a lot of attention in recent years, both from the discrete and continuum points of view (as the scaling limit is a modified Continuous State Branching Process). We focus on the limiting genealogical structure, which is much more delicate to study. In the critical case (all distributions have average offspring 1), we show that under mild second moment assumptions on the sequence of offspring distributions, a BPVE conditioned to be large converges to the Brownian Continuum Random Tree, as in the standard Galton-Watson setting. The varying environment adds asymmetry and dependencies in many places. This requires numerous changes to the usual arguments. In particular we employ a (to our knowledge) new connexion between the Łukasiewicz path and the height process. This is a joint work with Daniel Kious and Cécile Mailler.
Dec 7	Wed	Robyn Muñoz (Portsmouth)	Cosmology, Relativity and Gravitation
15:00		Simulations of a quasi-spherical cosmological collapse and gravito-electromagnetic and Petrov invariant characterisation
		Hicks LT10
	Abstract: We look into whether the spherical collapse model (SCM) is a good approximation in a numerical relativity cosmological simulation, and describe the spacetime's evolution during nonlinear structure formation. In the simulation, we evolve a quasi-spherical collapsing structure, where fully nonlinear initial conditions are provided by perturbing the $\Lambda$CDM model with the comoving curvature perturbation $\mathcal{R}_c$, defined as a 3-dimensional sinusoidal. We then have a grid of quasi-spherical over-densities connected through filaments and surrounded by under-densities. This is implemented in the synchronous comoving gauge, using a dust perfect fluid description of cold dark matter, and then it is fully evolved with the Einstein Toolkit code. We find that the SCM is an excellent approximation at the peak of the over-density, where we observe no shear. Additionally, we characterise the expansion of the turn-around boundary and show how it depends on the initial distribution of matter. Then for the spacetime, we find the electric and magnetic parts of the Weyl tensor to be strongest along and around the filaments respectively. We classify the spacetime as Petrov type I everywhere but identify the leading order behaviour. Along the filaments, it's of type D, while the centre of the over-density remains conformally flat, type O, in line with the SCM. The surrounding region demonstrates a sort of peeling-off in action, with the spacetime transitioning between different Petrov types as non-linearity grows with the production of gravitational waves.
Dec 8	Thu	Jacob Saunders (Sheffield)	Galois Cohomology Learning Seminar
10:00		Cohomological dimension, Part II
		Hicks Seminar Room J11
Dec 8	Thu	James Brotherston (Sheffield)	Topology Seminar
16:00		Monoidal model categories relating to spectral sequences
		Hicks Seminar Room J11
	Abstract: I'll introduce some model categories of Cirici, Egas Santander, Livernet and Whitehouse on the categories of filtered chain complexes and bicomplexes (as well as some newer intermediary ones indexed by finite non-empty subsets $S$ of the naturals). Their weak equivalences are determined as isomorphisms on the $(r+1)$-page of the associated spectral sequences where $r = \max S$. I'll show that these are all Quillen equivalent via a zig-zag of totalisation and shift-décalage adjunctions so they all present the same homotopy category. I'll also demonstrate the model structures of filtered chains are in fact monoidal model categories satisfying the monoid axiom. By a result of Shipley and Schwede, we then obtain model structures of filtered differential graded algebras with the same weak equivalences enhancing previous work of Halperin and Tanré.
Dec 12	Mon	Mikhailo Dokuchaev ( São Paulo)
16:00		Partial actions and strong equivalence of graded algebras
		Hicks Seminar Room J11
	Abstract: We introduce the notion of a strong equivalence between group graded algebras and prove that any partially-strongly-graded algebra by a group G is strongly-graded-equivalent to the skew group algebra by a product partial action of G. We show that strongly-graded-equivalence preserves strong gradings and is nicely related to Morita equivalence of product partial actions. Furthermore, we prove that strongly-graded-equivalent partially-strongly-graded algebras with orthogonal local units are stably isomorphic as graded algebras. This is a part of a joint work with Fernando Abadie and Ruy Exel.
Dec 14	Wed	Bodan Arsovski (UCL)	Number Theory seminar
14:00
		Hicks Seminar Room J11
Dec 15	Thu	Manuel Luna Bennasar (Universitat Illes Balears (UIB), Palma de Mallorca, Spain)	SP2RC/ESPOS seminar
10:00		Interaction of solar jets with filaments: Triggering of large-amplitude filament oscillations
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: Some observations show that jets impact solar filaments producing large-amplitude oscillations in these structures. The seminar will consist of two parts. In the first part the model proposed by Luna & Moreno-Insertis (2021) will be presented. This work suggests a scenario for the generation of the jet and its interaction with the filament. It was found that there are two phases in the jet, eruptive and quiescent, associated with two different reconnection phases. Jet flows emanating from the reconnection regions collide with the prominence producing significant displacements of its heavy mass and large-amplitude oscillations are established. In the second part of the seminar, a recent work will be shown in which two observational case studies are analysed. The jet environment and how it impacts the filament is studied in detail. The oscillations of the filament are also studied and seismology is applied to infer the structure and intensity of the magnetic field. We conclude that both cases presented are consistent with the numerical model.
Jan 12	Thu	Misha Feigin (Glasgow)
14:00		WDVV and commutativity equations, and their rational and trigonometric solutions
		Hicks Seminar Room J11
	Abstract: In the theory of WDVV equations $F_i G^{-1} F_j = F_j G^{-1} F_i$ the constant matrix $G$ is usually assumed to be a linear combination of the matrices $F_i$ of the third order derivatives of the prepotential $F$. I would like to explain that this assumption follows from the equations under a non-degeneracy condition. Then, these equations admit a big class of rational solutions determined by configurations of vectors known as V-systems which include root systems. In the trigonometric settings the situation is much more restrictive, and known examples are given by non-simply-laced root systems and their projections.
Feb 7	Tue	Remke Kloostermann (Padua)
11:00		Deformations of hypersurfaces with non-constant Alexander polynomial
		Hicks Seminar Room J11
	Abstract: Let $X$ be an irreducible hypersurface in $P^n$ of degree $d$. Suppose $X$ has at most isolated singularities. Then $h^i(X)= h^i(P^n)$ holds for $i\not \in \{ n-1,n,2n-2\}$. Smooth hypersurfaces and most hypersurfaces with isolated singularities satisfy the equality $h^n(X)=h^n(P^n)$. In this talk we consider the case where $h^n(X)>h^n(P^n)$, i.e., hypersurfaces with defect. Moreover, we will limit ourselves to hypersurfaces with at most semi- weighted homogeneous (e.g., ordinary multiple points or ADE-singularities). We show that if $(d,n)$ is not in an explicit finite list then the equianalytic deformation space of $X$ is not $T$-smooth, i.e., this space is nonreduced or its dimension is larger than expected. A similar statement holds true for $X$ if the $d$-fold cover $Y$ of $P^n$ ramified along $X$ satisfies $h^{n+1}(Y)>h^{n+1}(P^{n+1})$. This latter result generalizes classical examples of B. Segre of degree $6m$ curves in $P^2$ with $6m^2$, $7m^2$, $8m^2$ and $9m^2$ cusps and deformation space larger than expected.
Feb 8	Wed	Johannes Girsch (Sheffield)	Pure Maths Colloquium
14:00
		Hicks Seminar Room J11
Feb 8	Wed	Matteo Lucca (Brussels)	Cosmology, Relativity and Gravitation
15:00		What can cosmology tell us about primordial black holes?
		Blackboard Collaborate
	Abstract: In this seminar I will review the main cosmological constraints that can be imposed on primordial black holes (PBHs), one of the most appealing and popular dark matter candidates to date. In particular, I will cover the limits that we can infer from the impact of PBH formation, evaporation and accretion on observables such as e.g., the CMB, the cosmic ray background and the 21 cm lines. I will also quickly discuss microlensing constraints. For each of these bounds I will provide a brief pedagogical introduction, an overview of the following constraints and a discussion about the many caveats that inevitably come with them.
Feb 16	Thu	Serena Maria Lezzi (INAF Capodimonte Astronomical Observatory, Italy)	SP2RC/ESPOS seminar
10:00		Multi-wavelength view of Dark Halos around active regions
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: The Dark Halos (DHs) are regions of reduced emission in the neighborhood of solar active regions (ARs). Since their discovery (Hale & Ellerman, 1903), DHs have been called with various names, the first one being circumfacules (Deslanders, 1930), as they were first identified in the chromosphere as faint areas surrounding plages in the Ca II K-line, and later also in the Ca II 8542 Å line (D’Azumbuja, 1930). Bumba & Howard (1965) proposed that the Ca II circumfacules are composed of dark features corresponding to dark Hα fibrils, and this suggestion was supported by different authors (e.g. Rutten et al. 2007, Pietarila et al. 2009). A typical chromospheric fibrillar DH normally has a counterpart also in the other layers of the solar atmosphere. Indeed, with the advent of UV and EUV observations, it has been possible to observe dark regions around ARs also in a wide range of spectral lines originating in Transition Region and low corona. DHs around ARs are seen as areas of reduced emission in many wavelengths, for instance in the SOHO/SUMER images in O V at 630 Å and S VI at 933 Å lines, as pointed out by Andretta et al. (2014), and in the SDO/AIA 171 Å waveband, as noted by Wang et al. (2011). DHs are very common solar features, yet we do not fully understand what their structure is, what determines their appearance, nor the physical mechanism that creates and sustains them. Moreover, because they are large-scale structures, of an extent comparable, if not larger, than that of the associated ARs, they may influence the irradiance of the Sun, especially during the maximum of the solar activity, when several ARs are present on the solar disk. Furthermore, DHs are sometimes mistaken for Coronal Holes (CHs) when seen in the UV and EUV. Nevertheless, to date there has not been a quantitative characterization that allows a clear distinction between these two solar features. In particular, the connectivity of DHs with the outer solar atmosphere and the solar wind must be different from the one of CHs in a way that is not yet clear. In this work we report preliminary results of the analysis of a comprehensive set of imaging and spectroscopic observations of the DH around AR 12706, observed on the solar disk on 22 April 2018, by using IRIS full-disk mosaics and SDO/AIA images, that together allow a tomography of the DH from the chromosphere up to the low corona. The first results highlight the main observational characteristics (line intensities, Mg II h & k fibrils) that can help distinguish between DHs and CHs. These characteristics can be used in future works aimed at systematically studying DHs.
Feb 20	Mon	Rita Neves (Madrid)	Cosmology, Relativity and Gravitation
14:00		Observational Imprints of Loop Quantum Cosmology
		Hicks LT C
	Abstract: In Loop Quantum Cosmology, the big-bang singularity is resolved in terms of a quantum bounce, connecting a contracting epoch of the Universe with an expanding one. After giving way to a period of decelerated expansion, standard slow-roll inflation begins. Cosmological perturbations will be affected by the pre-inflationary dynamics, as well as by quantum corrections to their equations of motion, leading to features in the primordial power spectra. In this talk we will analyse these features against CMB data, obtaining constraints for the parameter of the model and investigating alleviations of the lensing and power suppression anomalies.
Feb 23	Thu	James Stewart (Manchester)	Plasma Dynamics Group
16:00		Oscillatory Reconnection: How waves emitted from merging magnetic flux ropes can be used as a seismological tool for the solar corona
		LT A (Hicks Building)
	Abstract: Oscillatory reconnection is a time-dependent relaxation process that takes place in highly conducting, resistive plasmas, such as those found in the solar corona. Oscillatory reconnection is characterised by the emission of magnetohydrodynamic waves away from the reconnection site. Numerous studies have found a connection between the properties of these emitted waves and the physical parameters of the background plasma, opening up the possibility of using oscillatory reconnection as an observational seismological tool for the solar corona. In this presentation, I will introduce the current state of oscillatory reconnection simulations and present ongoing work by the Manchester Solar Plasma Group that aims to link this mechanism to solar flare data.
Feb 28	Tue	Tobias Berger (Sheffield)	Number Theory seminar
13:00		R=T theorems for weight one modular forms
		Hicks Seminar Room J11
	Abstract: I will present recent joint work https://arxiv.org/abs/2203.09434 with Kris Klosin (CUNY) on the modularity of residually reducible ordinary 2-dimensional p-adic Galois representations with determinant a finite order odd character. When this finite order character is quadratic we prove modularity by classical CM weight one forms, otherwise by non-classical weight 1 specialisations of Hida families.
Mar 1	Wed	Evgenios Kakariadis (University of Newcastle)	Pure Maths Colloquium
14:00		Morita equivalence for operator systems
		Hicks Seminar Room J11
	Abstract: In ring theory, Morita equivalence preserves many properties of the objects, and generalizes the isomorphism equivalence between commutative rings. A strong Morita equivalence for selfadjoint operator algebras was introduced by Rieffel in the 60s, and works as a correspondence between their representations. In the past 30 years there has been an interest to develop a similar theory for nonselfadjoint operator algebras and operator spaces with much success. Taking motivation from recent work of Connes and van Suijlekom, we will present a Morita theory for operator systems. We will give equivalent characterizations of Morita equivalence via Morita contexts, bihomomoprhisms and stable isomorphism, while we will highlight properties that are preserved in this context. Time permitted we will provide applications to rigid systems, function systems and non-commutative graphs. This is joint work with George Eleftherakis and Ivan Todorov.
Mar 2	Thu	Ieke Moerdijk (Sheffield)	Topology Seminar
16:15		An elementary approach to bar-cobar duality for functors
		Hicks Seminar Room J11
	Abstract: I will explain a version of bar-cobar (or "Koszul") duality between covariant and contravariant functors on a category of trees, the proof of which is elementary and explicit. The (known) duality for linear operads is a special case, as is the (new) extension to linear infinity-operads. Reference: Hoffbeck-Moerdijk, Homology of infinity-operads, Arxiv
Mar 3	Fri	Ronish Mugatwala (Sheffield)	SP2RC/ESPOS seminar
13:00		Forecasting CME arrival in the heliosphere: The P-DBM application for statistical studies.
		Google meet link: https://meet.google.com/ciq-zovu-rzm
	Abstract: Abstract: One of the goals of Space Weather studies is to achieve a better understanding of impulsive phenomena, such as Coronal Mass Ejections (CMEs), in order to improve our ability to forecast them and reduce the risk to our technologically driven society. To do this, it is crucial to assess the application of theoretical models or even to create models that are entirely data-driven.The quality and availability of suitable data are of paramount importance. We have already merged public data about CMEs from both in-situ and remote instrumentation in order to build a database (DB) of CME properties. To evaluate the accuracy of such a DB and confirm the relationship between in-situ and remote observations, we have employed the drag-based model (DBM). DBM is an analytical model that assumes the aerodynamic drag caused by the surrounding solar wind to be the primary factor in the interplanetary propagation of CMEs. Here, we explore the parameter space for the drag parameter and solar wind speed using a Monte Carlo approach to analyse how well the DBM described the propagation of CMEs. With this method, we validate and/or correct the initial hypotheses about solar wind speed, and also yield additional information about CMEs. Using a data-driven approach, this procedure allows us to present a homogeneous, reliable, and robust dataset for the investigation of CME propagation.
Mar 8	Wed	Samuele Anni (Aix-Marseille Université)	Pure Maths Colloquium
14:00		Isomorphisms of modular Galois representations and graphs
		Hicks Seminar Room J11
	Abstract: In this talk, I will explain how to test efficiently and effectively whether two odd modular Galois representations of the absolute Galois group of the rational numbers are isomorphic. In particular, I will present new optimal bounds on the number of traces to be checked (joint work with Peter Bruin, University of Leiden). I will also briefly discuss graphs of isomorphisms associated to such objects, related results on Hecke algebras, and a database of modular representations.
Mar 8	Wed	Benjamin Berczi (Nottingham)	Cosmology, Relativity and Gravitation
15:00		Gravitational collapse of quantum fields
		Hicks LT9
	Abstract: The behaviour of quantum fields around black holes has been in the forefront of research for almost half a century, since the discovery of Hawking radiation in 1974. However, we still know remarkably little about the details of the evaporation of black holes beyond first order approximations. My talk will introduce our novel formalism using which a fully quantum mechanical field can be simulated to collapse into a black hole, and discuss how the quantum effects can be studied. It will be explained how we relate the semiclassical simulations to purely classical ones using a coherent state as the chosen quantum state. Initial results of the quantum effects around the formed black hole will be presented as well.
Mar 9	Thu	Julie Rasmusen (Warwick)	Topology Seminar
16:00		THR of Poincaré infinity-categories
		Hicks Seminar Room J11
	Abstract: In recent years work by Calmés-Dotto-Harpaz-Hebestreit-Land-Moi-Nardin-Nikolaus-Steimle have moved the theory of Hermitian K-theory into the framework of stable infinity-categories. I will introduce the basic ideas and notions of this new theory, but as it is often the case when working with K-theory in any form, this can be very hard to describe. I will therefore introduce a tool which might make our life a bit easier: Real Topological Hochschild Homology. I will explain the ingredients that goes into constructing in particular the geometric fixed points of this as a functor, generalising the formula for ring spectra with anti-involution of Dotto-Moi-Patchkoria-Reeh.
Mar 9	Thu	Ashley Willis (Sheffield)	Plasma Dynamics Group
16:00		Optimisation problems in transitional turbulence and MHD
		LT4 (Hicks Building)
	Abstract: A typical optimisation problem might involve the minimisation/maximisation of a cost/output by the variation of a few discrete parameters, e.g. sale price or a production rate. But what if we want to optimise a whole field, e.g. optimise a velocity field to maximise mixing in a given container? Now our 'parameter' u(x) is actually a huge parameter set to be optimised, measured by the number of finite difference points or spectral coefficients required to represent u(x). Until recently, methods to optimise such states were considered too computationally expensive. However, it has been recognised these problems can be formulated in an iterative Lagrangian framework, where each iteration 'only' costs a few simulations (rather than thousands of simulations, attempting to vary the parameters one by one). Using this framework, we look at some fundamental questions in fluid mechanics and MHD: - At the same flow rates in pipe, channel and Couette flows, either smooth laminar flow or turbulence can be observed. What is the minimal flow disturbance required to switch from laminar to turbulent flow (e.g. to enhance mixing)? - What is the minimal body force required to cause a switch from turbulence to laminar flow (e.g. to reduce turbulent drag)? - In MHD, what is the minimal flow required to generate a magnetic field (kinematic dynamo)? - How do we find configurations where the flow and magnetic field determine each other's structure (subcritical self-consistent dynamo)?
Mar 14	Tue	Haluk Sengun (Sheffield)	Number Theory seminar
13:00		K-theory and automorphic forms
		Hicks Seminar Room J11
	Abstract: My research in the recent years have been guided by the simple question: "Why not consider K-theory instead of ordinary cohomology in the study of arithmetic groups and automorphic forms?". Here I mean not only the topological K-theory or arithmetic manifolds but also the operator K-theory of the various C*-algebras associated to arithmetic groups; such as group C*-algebras, boundary crossed product algebras... In this talk, I will sketch basics around cohomology of arithmetic groups and automorphic forms, and then will give about some samples from my K-theoretic works, but I will mainly be raising questions some of which I hope will lead to conversations between number theorists and algebraic topologists in the department.
Mar 16	Thu	Andy To (Mullard Space Science Laboratory, University College London, UK)	SP2RC/ESPOS seminar
10:00		Coronal Plasma Composition Evolution and Solar Activity
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: Composition of plasma in the solar corona is a tracer of the flow of plasma and energy from the solar interior. A complete understanding of coronal abundances not only provides us another perspective to look at complex processes such as wave propagation, wave absorption, convection, reconnection, and reconfiguration of magnetic fields and coronal heating, but it also has significant implications for solar-like stars. The method to parameterise and study coronal elemental abundances, is to use the first ionisation potential (FIP) bias, defined as taking the ratio of an element’s coronal to photospheric abundance with respect to H. In this seminar, we introduce FIP bias as a proxy to understand processes in different solar structures, ranging from small brightenings to active regions, using a wide range of techniques such as extreme-ultraviolet and radio imaging, and spectroscopy to study to the evolution of these solar structures, and interpret the physical processes underneath.
Mar 17	Fri	Prof Huw Morgan (Aberystwyth University)	SP2RC/ESPOS seminar
13:00		Observable constraints on magnetic field extrapolations above the photosphere: mapping the propagation of solar atmospheric waves
		Google meet link: https://meet.google.com/ciq-zovu-rzm
	Abstract: Coronal magnetic fields are extrapolations of the observed photospheric field based on certain physical assumptions. One crucial parameter that is difficult to constrain observationally is , which dictates the twist of a field line in the corona. A few recent works e.g.1,2 are able to constrain  through tracing the projected position of coronal loops as observed in extreme ultraviolet (EUV) images, thus a magnetic model is constructed where the field lines are constrained by both the photospheric field and the field line distribution in the corona. These studies are limited to a small number of field lines in active regions, where the coronal loops are clearly seen in images, and can be traced (manually, or automatically). I present here a novel image processing method, applied to EUV image time series, that reveals coherent and continuous faint motions everywhere in the corona 3 . These are signatures of slow magnetic waves. A modified Lucas-Kanade algorithm results in a mapping of the wave velocity field across broad regions of the low corona. The waves must follow the underlying magnetic field, thus the velocity field lines are a proxy for the magnetic field line distribution, as seen in projection by the observer. I present further evidence, based on a comparison with the distribution of the photospheric network, and with a potential field magnetic model, that the velocity field is closely related to the magnetic field 4 . Thus, in the near future, we plan to use maps of the wave velocity field, combined with photospheric field measurements, to build magnetic field extrapolations where  is directly constrained by EUV observations across broad regions of the corona - including active regions, coronal holes, and the elusive quiet Sun. This approach will enable observationally-constrained magnetic models to be built routinely and efficiently, and promises a major breakthrough in probing the magnetic environment of the solar atmosphere.
Mar 23	Thu	Tudor Padurariu (Columbia)	The Sheffield Geometry and Physics Seminar
13:00		The stack of commuting matrices via BPS spaces
		Hicks Seminar Room J11
	Abstract: The variety of commuting matrices is an important space in algebraic geometry, and has been studied from various perspectives. The stack of commuting matrices M is the same as the stack of zero dimensional sheaves in the plane, and can be used to define various Hall algebras that act on cohomologies of the Hilbert scheme of points in the plane. In this talk, I will talk about cohomologies of the stack M. First, I will recall results of Davison and Davison-Meinhardt about the Borel-Moore homology of M. These results are proved via an analysis of the BPS sheaves of points in the three dimensional affine space. Next, I will discuss (partial) analogues of these results for the K-theory and the category of coherent sheaves on M. The central objects are a categorical replacement of the BPS sheaves. The talk is based on joint results with Yukinobu Toda.
Mar 23	Thu	Omar Kidwai (Birmingham)	The Sheffield Geometry and Physics Seminar
14:30		Refined BPS invariants from (refined) topological recursion
		Hicks Seminar Room J11
	Abstract: Recently, a relationship between BPS invariants of four-dimensional supersymmetric QFTs (equivalently, Donaldson-Thomas invariants of certain 3CY triangulated categories) and the Eynard-Orantin topological recursion (which computes invariants of "spectral curves'' originally appearing in the theory of matrix models), was observed for a class of fundamental examples. We review both formalisms and explain how to modify the topological recursion to obtain the "$\beta$-deformed'' or "refined" topological recursion when the initial data is sufficiently nice. For the simplest such examples, we show how the corresponding free energies can be expressed in terms of a new collection of refined BPS invariants which, unlike the unrefined case, do not seem to have appeared in the Donaldson-Thomas theory to date. Based on joint works with K. Osuga.
Mar 23	Thu	Catherine Blume (Colorado at Boulder)	Plasma Dynamics Group
16:00		Rossby Waves in the Sun
		meet.google.com/npm-yooq-nix
	Abstract: Recent observations of Rossby waves and other more exotic forms of inertial oscillations in the Sun’s convective zone have kindled the hope that such waves might be used as a seismic probe of the Sun’s interior. Their presence also raises questions about their potential role in the solar cycle. Here we present a suite of 3D numerical simulations in full spherical geometry that model the Sun’s convective zone and upper radiative interior. With these models, we demonstrate that Rossby waves are ubiquitous within the radiative interior as well as within the convective zone, potentially explaining the large horizontal velocities that have been previously seen in the radiative interior of numerical models. Their presence in the radiative zone implies that the Sun’s radiative interior is not quiescent, but instead may play a role in the dynamics of the tachocline. We also demonstrate the presence of gravity waves and thermal Rossby waves.
Mar 29	Wed	Polyxeni Spilioti (University of Goettingen)	Pure Maths Colloquium
14:00		On the spectrum of twisted Laplacians and the Teichmüller representation
		Hicks Seminar Room J11
	Abstract: In this talk, we will present some results concerning the spectrum of Laplacians with non unitary twists acting on sections of flat vector bundles over compact hyperbolic surfaces. These non self-adjoint Laplacians have discrete spectrum inside a parabola in the complex plane. For representations of the fundamental group of the base surface which are of Teichmüller type, we investigate the high energy limit and give a precise description of the bulk of the spectrum where Weyl’s law is satisfied in terms of critical exponents of the representation which are completely determined by the Manhattan curve associated to the Teichmüller deformation. This is joint work with Frédéric Naud.
Mar 29	Wed	Alessia Platania (Perimeter Institute)	Cosmology, Relativity and Gravitation
15:00		Sifting quantum black holes through the principle of least action
		Hicks LT9
	Abstract: We tackle the question of whether regular black holes or other alternatives to the Schwarzschild solution can arise from an action principle in quantum gravity. Focusing on an asymptotic expansion of such solutions and inspecting the corresponding field equations, we demonstrate that their realization within a principle of stationary action would require either fine-tuning, or strong infrared non-localities in the gravitational effective action. This points to an incompatibility between large-distance locality and many of the proposed alternatives to classical black holes.
Mar 30	Thu	Giuseppe Capuano (University of Catania, Italy)	SP2RC/ESPOS seminar
10:00		Solar corona diagnostics with Metis observations
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: The solar corona has been investigated in the last decades through observations coming from several spacecraft. The Metis coronagraph, aboard the ongoing Solar Orbiter mission, extends the UVCS/SOHO spectrocoronagraph observations of the scattered ultraviolet emission of the coronal plasma performed during solar activity cycle 23, by simultaneously imaging the coronal visible light polarized brightness (VL pB), in the spectral bandpass 580-640 nm, and the coronal ultraviolet H I Lyα emission, in the spectral window 121.6 ± 10 nm. We present here some specific observations, such as those taken on May 15, 2020, from which detailed information about the coronal outward velocity were inferred by applying the Doppler dimming technique. Other results on the coronal solar wind outflow velocity were obtained by considering the quadrature of Solar Orbiter and PSP with respect to the Sun, when the same parcel of plasma was observed remotely with Metis between 3.5 R☉ and 6.3 R☉ on January 17, 2021, on the East limb and in situ by PSP at about 22 R☉ on January 18, 2021. In this case, information on several coronal parameters were obtained with unprecedented details, thanks to the high quality of Metis and PSP data. Finally, other results concern the first CME observed with Metis on January 16-17, 2021, during low-cadence synoptic mode observations. In this case, also considering data coming from instruments onboard other spacecraft and on Solar Orbiter, a 3D reconstruction and physical information of this structure were obtained. Therefore, Metis, even when operates in synoptic mode and in synergistic coupling with other instruments, allows to get novel and detailed information on the structure of the solar corona with an accuracy never reached until now.
Mar 30	Thu	Neil Strickland (Sheffield)	Topology Seminar
16:00		Global rational representation theory (joint with Luca Pol)
		Hicks Seminar Room J11
	Abstract: Let U be the category of finite groups and conjugacy classes of surjective homomorphisms, or some reasonable subcategory of that. Let A be the category of contravariant functors from U to rational vector spaces (which is equivalent to a certain category of globally equivariant spectra with rational homotopy groups). The category A has some unusual properties: there is a good theory of duality but finitely generated projective objects are not strongly dualisable, all projective objects are injective but not vice-versa, and so on. This makes it difficult to analyse the Balmer spectrum of the associated derived category, but we will explain some progress towards that goal.
Mar 31	Fri	Ricardo Gafeira (Coimbra)	SP2RC/ESPOS seminar
13:00		Long-term variation of quiet sun Mg II h&k lines
		Google Meet
	Abstract: The solar atmosphere undergoes several changes during the solar cycle. Those changes can be identified by observing several solar features and their respective dynamics, which can be observed in many different wavelengths, and by analyzing the variations in the total solar irradiance. The latter is characterized by an increase in the total solar irradiance during the solar maximum and a decrease in the decay phase. In this talk, we will present the intensity variations of the Mg II h&k lines emission peak, observed by IRIS, under quiet sun conditions close to the disk center over the decaying phase of the solar cycle. The observed variations will then be interpreted and put in the context of the solar atmospheric physical conditions.
Apr 13	Thu	Adur Pastor Yabar (Stockholm University, Sweden)	SP2RC/ESPOS seminar
10:00		Quiet Sun radiative losses as inferred from spatially coupled inversions
		Zoom
	Abstract: The solar heating problem involves a coupled system (including the photosphere and chromosphere), thus requiring its study as a whole system. This requirement often leads to the combination of observations with different instrumental effects. One important missing piece in this context is the capability to observationally constrain the various physical mechanisms that heat the outer layers as predicted from numerical simulations. In this contribution we present the implementation of a newly-developed inversion algorithm that expands the capabilities of the NLTE inversion code STiC to better handle inversions combining multi-resolution observations, which can provide more constrained physical inferences. After we have checked its performance, we apply this inversion method to a quiet-Sun area co-observed with the SST (CRISP and CHROMIS) and IRIS spectrograph. After inferring the various physical properties of the atmosphere we compute the radiative losses from different sources and discuss their potential physical origin.
Apr 14	Fri	Joseph A Scalisi (SP2RC (UoS))	SP2RC/ESPOS seminar
13:00		Mathematical Modelling of Solar Plasma Jets
		Google Meet
Apr 20	Thu	Abraham Chian (Adelaide)	Plasma Dynamics Group
10:00		Lagrangian chaotic saddles & Lagrangian coherent structures in solar supergranular turbulence
		/ Google Meet
	Abstract: First, we report observational evidence of Lagrangian chaotic saddles in plasmas, given by the intersections of finite-time unstable and stable manifolds, using an ≈ 22 h sequence of spacecraft images of the horizontal velocity field of the quiet-Sun photosphere. A set of 29 persistent objective vortices with lifetimes varying from 28.5 to 298.3 min are detected by computing the Lagrangian averaged vorticity deviation. The unstable manifold of the Lagrangian chaotic saddles computed for ≈ 11 h exhibits twisted folding motions indicative of recurring vortices in a magnetic mixed-polarity region. We show that the persistent objective vortices are formed in the gap regions of Lagrangian chaotic saddles at supergranular junctions. Next, we discuss the spatiotemporal dynamics of vorticity and magnetic field in the region of a long-duration photospheric vortex at a supergranular junction. We show that in a 30-min interval during the vortex lifetime, the magnetic field is intensified at the centres of two merging magnetic flux tubes trapped inside the vortex boundary. Moreover, we show that the electric current density is intensified at the interface boundary layers of merging tubes, resulting from strong vortical downflows in a supergranular vertex. Evidence of Lagrangian chaos and vortex stretching in the photospheric plasma turbulence responsible for driving the intensification of magnetic fields is analysed. In particular, we report the first solar observation of the intensification of electromagnetic energy flux resulting from the merger of magnetic flux tubes.
Apr 20	Thu	Nitin Chidambaram (Edinburgh)	The Sheffield Geometry and Physics Seminar
14:30		Gaiotto vectors from topological recursion
		Hicks Seminar Room J11
	Abstract: The Alday-Gaiotto-Tachikawa (AGT) conjecture in physics predicts a relationship between 2d conformal field theories and certain 4d gauge theories. A precise mathematical version (proved by Maulik-Okounkov, Schiffmann-Vasserot and others) states that the equivariant cohomology of the moduli space of instantons (4d side) is a module of a certain W-algebra (2d side), and that the fundamental class of the moduli space is a Whittaker vector in the W-algebra module, known as the Gaiotto vector. I will show how one can realize this Gaiotto vector as the partition function of an Airy structure, and thereby relate it to the topological recursion formalism of Eynard and Orantin. This means that one can compute the Nekrasov instanton partition function (which is the norm squared of the Gaiotto vector) using topological recursion techniques. Time permitting, I will discuss some possible applications (all work-in-progress) of this relationship including extensions to Argyres-Douglas theories, relations to Hurwitz theory and matrix models, and connections to integrability. The talk is based on joint work with Vincent Bouchard, Gaetan Borot and Thomas Creutzig.
Apr 21	Fri	Elena Popova	SP2RC/ESPOS seminar
13:00		Superflares and space weather near exoplanets
		Learning Lab G34a (25) in Hicks Building / Google Meet
	Abstract: At present, in connection with the intensive development of instruments for observing stars and exoplanets, the problem of analyzing the possible habitability of exoplanets is very actual. One of the important factors of auspicious conditions for the emergence of life are favorable radiation conditions. In talk we present various aspects of the space weather near exoplanets and in particular the occurrence of strong flares on host stars, which can prevent the formation of biological structures.
Apr 26	Wed	Jonathan Betts (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Machine Learning & Cosmological Structure Formation in Modified Gravity
		Hicks LT9
	Abstract: In recent years progress in the field of high performance computing systems has increased the availability of cosmological N-body simulations. These datasets have been computed for Lambda-CDM and a variety of modified gravity cosmologies. One behaviour these data can interrogate is the formation of cosmological structures. Structure formation is largely solved in Lambda-CDM using Extended-Press-Schechter spherical collapse. Screened modified gravities introduce extra forces that may mean this formalism is no longer valid. Machine learning is known to be useful in elucidating empirical information about highly non-linear systems from large quantities of training data. We used the machine learning method of random forest classifiers to study the formation of structures in screened modified gravities, in particular f(R) and nDGP gravity. We examine the differences between models that have learned structure formation from each gravity, as well as a model that has learned from Lambda-CDM data. We also test the generalisability of the Lambda-CDM model on data from f(R) and nDGP gravities of varying strengths, and therefore the generalisability of Extended-Press-Schechter spherical collapse to these types of modified gravity.
Apr 26	Wed	Nick Kuhn (Virginia)	Topology Seminar
16:00		Chromatic Smith Fixed Point Theory
		Hicks Seminar Room J11
	Abstract: The study of the action of a finite p-group G on a finite G-CW complex X is one of the oldest topics in algebraic topology. In the late 1930's, P. A. Smith proved that if X is mod p acyclic, then so is X^G, its subspace of fixed points. A related theorem of Ed Floyd from the early 1950's says that the dimension of the mod p homology of X will bound the dimension of the mod p homology of X^G. The study of thick tensored categories in the category of G-spectra has led to the problem of identifying "chromatic" variants of these theorem, with mod p homology replaced by the Morava K-theories (at the prime p). An example of a new chromatic Floyd theorem is the following: if G is a cyclic p-group, then the dimension over K(n)* of K(n)*(X) will bound the dimension over K(n-1)* of K(n-1)*(X^G). These chromatic fixed point theorems open the door for new applications. For example, one can deduce that a C_2 action on the 5 dimensional Wu manifold will have fixed points that have the rational homology of a sphere. In a different direction, at the prime 2, we can show quick collapsing of the AHSS computing the Morava K-theory of some real Grassmanians: this is a non-equivariant result. An early result in this area was by Neil Strickland. My own contributions have included joint work with Chris Lloyd and also William Balderrama. In my talk, I'll try to give an overview of some of this.
Apr 27	Thu	Dieter Nickeler (Astronomical Institute of the Czech Academy of Sciences, Czech Republic)	SP2RC/ESPOS seminar
10:00		Fragmented currents induced by nonlinear 3D flows and their potential for coronal heating
		Zoom
	Abstract: Many magnetic structures in the solar atmosphere evolve rather slowly so that they can be assumed as (quasi-)static or (quasi-)steady and represented via magneto-hydrostatic (MHS) or magneto-hydrodynamic (MHD) equilibria, respectively. While exact 3D solutions would be desired, they are extremely difficult to find in steady MHD. We construct solutions with magnetic and flow vector fields that have three components depending on all three coordinates. We show that the non-canonical transformation method produces quasi-3D solutions of steady MHD by mapping 2D or 2.5D MHS equilibria to strongly related steady-MHD states, displaying highly complex currents. The existence of geometrically complex 3D currents within symmetric field-line structures provide the base for efficient dissipation of the magnetic energy in the solar corona by Ohmic heating. We also discuss the possibility of achieving force-free fields, and find that they only arise under severe restrictions of the field-line geometry and of the magnetic flux density distribution.
Apr 27	Thu	Nicola Gambino (Manchester)	Topology Seminar
16:00		The effective model structure
		Hicks Seminar Room J11
	Abstract: For a category E with finite limits and well-behaved countable coproducts, we construct a new Quillen model structure on the category of simplicial objects in E, which we call the effective model structure. The effective model structure generalises the Kan-Quillen model structure on simplicial sets; in particular, its fibrant objects can be viewed as infinity-groupoids (i.e. Kan complexes) in E. After introducing the main definitions and outlining the key steps of the proof of the existence of the effective model structure, I will describe some of its peculiar properties and what they mean in terms of its associated infinity-category. This is based on joint work with Simon Henry, Christian Sattler and Karol Szumiło (https://doi.org/10.1017/fms.2022.13).
May 2	Tue	Michael Yiasemides (Nottingham)	Number Theory seminar
13:00		Divisor Sums and Hankel Matrices
		Hicks Seminar Room J11
	Abstract: In this talk I will demonstrate a new approach to evaluating divisor sums, such as the variance of the divisor function over short intervals, and divisor correlations. The approach makes use of additive characters to translate the problem from a number theoretic one to a linear algebraic one involving Hankel matrices. I will briefly discuss extensions to other Diophantine equations, as well as indicate further connections between Hankel matrices and number theory.
May 3	Wed	Neil Strickland (University of Sheffield)	Pure Maths Colloquium
14:00		Ambidexterity
		Hicks Seminar Room J11
	Abstract: Ambidexterity refers to a situation where we have two functors $F\colon\mathcal{C}\to\mathcal{D}$ and $G\colon\mathcal{D}\to\mathcal{C}$ such that $F$ is both left adjoint and right adjoint to $G$. There are elementary examples involving complex representation theory of finite groups and groupoids, and deep examples involving chromatic cohomology of finite $\infty$-groupoids (or equivalently, $\pi$-finite spaces), as well as various other examples of intermediate depth. I will survey some of these ideas, with emphasis on applications in chromatic stable homotopy theory.
May 3	Wed	Debleena Thacker (Durham)	Probability seminar
15:00		Continuous-time digital search tree and a border aggregation model
	Abstract: We consider the continuous-time version of the random digital search tree, and construct a coupling with a border aggregation model as studied in Thacker and Volkov (2018), showing a relation between the height of the tree and the time required for aggregation. This relation carries over to the corresponding discrete-time models. As a consequence we find a very precise asymptotic result for the time to aggregation, using recent results by Drmota et al. (2020) for the digital search tree. This is joint work with Svante Janson.
May 4	Thu	Alan Thompson (Loughborough)	The Sheffield Geometry and Physics Seminar
13:00		Pseudolattices, degenerations, and fibrations of K3 surfaces
		Hicks Seminar Room J11
	Abstract: I will report on joint work in progress with Luca Giovenzana. I will describe some developments in the abstract theory of quasi del Pezzo pseudolattices, before showing how this theory arises naturally in the contexts of type II degenerations of K3 surfaces and elliptically fibred K3 surfaces. This can be thought of as a manifestation of mirror symmetry; I will discuss what it could tell us about mirror symmetry for K3 surfaces and the 2-dimensional Fano/LG correspondence.
May 4	Thu	Benoit Vicedo (York)	The Sheffield Geometry and Physics Seminar
14:30		2d Integrable Field Theories from 4d Chern-Simons
		Hicks Seminar Room J11
	Abstract: In recent years various unifying frameworks for understanding 2d integrable field theories have emerged. In this talk I will review the approach based on 4d Chern-Simons theory, due to Costello and Yamazaki, and describe recent progress towards extracting general 2d integrable fields theories from 4d Chern-Simons theory.
May 4	Thu	John Greenlees (Warwick)	Topology Seminar
16:00		Rational equivariant cohomology theories for compact Lie groups
		Hicks Seminar Room J11
	Abstract: The overall project is to build an algebraic model for rational G-equivariant cohomology theories for all compact Lie groups G. When G is small or abelian this has been done. In general, the model is expected to take the form of a category of sheaves of modules over a sheaf of rings over the space of closed subgroups of G. The talk will focus on structural features of the expected model for general G such as those above, and feature recent joint work with Balchin and Barthel.
May 4	Thu	Tiago Pereira (Oslo)	Plasma Dynamics Group
16:00		Fast 3D non-LTE spectral synthesis with neural networks
		Google Meet
	Abstract: Three-dimensional non-LTE calculations are required to forward-model the strongest spectral lines in the solar chromosphere. They are also the gold standard for detailed chemical analysis in stellar atmospheres. However, such calculations require copious amounts of computing time, on the order of millions of CPU hours, and are much more time-consuming than running the 3D simulations themselves. I will give an overview of the problem and present a new approach using neural networks to dramatically speed up 3D NLTE spectral synthesis. This approach, implemented in the open-source code SunnyNet, uses a database of previous calculations to learn the translation from LTE to non-LTE atomic populations. By feeding a new atmosphere, we can then use SunnyNet to predict its non-LTE populations and subsequently compute synthetic spectra for any viewing angle. We tested this approach with 3D simulations ran with the Bifrost code for the synthesis of Hα profiles, a line strongly affected by 3D NLTE effects. Our method leads to a speedup of about 10^5 times compared to traditional methods, when running on a single GPU. The quality of the predicted populations is best when using different timesteps of the same simulation for training and testing, and translates to typical differences of less than 4% in the Hα spatially-averaged intensity spectra. Synthetic images at the Hα line core reproduce chromospheric fibrils very well, strongly suggesting that SunnyNet is learning 3D radiative transfer, since fibrils are absent in 1D calculations. The results are less reliable when different types of simulations are used for the training and the testing. I will discuss the current limitations and caveats, and discuss possible applications of SunnyNet and future improvements.
May 10	Wed	Louis Hamaide (King's College London)	Cosmology, Relativity and Gravitation
15:30		Black Hole Information Recovery from Gravitational Waves
		Hicks LT10
	Abstract: We study the classical and quantum black hole information in gravitational waves from a black hole's history. We review the necessary concepts regarding quantum information in many-body systems to motivate information retrieval and content in gravitational waves. We then show the first step in an optimal information retrieval strategy is to search for information in gravitational waves, compared to searching for correlations in Hawking radiation. We argue a large portion of the information of the initial collapsing state may be in the gravitational waves. Using the Zerilli equation for particles falling radially into Schwarzschild black holes, we then describe a method to retrieve full classical information about infalling sources, including masses, infall times and angles.
May 11	Thu	Marco Fazzi (Uppsala)	The Sheffield Geometry and Physics Seminar
09:30		Holography, matrix factorizations, and K-stability
		Hicks Seminar Room J11
	Abstract: Placing D3-branes at conical Calabi-Yau threefold singularities produces many AdS5/CFT4 duals. Recent progress in differential geometry has produced a technique, called K-stability, to recognize which singularities admit conical Calabi-Yau metrics. On the other hand, the algebraic technique of noncommutative crepant resolutions (NCCRs) has been developed to associate a quiver to a singularity. In favorable situations (such as the hypersurface case), producing an NCCR is equivalent to finding suitable matrix factorizations of the hypersurface. I will put together K-stability and NCCRs to produce new AdS5/CFT4 pairs, beyond the well-known toric setup.
May 11	Thu	Alexander Kasprzyk (Nottingham)	The Sheffield Geometry and Physics Seminar
11:00		Machine learning the dimension of Fano varieties
		Hicks Seminar Room J11
	Abstract: In this talk I shall discuss recent work with Tom Coates and Sara Veneziale in which we successfully recover the dimension of a Fano variety X directly from the regularized quantum period of X via machine learning. We apply machine learning to the question: does the quantum period of a Fano variety X know the dimension of X? Note that there is as yet no theoretical understanding of this. We show that machine learning techniques can recover the dimension with > 80% accuracy, demonstrating that machine learning can pick out structure from complex mathematical data in situations where we lack a theoretical understanding. It also gives positive evidence for the assertion (which is proven for smooth Fanos in low dimensions, but unknown in general) that the quantum period of a Fano variety determines that variety.
May 11	Thu	Luciana Bonatto (MPIM Bonn)	Topology Seminar
16:00		Generalised Configuration Spaces
		Hicks Seminar Room J11
	Abstract: Configuration spaces are, on the one hand, powerful invariants and, on the other, spaces with many computable properties. They have also been shown to provide concrete models for homotopy-theoretical constructions such as the free E_n-algebras and the infinite loop spaces associated to stable homotopy theory. These spaces have been generalised in (at least) two directions: the first allows for controlled interactions between the particles of the configuration (for instance allowing some collisions), and the other looks at configurations not of points, but of more general submanifolds. In this talk we will discuss these generalisations, and how they lead to powerful constructions such as factorization homology. We will also discuss in which cases these spaces still carry desirable computational properties seen in the classical configuration spaces, such as homological stability.
May 12	Fri	Simone Chierichini (Sheffield)	SP2RC/ESPOS seminar
13:00		Modelling CME arrival with Machine Learning
		Google meet link: https://meet.google.com/ciq-zovu-rzm
	Abstract: Space weather phenomena have long captured the attention of the scientific community and, along with the recent technological development, the awareness that such phenomena can (and do) interfere with human activity on Earth has grown considerably. Coronal Mass Ejections (CMEs), together with solar flares and solar energetic particle events, are one of the main drivers of space weather. Therefore developing tools to provide information on their arrival at Earth’s nearby space became increasingly important. Liu et al. (2018) developed the CAT-PUMA tool, to obtain a fast and more accurate prediction of CME transit times. CAT-PUMA employs Support Vector Machine technique, based on a regression algorithm. In this work, we investigate further the potential of a Machine Learning approach to study the arrival of CMEs on Earth and explore its limitations. Furthermore, we present a new application of CAT-PUMA, employing Supervised Learning to obtain vital information about the arrival of CMEs at Earth. We trained three models, Support Vector Machine, Random Forest and Extreme Gradient Boosting (XGBoost), to obtain predictions on the Geo-effectiveness and arrival time of CMEs at Earth and compared their performance. The results show that supervised learning models can achieve a very promising performance, but are nevertheless dependent on evaluation metrics. Relying on optimistic evaluation criteria leads to models capable of producing transit time predictions with an error of 7 hours; while considering more conservative criteria, errors do not fall below 10 hours. Finally, we apply an interpretive approach to the proposed models in an attempt to extract as much information as possible from this study about the capabilities of Machine Learning in predicting the arrival of CMEs on Earth and possibly complement the predictions to help enhance the real-time estimation of the threat posed by CMEs.
May 17	Wed	Min Lee (University of Bristol)	Pure Maths Colloquium
14:00		Frobenius numbers and further - equidistribution of rational points on the expanding horospheres
		Hicks Seminar Room J11
	Abstract: Fix a finite set R of positive integers bigger than one with no common factors. The Frobenius number for R is the largest number that cannot be written as a linear combination of the integers in R with non-negative integral coefficients. In general, Frobenius numbers fluctuate. To study such things, we search for structures. Here, the given set of positive integers R can be a point in the lattices studied in the dynamics and number theory crossover. We study the behaviour of these rational points on expanding closed horospheres in the space of lattices. The equidistribution of these rational points is proved by Einsiedler, Mozes, Shah and Shapira (2016). Their proof uses techniques from homogeneous dynamics and relies particularly on measure-classification theorems, due to Ratner. We pursue an alternative strategy based on Fourier analysis, Weil's bound for Kloosterman sums, recently proved bounds (by M. Erdélyi and Á. Tóth) for matrix Kloosterman sums, Roger's formula, and the spectral theory of automorphic functions. This is a joint work with D. El-Baz, B. Huang, J. Marklof and A. Strömbergsson.
May 17	Wed	Nuno M Santos (Aveiro and Lisbon)	Cosmology, Relativity and Gravitation
15:00		Synchronized bosonic hair: equilibrium solutions
		Blackboard Collaborate
	Abstract: Bosonic fields can spin down rotating black holes (BHs) via superradiance. If massive, they may remain trapped in the vicinity of a BH and endow it with hair co-rotating in synchrony with the event horizon. An illustrative example of this mechanism is the family of BHs with synchronized hair, that can co-exist with Kerr BHs and emerge dynamically from them at some scales. In this talk, I will first explore the features of BHs with vanishingly little (scalar and vector) hair, drawing their similarity to the atomic orbitals of the electron in a hydrogen atom. Then, I will discuss how hairy such BHs can become from the growth and saturation of superradiant instabilities. Finally, I will address the thermodynamic stability of BHs with synchronized hair in the canonical ensemble.
May 18	Thu	Hidetaka Kuniyoshi (Tokyo)	Plasma Dynamics Group
10:00		Magnetic Tornado Properties: A Substantial Contribution to the Solar Coronal Heating via Efficient Energy Transfer
		https://meet.google.com/upk-kxip-exo
	Abstract: Solar coronal heating models are beginning to be extrapolated to modeling the coronae of exoplanet host stars to investigate their habitabilities. Thus, understanding the details of the solar coronal heating mechanism is significant for planetary science also. Recently, magnetic tornadoes, characterized as coherent, rotating magnetic field structures extending from the photosphere to the corona, have drawn growing interest as a possible means of efficient energy transfer into the corona. Despite its acknowledged importance, the underlying physics of magnetic tornadoes remains still elusive. In this talk, I’m going to talk about our recent work Kuniyoshi et al. (2023) and the plan for our future work. In our study, we conduct a three-dimensional radiative magnetohydrodynamic simulation that encompasses the upper convective layer and extends into the corona, with a view to investigating how magnetic tornadoes are generated and efficiently transfer energy into the corona. We find that a single event of magnetic flux concentration merger on the photosphere gives rise to the formation of a single magnetic tornado. The Poynting flux transferred into the corona is found to be four times greater in the presence of the magnetic tornado, as compared to its absence. This increase is attributed to a reduction in energy loss in the chromosphere, resulting from the weakened magnetic energy cascade. Based on an evaluation of the fraction of the merging events, our results suggest that magnetic tornadoes contribute approximately 50% of the Poynting flux into the corona in regions where the coronal magnetic field strength is 10 G.
May 18	Thu	James Cranch (Sheffield)	Topology Seminar
16:00		What is a polynomial?
		Hicks Seminar Room J11
	Abstract: In this mostly expository talk. I'll explain some (different) recipes for defining concepts of "polynomial map" and "polynomial functor" in various settings. I'll explain what some of this has to do with algebraic K-theory, and mention several things I don't know.
May 18	Thu	Calum Webb (Sheffield Methods Institute)	RSS Seminar
17:00		Creating change when everyone thinks they’re an outlier: Convincing local authority audiences to care about abstract statistical models using interactive data visualisation
		Hicks Room K14
	Abstract: You’ve just finished a large research project, published papers in academic journals containing interesting statistical models about an important social problem, and now you’re presenting the findings to local policymakers and directors of services to try and create a positive impact. The only problem is everyone you speak to tells you that they’re glad they’re not the average that your models are referring to; in fact, they’re the exception, they say. This short presentation will talk about how I have tried to use interactive data visualisation tools developed with the Shiny package in R to try to encourage local authorities to engage with the implications from the statistical models in my research. The presentation will showcase the Child Welfare Inequalities Project App (www.cwip-app.co.uk); discuss my experiences as an amateur learning the tools used to build it as well as its reception; and explain where I see the potential benefits of such applications for quantitative research as a way to allow audiences to engage with questions about counterfactuals, interactions, and random effects in a bespoke way.
May 22	Mon	Lisa Hampson (Novartis)	Statistics Seminar
14:00		Bayesian methods to improve quantitative decision making in drug development and the role of expert elicitation
		Hicks LT 6 / meet.google.com/ony-uzab-qyz
	Abstract: There are several steps to confirming the safety and efficacy of a new medicine. A sequence of trials, each with its own objectives, is usually required. Bayesian measures of risk, such as assurance or more generally probability of success (PoS), can be useful for informing decisions about whether a medicine should transition from one stage of development to the next. In this presentation, we describe a Bayesian approach for calculating PoS before pivotal (confirmatory) clinical trials are run which synthesizes internal clinical data, industry-wide success rates, and expert opinion or external data if needed. In particular, where there are differences between early phase and confirmatory trials due to a change in outcome for example, we propose eliciting expert judgements to relate existing data to the unknown quantities of interest. We discuss two approaches for establishing a multivariate distribution for several related efficacy treatment effects within the Sheffield Elicitation Framework (SHELF) and describe how they were applied to evaluate the PoS of the registrational program of an asthma drug. We conclude by reflecting on some of the opportunities and practical challenges encountered when using elicitation to support the evaluation of PoS.
May 22	Mon	Sam Dolan (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Metric perturbations of Kerr spacetime in Lorenz gauge: a new method
		Hicks LT10
	Abstract: Black hole perturbation theory is a key tool for modelling compact-binary inspirals, and their associated gravitational wave signatures, particularly in the case where the ratio of the masses of the two bodies is far from unity. For many applications, it is advantageous to work in the Lorenz gauge, so that the metric perturbation is governed by a tensor wave equation of a manifestly hyperbolic form (i.e. hyperbolic PDEs). In this talk, I will describe a new separation-of-variables method for obtaining the metric perturbations of Kerr spacetime, that is, for a rotating black hole. In this scheme, the metric perturbation is constructed in the frequency domain from scalar variables that satisfy decoupled *ordinary* differential equations. For the case of a particle moving on a circular equatorial orbit of Kerr spacetime, I will compare the results of the new method with existing numerical results from a 2+1D time-domain code developed in Southampton. This talk is based on work with Barry Wardell, Chris Kavanagh and Leanne Durkan.
May 22	Mon	Jelena Grbic (Southampton)	Topology Seminar
16:00		Higher Whitehead maps in polyhedral products
		Hicks Seminar Room J11
	Abstract: We define generalised higher Whitehead maps in polyhedral products. By investigating the interplay between the homotopy-theoretic properties of polyhedral products and the combinatorial properties of simplicial complexes, we describe new families of relations among these maps, while recovering and generalising known identities among Whitehead products. This is joint work with George Simmons and Matthew Staniforth.
May 24	Wed	Robert Fraser (Wichita State University)	Pure Maths Colloquium
14:00		Two strategies for Fourier decay of measures in Diophantine approximation
		Google Meet
	Abstract: In 1980 and 1981, Kaufman constructed measures with polynomial Fourier decay on the set of badly-approximable numbers and the set of well-approximable numbers. The strategy for the badly-approximable numbers uses the continued fraction expansion together with a change-of variables, and the strategy for the well-approximable numbers uses the cancellation of an exponential sum. We will discuss the application of both of these strategies to the set of numbers approximable to exact order introduced by Bugeaud. This talk is based on joint work with Reuben Wheeler.
May 25	Thu	Liana Heuberger (Bath)	The Sheffield Geometry and Physics Seminar
13:00		Laurent inversion and applications
		Hicks Seminar Room J11
	Abstract: I will discuss how to use Laurent inversion, a technique coming from mirror symmetry which constructs toric embeddings, to study the local structure of the K-moduli space of a K-polystable toric Fano variety. More specifically, starting from a given toric Fano 3-fold X of anticanonical volume 28 and Picard rank 4, and combining a local study of its singularities with the global deformation provided by Laurent inversion, we are able to conclude that the K-moduli space is rational around X. This is joint work with Andrea Petracci.
May 25	Thu	Soheyla Feyzbakhsh (Imperial College)	The Sheffield Geometry and Physics Seminar
14:30		Explicit formulae for rank zero DT invariants
		Hicks Seminar Room J11
	Abstract: Fix a Calabi-Yau 3-fold X of Picard rank one satisfying the Bogomolov-Gieseker conjecture of Bayer-Macrì-Toda, such as the quintic 3-fold. I will first describe explicit formulae relating rank zero Donaldson-Thomas (DT) invariants to Pandharipande-Thomas (PT) invariants using wall-crossing with respect to weak Bridgeland stability conditions on X. As applications, I will find sharp Castelnuovo-type bounds for PT invariants, and explain how combining these explicit formulae with S-duality in physics enlarges the known table of Gopakumar-Vafa (GV) invariants. The second part is joint work with string theorists Sergei Alexandrov, Albrecht Klemm, Boris Pioline and Thorsten Schimannek.
May 25	Thu	Carsten van de Bruck (Sheffield)	Cosmology, Relativity and Gravitation
15:00		How to link primordial perturbations to CMB anisotropies - I
		Hicks LT10
	Abstract: I give a brief overview on how to link processes in the very early universe (think inflation) to CMB anisotropies. In my first presentation I will briefly talk about the issue of gauges in cosmological perturbation theory, how the CMB anisotropies are described (i.e. what are the famous C_l’s?) and discuss the Sachs-Wolfe effect. In the second presentation I will discuss how primordial perturbations are produced in single field inflation and how the primordial power spectrum is calculated. I will also summarise the changes which happen if inflation is driven by more than one field.
May 26	Fri	Carsten van de Bruck (Sheffield)	Cosmology, Relativity and Gravitation
15:00		How to link primordial perturbations to CMB anisotropies - II
		Hicks LT10
	Abstract: I give a brief overview on how to link processes in the very early universe (think inflation) to CMB anisotropies. In my first presentation I will briefly talk about the issue of gauges in cosmological perturbation theory, how the CMB anisotropies are described (i.e. what are the famous C_l’s?) and discuss the Sachs-Wolfe effect. In the second presentation I will discuss how primordial perturbations are produced in single field inflation and how the primordial power spectrum is calculated. I will also summarise the changes which happen if inflation is driven by more than one field.
May 31	Wed	Prof. Abraham Chian (University of Adelaide, Australia & National Institute for Space Research (INPE), Brazil)	Plasma Dynamics Group
14:00		Complex dynamics of stochastic chaotic flows in fluids and plasmas
		Hicks LT10
	Abstract: Turbulence in fluids and plasmas exhibits complex dynamics and structures ubiquitous in nature, e.g., cardiovascular haemodynamics, shallow-water ocean dynamics, galactic centre plasma dynamics, and solar-terrestrial plasma dynamics. Transient coherent structures known as chaotic saddles are the building blocks of turbulence. Hyperbolic and elliptic Lagrangian coherent structures provide accurate identification of transport barriers in turbulence. We report the first observational evidence of Lagrangian chaotic saddles in plasmas, given by the intersections of finite-time unstable and stable manifolds, using a sequence of spacecraft images of the horizontal velocity field of the quiet-Sun photosphere. We show that the persistent objective vortices are formed in the gap regions of Lagrangian chaotic saddles at supergranular junctions. Next, we discuss the spatiotemporal dynamics of vorticity and magnetic field in the region of a long duration photospheric vortex at a supergranular junction. We show that in an interval during the vortex lifetime, the magnetic field, the electric current density, and the electromagnetic energy flux are intensified in a region of two merging magnetic flux tubes trapped inside the vortex boundary, which is a signature of chaotic stretching-twisting-folding acting in turbulence.
Jun 1	Thu	Oliver Rice (Durham)	Plasma Dynamics Group
16:00		Eruptivity of Magnetic Flux Ropes in the Solar Corona
		https://meet.google.com/xyw-iuaq-ysb
	Abstract: In a recent study, we investigate which scalar quantity or quantities can best predict the loss of equilibrium and subsequent eruption of magnetic flux ropes in the solar corona - one of the main causes of significant space weather events. In our numerical models the flux rope is produced self-consistently by flux cancellation combined with gradual footpoint shearing of a coronal arcade that is open at the outer boundary, representing the magnetic field in decaying active regions on the Sun. We use both full MHD (magnetohydrodynamics) in cartesian coordinates and the magnetofrictional approach in cartesian and polar coordinates, and by running thousands of 2.5D simulations find that there are several scalar criteria that could theoretically be used as a proxy for eruptivity, discussing the established 'eruptivity index' alongside newly-defined diagnostic ratios that appear to be very good predictors of eruptive behaviour.
Jun 7	Wed	Gaspard Poulot (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Scalar field dark matter and dark energy: A hybrid model for the dark sector
		TBA
	Abstract: Diverse cosmological and astrophysical observations strongly hint at the presence of dark matter and dark energy in the Universe. One of the main goals of Cosmology is to explain the nature of these two components. It may well be that both dark matter and dark energy have a common origin. In this talk, I describe a model in which the dark sector arises due to an interplay between two interacting scalar fields. Employing a hybrid inflation potential, I show that the model can be described as a system of a pressureless fluid coupled to a light scalar field. I then discuss this setup's cosmological consequences and the observational signatures in the cosmic microwave background radiation and the large-scale structures.
Jun 9	Fri	Andreas Wagner	SP2RC/ESPOS seminar
13:00		Analyzing Early-Stage CME Flux Ropes from data-driven modelling of AR12473: FR Identification and Relaxation Analysis
		Google meet link: https://meet.google.com/ciq-zovu-rzm
	Abstract: The initial evolution phase of a CME flux rope (FR) yields crucial information about their space weather impacts. Thus, we study this early phase by employing data-driven simulations, which have shown to be well-suited to model the low coronal FR evolution. The extraction of relevant field lines of the forming and (potentially) erupting structure is not trivial, however. Therefore, we develop a semi-automatic extraction and tracking scheme for CME flux ropes for simulation data. The extraction procedure makes use of the twist parameter in combination with mathematical morphology algorithms. We subsequently apply it to time-dependent data-driven magnetofrictional modelling (TMFM) results of active region AR12473. In particular, we investigate the evolution of FR properties and stability in relation to the data-driving nature of the simulations.
Jun 22	Thu	Jörn Warnecke (Max Planck Institute for Solar System Research, Germany)	SP2RC/ESPOS seminar
10:00		Numerical evidence for a small-scale dynamo approaching solar magnetic Prandtl numbers
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: Magnetic fields on small scales are ubiquitous in the Universe. Although they can often be observed in detail, their generation mechanisms are not fully understood. One possibility is the so-called small-scale dynamo (SSD). Prevailing numerical evidence, however, appears to indicate that an SSD is unlikely to exist at very low magnetic Prandtl numbers (PrM) such as those that are present in the Sun and other cool stars. Here we have performed high-resolution simulations of isothermal forced turbulence using the lowest PrM values achieved so far. Contrary to earlier findings, the SSD not only turns out to be possible for PrM down to 0.0031 but also becomes increasingly easier to excite for PrM below about 0.05. We relate this behaviour to the known hydrodynamic phenomenon referred to as the bottleneck effect. Extrapolating our results to solar values of PrM indicates that an SSD would be possible under such conditions.
Jun 22	Thu	Istvan Ballai (Sheffield)	Plasma Dynamics Group
16:00		Parametric instability/decay driven by ionisation-recombination waves in the solar atmosphere
		LT11 (Hicks Building)
	Abstract: Non-linear and non-propagating ionisation-recombination (i-r) waves can appear in partially ionised solar atmospheric plasmas leading to a time-dependent density of charged particles. This wave can parametrically couple to other MHD wave (here we discuss only Alfvén waves) leading to a various fate of the MHD waves, depending on the strength of collisional coupling between particles. Here I am going to present some mathematical progress on the quantitative description of i-r waves, as well as the method of determining the width of parametric instability.
Jun 23	Fri	Slava Bourgeois (SP2RC (UoS))	SP2RC/ESPOS seminar
13:00		Solar feature contouring with Mathematical Morphology/Machine Learning techniques
		Google meet link: https://meet.google.com/ciq-zovu-rzm
	Abstract: We use an image processing method called Mathematical Morphology (MM) to pinpoint different types of solar features (e.g., sunspots, faculae, coronal jets, flux rope structures, etc.) suspected to be responsible for strong solar activity and geoeffective eruptions. We validate the MM method by comparing the sunspot areas defined by the MM contours with other existing and reliable sunspot area catalogues (e.g., the hand-drawn Debrecen Heliophysical Observatory (DHO) catalogue and the cross-calibrated Mandal et al. (2020) catalogue). We can then apply the MM method to the identification of more complex features. For instance, we find the so-called delta-sunspots by overlaying Solar Dynamics Observatory (SDO)/Helioseismic and Magnetic Imager (HMI) magnetograms and intensity images. However, the MM method also has limitations as it is affected by the strong effect of adverse weather conditions in solar images, and the fine-tuning of its parameters can only be done manually. In this way, Machine Learning (ML) techniques could prove to be very useful when combined with the MM method in what is called a Morphological Neural Network (e.g., Mondal et al. for de-raining images). The Neural Network complements the MM method by making it automatic and giving good performance metrics, while significantly reducing its number of parameters and providing some insight into the black-box model.
Jun 29	Thu	Samuel Skirvin (Katholieke Leuven)	Plasma Dynamics Group
16:00		Alfvénic motions arising from inclined acoustic wave drivers in 3D MHD simulations of coronal loops
		LT9 (Hicks Building)
	Abstract: Alfvénic motions are ubiquitous in the solar corona and their observed properties are closely linked to those of photospheric p-modes. However, it is still unclear how a predominantly acoustic wave driver is related to these transverse oscillations in the magnetically dominated solar corona. I will talk about our 3D MHD numerical simulation which models a straight, expanding coronal loop in a gravitationally stratified solar atmosphere. We implement a driver locally at one foot-point corresponding to an acoustic-gravity wave which is inclined with respect to the vertical axis of the magnetic structure and is equivalent to a vertical driver incident on an inclined loop. We show that transverse motions are produced in the magnetic loop and study the resulting modes in the theoretical framework of a magnetic cylinder model. I will also discuss some physical properties of the Alfvénic perturbations including their speeds, velocity amplitudes and periods. Finally I will present a brief discussion on the energetics of the resulting wave modes and avenues of future work to extend the current study from other interesting features developing in the simulation.
Jun 30	Fri	Marc Schiffer (Perimeter Institute)	Cosmology, Relativity and Gravitation
15:00		Using matter to explore asymptotic safety with functional and lattice methods
		Hicks LT10
	Abstract: Asymptotically safe quantum gravity might provide a unified description of the fundamental dynamics of quantum gravity and matter. The realization of asymptotic safety, i.e., of scale symmetry at high energies, constraints the possible interactions and dynamics of a system. In this talk, I will first introduce the scenario of asymptotic safety for gravity with matter, and explain how it can be explored using functional methods. I will then emphasize, how the constraints on the microscopic dynamics of gravity and matter arising from quantum scale symmetry can turn into constraints on fundamental parameters of our universe, when combined with phenomenological observations. Finally, I will highlight how non-dynamical scalar fields can be used to investigate whether lattice methods, in particular Euclidean dynamical triangulations, are a suitable tool to investigate asymptotic safety.
Jul 13	Thu	Fisal Asiri (Sheffield)	Plasma Dynamics Group
16:00		Slow body MHD waves in inhomogeneous magnetic flux tubes
		meet.google.com/tng-dcsb-sso
	Abstract: Intense magnetic waveguides such as pores, sunspots, coronal loops, fibrils, etc. are ideal environments for the propagation of guided magnetohydrodynamic (MHD) waves. In general the theoretical description of wave propagation within these structures considers plasma parameters (density, pressure, temperature, magnetic field, etc.) to be constant. For an improved modelling of waves one needs to understand the modifications in wave properties in realistic waveguides such as sunspots, where the plasma shows a transversal density profile inhomogeneity. The present study investigates the propagation characteristics and the spatial structure of slow body MHD eigenmodes in a magnetic flux tube with circular cross section with inhomogeneous equilibrium density distribution under solar photospheric conditions in the short wavelength limit. The equilibrium density profile inhomogeneity is represented by a local circular density enhancement or depletion whose strength, size and position can change. The task was addressed numerically with use of the Fourier-Chebyshev Spectral method (FCS). The radial and azimuthal variation of eigenfunctions is obtained by solving a Helmholtz-type partial differential equation with Dirichlet boundary conditions. The inhomogeneous transverse equilibrium density profile results in modified eigenvalues and eigenvectors. It was found that modification in the equilibrium density distribution leads to a decrease in the eigenvalues and the spatial structure of modes ceases to be global harmonic oscillations, as the modes migrate towards regions of lower density. Comparing the homogeneous case and the cases corresponding to depleted density enhancement, the dimensionless phase speed undergoes a significant drop in its value (at least 40%). In contrast to the density enhancement, the slow body modes investigated here preserve their morphology in terms of their spatial structure. We carry out a parametric analysis to determine the importance of the physical parameters on the dimensionless phase speed of slow body modes corresponding to the spatial structure of the total pressure perturbation under photospheric conditions. The presented model can be considered a first attempt to study theoretically the properties of slow magnetoacoustic body waves in magnetic flux tubes modelling pores and the umbra of sunspots with local density inhomogeneities labeled as umbral dots.
Jul 18	Tue	Timothy Trudgian (UNSW Canberra at ADFA)	Number Theory seminar
13:00		The Riemann Hypothesis: severely undervalued at a meagre one million dollars.
		Hicks Seminar Room J11
	Abstract: Even though a solution to the Riemann Hypothesis lands the lucky solver with a million dollars (and USD at that!) this still seems very cheap, given the difficulty of the problem. I shall outline some history of the problem and the very limited partial progress towards it.
Sep 26	Tue	TBA	Number Theory seminar
13:00
		Hicks Seminar Room J11 / Google Meet
Sep 28	Thu	Muralikrishnan Gopalakrishnan Meena (Oak Ridge National Laboratory)	Plasma Dynamics Group
16:00		Vortical network connectors for turbulence modification
		https://meet.google.com/piy-dqag-wym
	Abstract: The interaction-driven evolution of complex systems in both natural and engineering contexts offers a unique opportunity to leverage graph theory for understanding their behavior as well as for modeling and modifying their evolution. This seminar aims to introduce a network (graph) community-based framework to perform flow-modification of turbulent vortical flows. The present framework captures vortical interactions on a network, where the vortical elements are viewed as the nodes and the vortical interactions are regarded as edges weighted by induced velocity from the Biot-Savart law. The network-based community detection algorithm is used to identify a group of closely interacting vortical elements, called communities. The inter- and intra-community interactions are used to identify the communities that have the strongest and weakest interactions amongst them, referred to as the connector and peripheral communities, respectively. For isotropic turbulence, the connector and peripheral communities correspondingly resemble shear-layer and vortex-core like structures. Results show that perturbing the connector structures enhances local turbulent mixing beyond what is achieved by perturbing the strongest vortex tube and shear-layer regions.
Oct 2	Mon	Andrew Krause (Durham)	Mathematical Biology Seminar
13:00
		Hicks Seminar Room J11
Oct 3	Tue	TBA	Number Theory seminar
13:00
		Hicks Seminar Room J11 / Google Meet
Oct 3	Tue	TBA	Algebra / Algebraic Geometry seminar
14:30
		Hicks Seminar Room J11
Oct 4	Wed	Tyler Kelly (Birmingham)	Pure Maths Colloquium
14:00		Moduli of genus-zero higher spin curves and their invariants
		Hicks Seminar Room J11
	Abstract: In mathematics, we like classifying objects. A moduli space is a space where each point represents a(n isomorphism class of a) space satisfying certain criteria, giving a geometric answer to a classification problem. Often the geometry of such spaces are interesting in our own right and their corresponding enumerative information has rich structure. We will study the case of genus-zero n-pointed curves and a generalisation where they are further equipped with an r-spin structure. Enumerative invariants built from their characteristic classes have rich structure due to generalisations of predictions of Witten confirmed by Kontsevich. We will explain approaches to understanding these invariants on a very concrete level through combinatorial structures like recursion and tropical geometry.
Oct 4	Wed	Ilay Hoshen (Tel Aviv)	Probability seminar
15:00		Simonovits's theorem in random graphs
		Hicks Seminar Room J11
	Abstract: Let $H$ be a graph with chromatic number $\chi(H) = r+1$. Simonovits's theorem states that the unique largest $H$-free subgraph of $K_n$ is its largest $r$-partite subgraph if and only if $H$ is edge-critical. We show that the same holds with $K_n$ replaced by $G_{n,p}$ whenever $H$ is also strictly 2-balanced and \begin{align*} p \geq C n^{-1/m_2(H)} \log(n)^{1/(e(H)-1)}, \end{align*} for some constant $C > 0$. This is best possible up to the choice of the constant $C$. This (partially) resolves a conjecture of DeMarco and Kahn, who proved the result in the case where $H$ is a complete graph. Moreover, we prove the result with explicit constant $C = C(H)$ that we believe to be optimal. Joint work with Wojciech Samotij.
Oct 4	Wed	Mariaveronica De Angelis (Sheffield)	Cosmology, Relativity and Gravitation
16:00		Multi-field inflation with kinetic couplings: theoretical predictions and observational constraints
		Hicks Seminar Room J11
	Abstract: In the two-field inflationary paradigm, it is commonly assumed that the kinetic coupling between the fields, resulting from a non-minimal coupling in the Jordan frame and leading to a curved field manifold in the Einstein frame, depends solely on one field. Our study delves into the situation where the kinetic coupling can instead vary with both fields. The aim of this study is to investigate adiabatic and isocurvature perturbations within these extended theories. Our analysis reveals that, while the evolution equation for the curvature perturbation remains unchanged when allowing coupling dependence on both fields, the effective mass of the entropy perturbation undergoes modifications. We analytically study the correlations between the models’ free parameters and present also a novel numerical method tailored to the study of general multi-field models. Our algorithm captures the dynamics of the fields throughout the entire inflationary phase, providing accurate predictions for observables such as the spectrum of primordial scalar perturbations, primordial gravitational waves, isocurvature modes, and the transfer of entropy to scalar modes after the horizon crossing. By sampling over the initial conditions of the fields and the free parameters of the model, we enable a Monte Carlo analysis, testing the theoretical predictions against observational data.
Oct 5	Thu	Tyler Kelly (Birmingham)
11:00		Open FJRW theory and mirror symmetry
		Hicks Seminar Room J11
	Abstract: FJRW theory is an enumerative theory built from characteristic classes corresponding to the moduli space of W-spin curves, a natural generalisation of higher spin curves. They can be interpreted as the enumerative geometry of gauged Landau-Ginzburg models. We construct an enumerative theory for an open version of FJRW invariants, over the moduli space of W-spin discs, rather than compact Riemann surfaces. We then will build the mirror to the original Landau-Ginzburg model as a generating function of open FJRW invariants, and prove a mirror symmetry statement. This is joint work with Mark Gross and Ran Tessler.
Oct 9	Mon	Raj Hossein (Sheffield)	Mathematical Biology Seminar
13:00
		Hicks Seminar Room J11
Oct 10	Tue	Ju-Feng Wu (University of Warwick)	Number Theory seminar
13:00		On $p$-adic adjoint $L$-functions for Bianchi cuspforms: the $p$-split case
		Hicks Seminar Room J11 / Google Meet
	Abstract: In the late '90's, Coleman and Mazur showed that finite-slope eigenforms can be patched into a rigid analytic curve, the so-called eigencurve. The geometry of the eigencurve encodes interesting arithmetic information. For example, the Bellaïche—Kim method showed that there is a strong relationship between the ramification locus of the (cuspidal) eigencurve over the weight space and the adjoint $L$-value. In this talk, based on joint work with Pak-Hin Lee, I will discuss a generalisation of the Bellaïche—Kim method to the Bianchi setting. If time permits, I will discuss an interesting question derived from these $p$-adic adjoint $L$-functions.
Oct 10	Tue	TBA	Algebra / Algebraic Geometry seminar
14:30
		Hicks Seminar Room J11
Oct 11	Wed	Markus Szymik (Sheffield)	Pure Maths Colloquium
14:00
		Hicks Seminar Room J11
Oct 11	Wed	Marco de Cesare (Naples)	Cosmology, Relativity and Gravitation
15:00		Interacting dark sector from the trace-free Einstein equations: cosmological perturbations with no instability
		Hicks Seminar Room J11
	Abstract: In trace-free Einstein gravity, the energy-momentum tensor of matter is not necessarily conserved and so the theory offers a natural framework for interacting dark energy models where dark energy has a constant equation of state w=-1. From the point of view of quantum gravity phenomenology, it has been argued that such violations of energy-momentum conservation might originate from discreteness at the Planck scale. We show that within this framework it is possible to build models where cosmological perturbations are free from instabilities, which are known to affect a large class of interacting dark energy models. We will also comment on the possibility that the models here considered may help alleviate the Hubble tension.
Oct 12	Thu	Daniel Graves (Leeds)	Topology Seminar
16:00		Homology of generalized rook-Brauer algebras
		Hicks Seminar Room J11
	Abstract: I will expand on the slogans I gave in last week's gong show. I'll give definitions of some generalizations of rook-Brauer algebras (and their subalgebras) by introducing equivariance and braiding. I'll discuss how we can identify the homology of some of these algebras with the group homology of braid groups and certain semi-direct product groups. I'll also discuss how we can deduce homological stability results and discuss some ideas for future work.
Oct 13	Fri	Piyali Chatterjee (IIA)	SP2RC/ESPOS seminar
13:00		Why do spicules spin in the images taken at the solar limb
		Google meet link: https://meet.google.com/ciq-zovu-rzm
	Abstract: Bunches of swaying spicules in the solar chromosphere exhibit a variety of complex dynamics that are clearly observed in the images of coronal hole regions. By calculating the line-of-sight integrated emission from three-dimensional radiative magnetohydrodynamic simulations, we obtain multiple episodes of rotation amongst clusters of spicules also reported in the sequence of high cadence observations on the solar limb. This perception of rotation, according to our findings, is associated with hot swirling plasma columns that we label as coronal swirling conduits (CoSCo). Some tall CoSCos seen in our simulations can potentially form by feeding on spicules and channeling this energy to the upper reaches of the solar atmosphere, even while the corresponding spicules fall back sun-ward.
Oct 13	Fri	Maria Giovanna Dainotti (National Astronomical Observatory of Japan)	Cosmology, Relativity and Gravitation
15:00		On the Hubble constant tension
		Hicks Seminar Room J11
	Abstract: The difference from 4$\sigma$ to 6$\sigma$ in the Hubble constant ($H_0$) between the values observed with the local probes (Cepheids and Supernovae Ia, SNe Ia) and the probes at high-z (Cosmic Microwave Background obtained by the Planck data) still challenges the astrophysics and cosmology community. Here, we investigate this tension obtained by using the SNe Ia gathered in the Pantheon sample and the Baryon Acoustic Oscillations, assuming $H_0=73.5 $ and $H_0=70 $ as the local value, and dividing the Pantheon sample in 3, 4, and 10 bins ordered in redshift.} For each bin, we run a Monte Carlo Markov-Chain (MCMC) analysis obtaining the value of $H_0$. Subsequently, the values of $H_0$ are fitted with the model $g(z)=\tilde{H_0}/(1+z)^\alpha$, where $\tilde{H_0}$ is $H_0(z=0)$ and $\alpha$ is the evolutionary parameter. Our results show that a decreasing trend with $\alpha\sim10^{-2}$ is still visible in this sample.} The $\alpha$ coefficient is compatible with zero between 1.1$\sigma$ and 2.2$\sigma$. This trend, if not due to statistical fluctuations, could be explained through a hidden astrophysical bias, such as the effect of stretch evolution, or it requires new theoretical models such as the $f(R)$ theories of gravity. Assuming a specific $f(R)$ model in the Jordan frame, we find that the results of our analysis remain unchanged. We conclude that this specific model is not appropriate for explaining the effect of the decreasing $H_0$. Furthermore, our analysis gives suggestions on how a cosmological model can be tested taking into account a parametrized evolution of the Hubble constant. A new analysis with SNe Ia, BAO, quasars and GRBs has been performed with new likelihood showing a less pronounced tension with the SNe Ia.
Oct 16	Mon	TBA	The Sheffield Geometry and Physics Seminar
10:00
		Hicks Seminar Room J11
Oct 16	Mon	TBA	The Sheffield Geometry and Physics Seminar
11:30
		Hicks Seminar Room J11
Oct 16	Mon	Alex Best (Journal Club) (Sheffield)	Mathematical Biology Seminar
13:00
		Hicks Seminar Room J11
Oct 17	Tue	TBA	Number Theory seminar
13:00
		Hicks Seminar Room J11 / Google Meet
Oct 17	Tue	TBA	Algebra / Algebraic Geometry seminar
14:30
		Hicks Seminar Room J11
Oct 18	Wed	Lassina Dembele (King's College London)	Black History Month Colloquium
14:00		How mentorship could help fight underrepresentation in STEM.
		LT-5
	Abstract: There is no denial that certain visible minorities are severely underrepresented in STEM. I hear people often say that the best way to fight underrepresentation is to have more role models from those minority groups. That is true, perhaps. However, I believe that there needs to be an intermediate solution until we reach that point when we have enough role models to have an impact. Based on my own personal experience, I want to explain how an innovative approach to mentorship can help fight underrepresentation.
Oct 18	Wed	Ruchika (INFN Rome)	Cosmology, Relativity and Gravitation
15:00		Reconciling JWST and HST with Planck
		Hicks Seminar Room J11
	Abstract: The recent observations from the James Webb Space Telescope have led to a surprising discovery of a significant density of massive galaxies with masses of $M \ge 10^{10.5} M_{\odot}$ at redshifts of approximately $z\sim 10$. This corresponds to a stellar mass density of roughly $\rho_*\sim 10^6 M_{\odot} Mpc^{-3}$. Despite making conservative assumptions regarding galaxy formation, this finding may not be compatible with the standard $\Lambda$CDM cosmology that is favored by observations of CMB Anisotropies from the Planck satellite. Parallely, SH0ES 2022 results confirmed more than 5 sigma deviation in determining the value of the Hubble Constant from the local distance ladder (using HST) and inverse distance ladder (utilizing Planck). Assuming both SH0ES and the Planck team are not making any errors, I will try to convince them that we need to look for new physics or new theoretical models to alleviate the discrepancy/cosmological crisis. We propose the G-Transition hypothesis, a negative cosmological constant model at low redshifts or Interacting Dark Energy/Early Dark Energy to come to the rescue. But before saying anything concrete, we need to see the similar effects in all cosmological probes.
Oct 19	Thu	Neil Strickland (Sheffield)	Topology Seminar
16:00		Double subdivision of relative categories
		Hicks Seminar Room J11
	Abstract: By a relative category we mean a category $\mathcal{C}$ equipped with a class $\text{we}$ of weak equivalences. Given such a thing, one can construct a simplicial set $N\mathcal{C}$, called the relative nerve. (In the case where $\text{we}$ is just the class of identity morphisms, this is just the usual nerve of $\mathcal{C}$.) Under mild conditions on $\mathcal{C}$, one can show that $N\mathcal{C}$ is a quasicategory (as defined by Joyal and studied by Lurie), and that the homotopy category of $N\mathcal{C}$ is the category of fractions $\mathcal{C}[\text{we}^{-1}]$. Lennart Meier gave a proof of this, but it depended on quoting a large body of theory related to model categories in the sense of Quillen. I will explain a different approach which instead uses more concrete combinatorial constructions with various specific finite posets.
Oct 23	Mon	Jack Jennings (Sheffield)	Mathematical Biology Seminar
13:00
		Hicks Seminar Room J11
Oct 24	Tue	Neil Strickland (Sheffield)	Astronomical Topology Working Group
09:00		Introduction to Chromatic Homotopy
		Hicks Seminar Room J11
	Abstract: This will be an introduction to chromatic homotopy theory, aiming to give the background required to understand the statement of the Telescope Conjecture.
Oct 24	Tue	Havard Damm-Jensen	Number Theory seminar
13:00		Diagonal Restrictions of Hilbert Eisenstein series
		Hicks Seminar Room J11 / Google Meet
	Abstract: Darmon and Vonk's theory of rigid meromorphic cocycles, or "RM theory", can be thought of as a $p$-adic counterpart to the classical CM theory. In particular, values of certain cocycles conjecturally behave similarly to values of the modular $j$-function at CM points. Recently, Darmon, Pozzi and Vonk proved special cases of these conjectures using $p$-adic deformations of Hilbert Eisenstein series. I will describe some ongoing work extending these results, and how to make their constructions effectively computable.
Oct 24	Tue	TBA	Algebra / Algebraic Geometry seminar
14:30
Oct 25	Wed	Reem Yassawi (Queen Mary University of London)	Pure Maths Colloquium
14:00		Automatic sequences in dynamics and number theory
		Hicks Seminar Room J11
	Abstract: An infinite sequence $a = (a_n)_{n\geq 0}$ is $q$-automatic if an is a finite-state function of the base-$q$ expansion of $n$. This means that there exists a deterministic finite automaton that takes the base-q expansion of $n$ as input and produces the symbol an as output for each $n \in \mathbb{N}$. Automatic sequences appear in diverse fields of mathematics, such as algebra, logic, number theory, and topological dynamics. They have the advantage of lend- ing themselves to computation, so that in each area there arise specific problems concerning automatic sequences, and much of the time, constructive solutions. I will give a background of their characterisations in algebra and dynamics, via Furstenberg’s, Cobham’s and Christol’s theorems. I will then talk about joint work with Eric Rowland and Manon Stipulanti, concerning automatic sequences in number theory, and also about joint work with Johannes Kellendonk, concerning automatic sequences in topological dynamics, ending with a topological invariant which seems to defy computation.
Oct 25	Wed	Syed Naqvi (Jagellonian U, Krakow)	Cosmology, Relativity and Gravitation
15:00		Chaos and Einstein-Rosen gravitational waves
		Blackboard Collaborate
	Abstract: In this study, we examine the Einstein-Rosen solution to investigate cylindrical standing gravitational waves. Similar to how standing mechanical waves reveal captivating features such as Chladni patterns and non-linear Faraday waves, these standing gravitational waves also provide valuable insights into non-linear aspects of general relativity. Our investigation reveals the existence of chaotic geodesics within the Einstein-Rosen spacetime, highlighting their sensitivity to initial conditions. This sensitivity is confirmed through the observation of an underlying fractal structure. We elucidate the source of this chaotic behaviour by examining the homoclinic and heteroclinic network. Furthermore, we attribute the intricate dynamics of test particles in this spacetime to the complex interplay between stable and unstable manifolds around hyperbolic points.
Oct 26	Thu	Merlin Mendonza (National Central University (Taiwan))	Plasma Dynamics Group
09:00		Association Between Magnetic Pressure Difference and the Movement of Solar Pores
		https://meet.google.com/cgd-xjdq-qxx / Google Meet
	Abstract: Solar pores are closely related to the concentration, dissipation, and transportation of solar magnetic flux. Their observable characteristics can provide constraints on models and simulations of magnetic flux emergence and formation. The specific property investigated in this study is their horizontal movement. The aim is to investigate whether the movement is correlated with any observable quantities. Our statistical analysis of 61 compact pores identified from the Spaceweather HMI Active Region Patches (SHARP) from 2011 to 2018 indicates that the direction of movement is often either parallel or antiparallel to the direction of maximum magnetic pressure difference at the opposite sides of the edges of the pores. The correlation coefficients for both the parallel and antiparallel cases are higher than 0.74. Despite the high correlation, our analysis using the transfer entropy indicates no significant causal relationship between the direction of motion and the direction of maximum magnetic pressure difference.
Oct 26	Thu	Marco Schlichting (Warwick)	Topology Seminar
16:00		On the relation between Hermitian K-theory and Milnor-Witt K-theory
		Hicks Seminar Room J11
	Abstract: Hermitian K-theory of a commutative ring R is the algebraic K-theory of finitely generated projective R-modules equipped with a non-degenerate symmetric/symplectic/quadratic form. The algebra generated in degree (1,1) modulo the Steinberg relation in degree (2,2) is called Milnor-Witt K-theory and plays an important role in A1-homotopy theory. Multiplicativity of Hermitian K-theory defines a graded ring homomorphism from Milnor-Witt K-theory to Hermitian K-theory. We prove a homology stability result for symplectic groups and use this to construct a map from Hermitian K-theory of a local ring to Milnor-Witt K-theory in degrees 2,3 mod 4. Finally, we compute the composition of the maps from Milnor-Witt to Hermitian and back to Milnor-Witt K-theory as multiplication with a particular integral form.
Oct 27	Fri	Simone Chierichini (UoS)	SP2RC/ESPOS seminar
13:00		A Bayesian approach to the drag-based modelling of ICMEs
		Google meet link: https://meet.google.com/ciq-zovu-rzm
	Abstract: Coronal Mass Ejections (CMEs) are huge clouds of magnetised plasma expelled from the solar corona that can travel towards the Earth and cause significant space weather effects.The Drag-Based Model (DBM) describes the propagation of CMEs in an ambient solar wind as analogous to an aerodynamic drag.The drag-based approximation is popular because it is a simple analytical model that depends only on two parameters, the drag parameter $\gamma$ and the solar wind speed $w$. DBM thus allows us to obtain reliable estimates of CME transit time at low computational cost. Previous works proposed a probabilistic version of DBM, the Probabilistic Drag Based Model (P-DBM), which enables the evaluation of the uncertainties associated with the predictions. In this work, we infer the "a-posteriori" probability distribution functions (PDFs) of the $\gamma$ and $w$ parameters of the DBM by exploiting a well-established Bayesian inference technique: the Monte Carlo Markov Chains (MCMC) method. By utilizing this Bayesian method through two different approaches, an ensemble and an individual approach, we obtain specific DBM parameter PDFs for two ensembles of CMEs: those travelling with fast and slow solar wind, respectively. Subsequently, we assess the operational applicability of the model by forecasting the arrival time of CMEs. While the ensemble approach displays notable limitations, the individual approach yields promising results, demonstrating competitive performances compared to the current state-of-the-art, with a mean absolute error (MAE) of 9.86 ± 4.07 hours achieved in the best-case scenario.
Oct 30	Mon	TBA	The Sheffield Geometry and Physics Seminar
10:00
		Hicks Seminar Room J11
Oct 30	Mon	TBA	The Sheffield Geometry and Physics Seminar
11:30
		Hicks Seminar Room J11
Oct 30	Mon	TBC	Mathematical Biology Seminar
13:00
		Hicks Seminar Room J11
Oct 31	Tue	Robert Kurinczuk (Sheffield)	Number Theory seminar
13:00		Blocks for classical p-adic groups
		Hicks Seminar Room J11
Oct 31	Tue	TBA	Algebra / Algebraic Geometry seminar
14:30
		Hicks Seminar Room J11
Nov 1	Wed	Eli Hawkins (University of York)	Pure Maths Colloquium
14:00		Quantization of Multiply Connected Manifolds
		Hicks Seminar Room J11
	Abstract: Given a compact Kähler manifold satisfying an integrality condition, the Berezin-Toeplitz geometric quantization construction produces matrix algebras; these fit together into a fundamental example of strict deformation quantization. The integrality condition can be circumvented by passing to the universal covering space, if the lift of the symplectic form is exact; in this case, the symplectic form determines a 2-cocycle of the fundamental group. The key to analyzing this construction is to use Hilbert $C^*$-modules, which generalize Hilbert spaces. The resulting algebras are more interesting than matrix algebras and are partially determined by index theorems. The simplest example is the noncommutative torus, and this gives higher-genus noncommutative Riemann surfaces as well.
Nov 2	Thu	Pablo Santamarina Guerrero (Instituto de Astrofísica de Andalucía, Spain)	SP2RC/ESPOS seminar
10:00		Magnetic structure analysis by applying persistent homology to Hinode and SDO magnetograms
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: The ability to encode and simplify all information about the shape and distribution of data has turned Topological Data Analysis (TDA) into one of the most relevant fields in state-of-the-art data analysis. Among all the tools of TDA, persistent homology has proven to be one of the most relevant techniques, and has been applied in numerous fields of study, such as biomedicine, chemistry, atomic physics, or image classification. In this work, we study what persistent homology can offer in the analysis of solar magnetograms, with the purpose of providing a new tool that will serve as foundation for further studies of magnetic structures on the solar surface. We propose an approach based on the use of persistence diagrams belonging to various filtrations in order to be able to capture the whole magnetic scene involving a mixture of positive and negative polarities. We have applied the analysis to quiet sun and active regions observations, taken with both Hinode/SOT and SDO/HMI, respectively. Persistent diagrams have proven to be able to encode the spatial structure complexity of the magnetic flux of active regions by identifying the isolated and connected (interacting) structures. Holes or pores are also displayed in persistent diagrams, allowing as well for the identification of interacting structures of opposite polarities in the form of ring-like structures. The overall temporal evolution of active regions, as well as small scale events in quiet sun such as magnetic flux cancellation and emergence are also displayed in persistent diagrams and can be studied by observing the evolution of the diagrams and tracking the relevant features.
Nov 2	Thu	Alex Corner (Sheffield Hallam)	Topology Seminar
16:30		Weak Vertical Composition
		Hicks Seminar Room J11
	Abstract: A usual test for a suitable semi-strict notion of n-category is that in its degenerate cases, it produces particular lower-dimensional monoidal structures as predicted by Baez and Dolan's Stabilisation Hypothesis. These structures are of interest in topology in that they produce algebraic homotopy n-types which are not equivalent to a fully strict notion of n-category. We are concerned with doubly-degenerate tricategories, which should produce a structure equivalent to a braided monoidal category. Gordon, Power, and Street show that in the case of Gray-categories, where interchange of 2-cells is weak but all other composition is strict, this is certainly the case. Joyal and Kock show further that the weakness, like a bump under a carpet, can be pushed solely into the horizontal units for 2-cells, and that this notion also matches braided monoidal categories in the doubly-degenerate case. In this talk I will introduce a notion of tricategory in which only the vertical composition of 2-cells is weak. These will be identified with categories strictly enriched in the category of bicategories and strict 2-functors with cartesian monoidal product, which, although constituting an unusual mix of weakness and strictness allows a very straightforward algebraic characterisation of weak vertical tricategories using the theory of 2-monads and 2-distributive laws. Thus far only object-level correspondences have been considered, but we show that with special consideration given to icon-like higher cells, we can form a 2-categorical totality of these degenerate structures, along with their weak maps and transformations, allowing us to give a full comparison with the 2-category of braided monoidal categories.
Nov 6	Mon	Tyler Cassidy (Leeds)	Mathematical Biology Seminar
13:00
		Hicks Seminar Room J11
Nov 7	Tue	Neil Strickland (Sheffield)	Astronomical Topology Working Group
09:00		The Telescope Conjecture as Galois theory of ring spectra
		Hicks Seminar Room J11
	Abstract: Let $X$ be a finite $p$-torsion spectrum of type $n$, which means that the Morava $K$-theory $K(n)_{*}(X)$ is nontrivial, but $K(m)_*(X)=0$ for $m\lt n$. By work of Devinatz, Hopkins and smith, there is a map $v\:\Sigma^dX\to X$ for some $d\gt 0$ such that $K(n)_{*}(v)$ is an isomorphism, and this is nearly natural in a certain sense. We can thus form the colimit $v^{-1}X$ of the sequence $X\to\Sigma^{-d}X\to\Sigma^{-2d}X\to\dotsb$. The Telescope Conjecture predicts that this should be the same as the Bousfield localisation $L_{K(n)}(X)$. There is a certain spectrum $E$ called Morava $E$-theory, with a natural action of a group $G$ called the Morava stabiliser group, with the property that $L_{K(n)}(X)$ is the spectrum $(E\wedge X)^{hG}$ of (homotopy) fixed points of the action (by an argument that is not too hard). There is a sense in which $E\wedge X$ is a Galois extension of $L_{K(n)}(X)$ with Galois group $G$, and various other Galois extensions with smaller Galois groups play an important role in the disproof of TC. I will attempt to explain some of these ideas.
Nov 7	Tue	Jeff Manning (Imperial College London)	Number Theory seminar
13:00		The Wiles-Lenstra-Diamond numerical criterion over imaginary quadratic fields
		Hicks Seminar Room J11
	Abstract: Wiles' modularity lifting theorem was the central argument in his proof of modularity of (semistable) elliptic curves over Q, and hence of Fermat's Last Theorem. His proof relied on two key components: his "patching" argument (developed in collaboration with Taylor) and his numerical isomorphism criterion. In the time since Wiles' proof, the patching argument has been generalized extensively to prove a wide variety of modularity lifting results. In particular Calegari and Geraghty have found a way to generalize it to prove potential modularity of elliptic curves over imaginary quadratic fields (contingent on some standard conjectures). The numerical criterion on the other hand has proved far more difficult to generalize, although in situations where it can be used it can prove stronger results than what can be proven purely via patching. In this talk I will present joint work with Srikanth Iyengar and Chandrashekhar Khare which proves a generalization of the numerical criterion to the context considered by Calegari and Geraghty (and contingent on the same conjectures). This allows us to prove integral "R=T" theorems at non-minimal levels over imaginary quadratic fields, which are inaccessible by Calegari and Geraghty's method. The results provide new evidence in favor of a torsion analog of the classical Langlands correspondence.
Nov 7	Tue	TBA	Algebra / Algebraic Geometry seminar
14:30
		Hicks Seminar Room J11
Nov 8	Wed	Daniel Graves (University of Leeds)	Pure Maths Colloquium
14:00		Homology of diagram algebras
		Hicks Seminar Room J11
	Abstract: Diagram algebras, such as the Brauer algebras and Temperley-Lieb algebras, have been studied for many years. They appear in wide-ranging places such as statistical mechanics, knot theory and representation theory. However, the study of the homology of these algebras is a very young field indeed, having emerged over the course of last decade. In this talk I will give an introduction to these diagram algebras, their homology and their connection to group homology and homological stability. Time permitting, I will discuss some recent generalizations of these algebras.
Nov 9	Thu	Wei Xing (Sheffield)	Statistics Seminar
14:00		Reliable AI for Engineering
		Hicks Seminar Room J11
	Abstract: Artificial intelligence (AI) has seismically shifted the landscape across multiple domains including scientific computing, manufacturing, and engineering. However, the importance of Reliable AI extends beyond what general AI can offer, particularly in scenarios where the stakes are high. Reliable AI, as the name suggests, emphasizes reliability, robustness, and trustworthiness, crucial for real-world applications where uncertainties and high-stakes decisions are the norms. In this talk, I will share our development of reliable AI techniques using Bayesian models and how these methods can be implemented to improve problems in integrated circuit design and some other broader applications in engineering such as digital twins.
Nov 9	Thu	Cosima Breu (St Andrews)	Plasma Dynamics Group
16:00		Vortices as energy channels into the solar corona
		https://meet.google.com/res-iojh-ths
	Abstract: From water spiralling into a sink drain to mesmerising giant storms on Jupiter, vortex motions are present throughout the universe on scales from the very small to the very large. Vortex flows have been found in the photosphere, chromosphere, and low corona in observations and simulations. It has been suggested that vortices play an important role in channeling energy and plasma into the corona. We investigate the importance of vortices for coronal heating using high-resolution simulations of coronal loops driven self-consistently by magnetoconvection. We performed 3D resistive MHD simulations with the MURaM code. Studying an isolated coronal loop in a Cartesian geometry allows us to resolve the structure of the loop interior. We find that the energy injected into the loop is generated by internal coherent motions within strong magnetic elements. A significant part of the resulting Poynting flux is channeled through the chromosphere in vortex tubes forming a magnetic connection between the photosphere and corona. Vortices have a complex relationship with the coronal emission, and I will discuss how these structures could potentially be observed in the corona.
Nov 13	Mon	TBA	The Sheffield Geometry and Physics Seminar
10:00
		Hicks Seminar Room J11
Nov 13	Mon	TBA	The Sheffield Geometry and Physics Seminar
11:30
		Hicks Seminar Room J11
Nov 13	Mon	Alexandria Volkening (Purdue/Cambridge)	Mathematical Biology Seminar
13:00
		Hicks Seminar Room J11
Nov 14	Tue	Dan Graves (Leeds)	Astronomical Topology Working Group
09:00		Background from stable homotopy theory
		Hicks Seminar Room J11
Nov 14	Tue	TBA	Number Theory seminar
13:00
		Hicks Seminar Room J11 / Google Meet
Nov 14	Tue	TBA	Algebra / Algebraic Geometry seminar
14:30
		Hicks Seminar Room J11
Nov 15	Wed	Emre Özülker (Istanbul Tech U.)	Cosmology, Relativity and Gravitation
15:00		Dark energy phenomenology, negative dark energy density, and the sign-switching $\Lambda$
		Hicks Seminar Room J11
	Abstract: A dark energy density that attained negative values in the past is phenomenologically motivated by the presence of this feature in parametric and nonparametric reconstructions of the cosmological functions based on the observational data, and also by the success of cosmological models that feature such a dark energy density in addressing the observational tensions. I show how a negative dark energy density can alleviate the tensions by focusing on the first peak in the cosmic microwave background power spectrum, and what happens to the equation of state parameter of such a (potentially effective) dark energy source when local energy-momentum conservation holds. I also argue a negative energy density is not theoretically problematic but even abundant in theoretical physics when treated as an effective source. In the second half, I focus on a specific dark energy model that features a negative density in the past, namely, the sign-switching cosmological constant model. I briefly describe how and why the model was introduced, describe its phenomena, show the latest constraints on its parameters, and discuss its extensions and underlying mechanisms.
Nov 15	Wed	Lukas Lüchtrath (Weierstrass Institude)	Probability seminar
16:00
		Hicks Seminar Room J11
Nov 16	Thu	Ieke Moerdijk (Sheffield)	Topology Reading Group
13:00		(Co)homology of categories and functor (co)homology
		Hicks Seminar Room J11
Nov 16	Thu	Callum Reader (Sheffield)	Topology Seminar
16:00		Optimal Transport from Enriched Categories
		Hicks Seminar Room J11
	Abstract: Imagine we have a metric space whose points we think of as warehouses, and whose distances give the cost of moving a unit of stock. Now imagine we have two probability distributions that tell us how much stock is in each warehouse. A classical problem from optimal transport theory asks: how we might rearrange one distribution into another with minimal cost? The 'minimal cost' in this scenario defines a metric on the space of all probability measures, this metric is called earth-mover's distance. Now instead of a metric space imagine we have a category enriched over the extended non-negative reals. As Lawvere points out, these enriched categories can be thought of as generalised metric spaces. We show that from this perspective, probability measures might be thought of as functors and the natural transformation object that exists between them is actually equal to the earth-mover's distance. What's more, we show that, when we take consider sub-probability measures - that is, measures with total mass less than one - the natural transformation object improves on the earth-mover's distance and can be intuited as the 'minimal cost of meeting demand'.
Nov 17	Fri	Yannik Schuler (Sheffield)
11:00
		Hicks Seminar Room J11
Nov 17	Fri	Andrew Fisher, Constantinos Papachristoforou (Sheffield)
16:00
		Hicks Seminar Room J11
Nov 20	Mon	Jonathan Potts (Sheffield)	Mathematical Biology Seminar
13:00
		Hicks Seminar Room J11
Nov 20	Mon	Richard Wilkinson (Nottingham)	Statistics Seminar
15:00		Adjoint-aided inference for latent force models
		Hicks Seminar Room J11
	Abstract: Linear systems occur throughout engineering and the sciences, most notably as differential equations. In many cases the forcing function for the system is unknown, and interest lies in using noisy observations of the system to infer the forcing, as well as other unknown parameters. In this talk I will show how adjoints of linear systems can be used to efficiently infer forcing functions modelled as Gaussian processes. Adjoints have recently come to prominence in machine learning, but mainly as an approach to compute derivatives of cost functions for differential equation models. Here, we use adjoints in a different way that allows us to analytically compute the least-squares estimator, or the full Bayesian posterior distribution of the unknown forcing. Instead of relying on solves of the original (forward model), we can recast the problem as n adjoint problems, where n is the number of data points. All that is required is the ability to solve adjoint systems numerically: it does not rely upon additional tractability of the linear system such as the ability to compute Green’s functions. We'll demonstrate this approach by inferring the pollution source in an advection-diffusion-reaction equation.
Nov 21	Tue	Dan Graves (Leeds)	Astronomical Topology Working Group
09:00		Topological Hochschild homology
		Hicks Seminar Room J11
	Abstract: I'll talk about THH for ring spectra, Tate spectra, the Frobenius and topological cyclic homology with a view towards understanding Proposition 1.1 in the Burklund, Hahn, Levy and Schlank preprint.
Nov 21	Tue	Ieke Moerdijk (Sheffield)	Topology Reading Group
12:00		(Co)homology of categories and functor (co)homology
		Hicks Seminar Room J11
Nov 21	Tue	Robert Rockwood (Kings)	Number Theory seminar
13:00
		Hicks Seminar Room J11 / Google Meet
Nov 21	Tue	TBA	Algebra / Algebraic Geometry seminar
14:30
		Hicks Seminar Room J11
Nov 22	Wed	Paul Johnson (Sheffield)	Pure Maths Colloquium
14:00		From Orbifold Hilbert schemes to Sec(x)
		Hicks Seminar Room J11
	Abstract: The Hilbert Scheme of points of n points in the plane is a smooth algebraic variety with a rich topology connected to partitions and representation theory. If G acts on a C^2, it also acts on the Hilbert scheme of points. The question of when certain G fixed point sets are nonempty winds up having a connection to zig-zag permutations, which are counted by the Taylor series coefficients of Tan(x) and Sec(x).
Nov 22	Wed	Jan Swart (Czech Academy of Sciences)	Probability seminar
15:00
		Hicks Seminar Room J11
Nov 22	Wed	Markus Fröb (Leipzig)	Cosmology, Relativity and Gravitation
15:00		Invariant observables in quantum gravity and graviton loop corrections to the Hubble rate and the Newtonian potential
		Blackboard Collaborate
	Abstract: I present work done in the last years on the construction of dynamical coordinate systems for highly symmetric backgrounds, such as Minkowski, de Sitter, and FLRW cosmologies, and which are needed in the relational approach to construct gauge-invariant observables in gravity. I show that it is possible to restrict the inevitable non-local contributions to the past light cone such that the obtained observables are causal. Lastly, I present some applications, namely the leading quantum gravitational corrections to the local expansion rate of our universe (the Hubble rate) and the Newtonian gravitational potential. Based on arXiv:1711.08470, arXiv:1806.11124, arXiv:2108.11960, arXiv:2109.09753, and arXiv:2303.16218
Nov 23	Thu	Alberto Cobos Rabano (Sheffield)	The Sheffield Geometry and Physics Seminar
10:00		Higher genus reduced GW invariants of projective space
		Hicks Seminar Room J11
	Abstract: The Gromov-Witten invariants of projective spaces are not enumerative in positive genera. The reason is geometric: the moduli space of genus-g stable maps has several irreducible components, which contribute in the form of lower-genera GW invariants. In genus one, Vakil and Zinger constructed a blow-up of the moduli space of stable maps and used it to define reduced Gromov-Witten invariants, which correspond to curve-counts in the main component. I will present a new definition of all-genera reduced Gromov-Witten invariants of complete intersections in projective spaces using desingularizations of sheaves. This is joint work with E. Mann, C. Manolache and R. Picciotto and can be found in arXiv:2310.06727.
Nov 23	Thu	Kohei Iwaki (Tokyo )	The Sheffield Geometry and Physics Seminar
11:30		Conifold gap property for the topological recursion free energy of an elliptic spectral curve
		Hicks Seminar Room J11
	Abstract: I’ll show that the topological recursion free energy of a family of elliptic spectral curves (which is related to Painlevé I through discrete Fourier transform) has a series expansion when a parameter tends to be large, and its leading term is written by the Bernoulli number. This shows the so-called conifold gap property in the above example. I’ll also explain a potential application of the result to the resurgence property. (Based on on-going joint work with N. Iorgov, O. Lisovyy and Y. Zhuravlov.)
Nov 23	Thu	Ieke Moerdijk (Sheffield)	Topology Reading Group
13:00		(Co)homology of categories and functor (co)homology
		Hicks Seminar Room J11
Nov 23	Thu	Yuqing Shi (MPIM Bonn)	Topology Seminar
16:00		Costabilisation of telescopic spectral Lie algebras
		Hicks Seminar Room J11
	Abstract: One can think of the stabilisation of an ∞-category as the ∞-category of objects that admit infinite deloopings. For example, the ∞-category of spectra is the stabilisation of the ∞-category of homotopy types. Costabilisation is the opposite notion of stabilisation, where we are interested in objects that allow infinite desuspensions. It is easy to see that the costabilisation of the ∞-category of homotopy types is trivial. Fix a prime number p. In this talk I will show that the costablisation of the ∞-category of T(h)-local spectral Lie algebras is equivalent to the ∞-category of T(h)-local spectra, where T(h) denotes a p-local telescope spectrum of height h. A key ingredient of the proof is to relate spectral Lie algebras to (spectral) Eₙ algebras via Koszul duality.
Nov 23	Thu	Dmitrii Kolotkov (Warwick)	Plasma Dynamics Group
16:00		Non-Adiabatic MHD Seismology of the Solar Corona
		https://meet.google.com/iiu-jtng-ujm,
	Abstract: A powerful technique for the diagnostics of physical conditions in active regions of the Sun’s corona is the method of coronal seismology, based on observations of magnetohydrodynamic (MHD) wave processes in high-resolution imaging data or indirectly as quasi-periodic pulsations in flaring light curves. Traditionally, coronal seismology is focused on the diagnostics of MHD properties of the Sun’s corona, such as the coronal magnetic field, plasma density, fine parallel and cross-field structuring, which are difficult to measure otherwise. In a series of recent works, it has been proven effective for probing not only MHD but also fundamental thermodynamic parameters of the coronal plasma through theoretical modelling and observations of MHD wave dynamics and stability in intrinsically non-adiabatic conditions and in the presence of a wave-induced thermal misbalance. In this talk, I present a few recent examples of the application of the method of non-adiabatic coronal seismology to probe such crucial parameters of the coronal plasma as energy transport coefficients, polytropic index, and heating function, regulating the delicate energy balance in the corona. More specifically, an apparent departure of the effective heat transfer coefficient from its classical Spitzer form is assessed seismologically under the assumptions of weak and full non-adiabaticity. The exact role of the effective polytropic index of the corona in the dynamics of non-adiabatic slow magnetoacoustic waves, its link with the effective thermal conduction coefficient, and shortcomings of the polytropic plasma approximation are discussed. I also show the potential of a recently developed theory of wave-induced thermal misbalance and a frequency-dependent damping of slow magnetoacoustic waves for constraining the link between the coronal magnetic field and the heating function, which is not directly available in extreme ultraviolet or soft X-ray observations traditionally used for coronal heating studies.
Nov 27	Mon	TBA	The Sheffield Geometry and Physics Seminar
10:00
		Hicks Seminar Room J11
Nov 27	Mon	TBA	The Sheffield Geometry and Physics Seminar
11:30
		Hicks Seminar Room J11
Nov 27	Mon	Lewis Bartlett (Georgia)	Mathematical Biology Seminar
13:00
		Hicks Seminar Room J11
Nov 28	Tue	TBA	Astronomical Topology Working Group
09:00		TBA
		Hicks Seminar Room J11
Nov 28	Tue	Ieke Moerdijk (Sheffield)	Topology Reading Group
12:00		(Co)homology of categories and functor (co)homology
		Hicks Seminar Room J11
Nov 28	Tue	Johannes Girsch (Sheffield)	Number Theory seminar
13:00		On families of degenerate representations of GL_n(F)
		Hicks Seminar Room J11 / Google Meet
	Abstract: Smooth generic representations of GL_n(F), i.e. representations admitting a nondegenerate Whittaker model, are an important class of representations, for example in the setting of Rankin-Selberg integrals. However, in recent years there has been an increased interest in non-generic representations and their degenerate Whittaker models. By the theory of Bernstein-Zelevinsky derivatives we can associate to each smooth irreducible representation of GL_n(F) an integer partition of n, which encodes the "degeneracy" of the representation. For each integer partition \lambda of n, we then construct a family of universal degenerate representations of type \lambda and prove some suprising properties of these families. This is joint work with David Helm.
Nov 28	Tue	TBA	Algebra / Algebraic Geometry seminar
14:30
Nov 28	Tue	Sofia Dias (York)	RSS Seminar
16:00		Evidence synthesis for decision making: making best use of relevant evidence
		Online / https://rss.org.uk/training-events/events/events-2023/local-groups/agm-webinar-evidence-synthesis-for-decision-making/
	Abstract: Preceded by Local Group AGM Meta-analyses are typically used to pool evidence from multiple studies in order to decide which treatment is most effective or cost-effective, out of several alternatives. When deciding which treatments to recommend for use in a national health service, we typically start with a well-defined decision problem specifying the patient population, interventions and outcomes of interest. A search of the literature for randomised controlled trials (RCTs) comparing the interventions of interest then follows, where evidence is collected and assessed for quality and relevance to the decision problem. Often evidence from available RCTs that does not exactly match our decision problem is classed as not directly applicable to the decision-problem (indirect evidence) and discarded. However, models that allow incorporation of such "indirect" evidence using reasonable assumptions may reduce uncertainty in estimates of treatment effectiveness, leading to better decisions. Network meta-analysis (NMA) extended the idea of pairwise meta-analysis to pool evidence on more than one intervention, allowing for indirect evidence on additional treatment comparisons to be incorporated. Whilst standard NMA methods are now well established, some recent extensions allow pooling of additional data, reducing uncertainty. After briefly introducing the principles of meta-analysis and NMA, the extension of NMA models to incorporate dose-response relationships will be described. Using examples, we will show how evidence on different doses of interventions can be combined to strengthen inferences and how key modelling assumptions can be checked. Some additional methodological extensions that allow other types of "indirect" evidence to be incorporated will also be outlined.
Nov 29	Wed	Veronique Fischer (University of Bath)	Pure Maths Colloquium
14:00		Sub-Riemannian quantum limits
		Hicks Seminar Room J11
	Abstract: We will start with a short discussion on semi-classical analysis to introduce the concept of quantum limits. We will present an overview of sub-Riemannian geometry and the recent developments of spectral geometry in this context, especially quantum limits on nilpotent Lie groups.
Nov 29	Wed	Manuel Reichert (Sussex)	Cosmology, Relativity and Gravitation
15:00		From fluctuating gravitons to Lorentzian quantum gravity
		Hicks Seminar Room J11
	Abstract: I will review recent progress in the asymptotic safety approach to quantum gravity. This includes the computation of momentum-dependent graviton correlation functions, the phase structure of the Standard Model of Particle Physics with asymptotically safe gravity, and the first computation directly in space-times with Lorentzian signatures via the spectral function of the graviton.
Nov 30	Thu	Ieke Moerdijk (Sheffield)	Topology Reading Group
13:00		(Co)homology of categories and functor (co)homology
		Hicks Seminar Room J11
Nov 30	Thu	Fiona Torzewska (Bristol)	Topology Seminar
16:00		Motion groupoids
		Hicks Seminar Room J11
	Abstract: The braiding statistics of point particles in 2-dimensional topological phases are given by representations of the braid groups. One approach to the study of generalised particles in topological phases, loop particles in 3-dimensions for example, is to generalise (some of) the several different realisations of the braid group. In this talk I will construct for each manifold M its motion groupoid $Mot_M$, whose object class is the power set of M. I will discuss several different, but equivalent, quotients on motions leading to the motion groupoid. In particular that the quotient used in the construction $Mot_M$ can be formulated entirely in terms of a level preserving isotopy relation on the trajectories of objects under flows -- worldlines (e.g. monotonic `tangles'). I will also give a construction of a mapping class groupoid $\mathrm{MCG}_M$ associated to a manifold M with the same object class. For each manifold M I will construct a functor $F \colon Mot_M \to MCG_M$, and prove that this is an isomorphism if $\pi_0$ and $\pi_1$ of the appropriate space of self-homeomorphisms of M is trivial. In particular there is an isomorphism in the physically important case $M=[0,1]^n$ with fixed boundary, for any $n\in\mathbb{N}$. I will discuss several examples throughout.
Dec 4	Mon	Claudia Rella (Geneva)	The Sheffield Geometry and Physics Seminar
10:00		Strong-weak duality and quantum modularity of resurgent topological strings
		Hicks Seminar Room J11
	Abstract: Quantizing the mirror curve of a toric Calabi-Yau threefold gives rise to quantum-mechanical operators. Their fermionic spectral traces produce factorially divergent power series in the Planck constant and its inverse, which are conjecturally captured by the Nekrasov-Shatashvili and standard topological strings via the TS/ST correspondence. In this talk, I will discuss a general conjecture on the resurgence of these dual asymptotic series, and I will present a proven exact solution in the case of the first spectral trace of local P^2. A remarkable number-theoretic structure underpins the resurgent properties of the weak and strong coupling expansions and paves the way for new insights relating them to quantum modular forms. Finally, I will mention how these results fit into a broader paradigm linking resurgence and quantum modularity. This talk is based on arXiv:2212.10606 and further work in progress with V. Fantini.
Dec 4	Mon	Artie Prendergast (Loughborough)	The Sheffield Geometry and Physics Seminar
11:30		Primitive selfmaps of Calabi—Yau varieties
		Hicks Seminar Room J11
	Abstract: Joint work with Inder Kaur. When studying dynamics of birational automorphisms on a variety, it is natural to focus on those which are “primitive”, roughly meaning not coming from lower dimensional varieties. For Calabi—Yau varieties, Oguiso gave a useful criterion for primitivity of a map in terms of the associated linear map on cohomology. This talk will explain how to upgrade Oguiso’s criterion slightly by also keeping track of convex geometry, and give a new example of a primitive birational automorphism in dimension 3.
Dec 4	Mon	TBC	Mathematical Biology Seminar
13:00
		Hicks Seminar Room J11
Dec 5	Tue	Ieke Moerdijk (Sheffield)	Topology Reading Group
12:00		(Co)homology of categories and functor (co)homology
		Hicks Seminar Room J11
Dec 5	Tue	Chris Birkbeck (UEA)	Number Theory seminar
13:00
		Hicks Seminar Room J11 / Google Meet
Dec 5	Tue	TBA	Algebra / Algebraic Geometry seminar
14:30
		Hicks Seminar Room J11
Dec 7	Thu	Ieke Moerdijk (Sheffield)	Topology Reading Group
13:00		(Co)homology of categories and functor (co)homology
		Hicks Seminar Room J11
Dec 7	Thu	Lukas Brantner (Oxford)	Topology Seminar
16:00		Deformations and lifts of Calabi-Yau varieties in characteristic p
		Hicks Seminar Room J11
	Abstract: Homotopy theory allows us to study infinitesimal deformations of algebraic varieties via (partition) Lie algebras. We apply this general principle to two classical problems on Calabi-Yau varieties Z in characteristic p. First, we show that if Z has torsion-free crystalline cohomology and degenerating Hodge-de Rham spectral sequence, then its mixed characteristic deformations are unobstructed. This generalises the BTT theorem to characteristic p. If Z is ordinary, we show that it moreover admits a canonical (and algebraisable) lift to characteristic zero, thereby extending Serre-Tate theory to Calabi-Yau varieties. This is joint work with Taelman, and generalises results of Achinger-Zdanowicz, Bogomolov-Tian- Todorov, Deligne-Nygaard, Ekedahl–Shepherd-Barron, Schröer, Serre-Tate, and Ward.
Dec 7	Thu	Ryan French (NSO)	Plasma Dynamics Group
16:00		Beyond the Standard Flare Model – Dynamics of QPPs, Fans & SADs
		(https://meet.google.com/oqv-inaw-fib / (https://meet.google.com/oqv-inaw-fib
	Abstract: The standard model is able to account for many of the phenomena observed in solar flares. However, some observed features, likely relating to the higher-energy nature of flare energy release, are yet to be tied into the standard model. Quasi-Periodic Pulsations (QPPs), flare fans and Supra-Arcade Downflows (SADs) are examples of such features. We investigate dynamics of these coronal plasma phenomena across 2-3 case studies – using data from Solar Orbiter/STIX, IRIS and Hinode-EIS.
Dec 8	Fri	Dr Zsolt Frei (ELTE)	SP2RC/ESPOS seminar
13:00		Review of Gravitational-wave Research at the beginning of O4 of LIGO
		Hicks Building LT10
	Abstract: I will give a brief historical introduction to experimental proofs of Einstein’s theory of general relativity. I will detail the attempts to detect gravitational waves with mass resonators and laser interferometers. After introducing LIGO (the Laser Interferometer Gravitational-wave Observatory detectors in the US), I will summarise the first detection, and all the science done with LIGO since the mid-2010s. I plan to talk about the contributions of our group - at Eotvos University in Budapest, Hungary - to the LSC (LIGO Scientific Collaboration). These include the development of data analysis techniques, a galaxy catalog to locate sources, modeling of astrophysical sources of gravitational waves, and the proposed development of a CubeSat fleet to better localize sources in the sky.
Dec 11	Mon	Ivan Tulli (Sheffield)	The Sheffield Geometry and Physics Seminar
10:00		Variations of BPS structures, quaternionic-Kähler metrics and S-duality
		Hicks Seminar Room J11
	Abstract: Inspired by constructions in Calabi-Yau compactifications of type IIA/B string theory, we explain how to construct quaternionic-Kähler (QK) manifolds from certain special variations of BPS structures. We furthermore specify a subclass of such QK metrics admitting a rather non-trivial SL(2,Z) action by isometries, related to S-duality in type IIB string theory. Along the way, we comment on relations to the TBA equations from Gaiotto-Moore-Neitzke, and joint work with M. Alim, A. Saha and J. Teschner. This is joint work with V. Cortés (arXiv:2105.09011, arXiv:2306.01463) based on several works in the physics literature by S. Alexandrov, D. Persson, B. Pioline, F. Saueressig, S. Vandoren and many more.
Dec 11	Mon	Nicholas Williams (Lancaster)	The Sheffield Geometry and Physics Seminar
11:30		Donaldson-Thomas invariants for the Bridgeland-Smith correspondence
		Hicks Seminar Room J11
	Abstract: Celebrated work of Bridgeland and Smith shows a correspondence between quadratic differentials on Riemann surfaces and stability conditions on certain 3-Calabi--Yau triangulated categories. Part of this correspondence is that finite-length trajectories of the quadratic differential correspond to categories of semistable objects of a fixed phase. Categories of semistable objects have an associated Donaldson--Thomas invariant which, in some sense, counts the objects in the category. Work of Iwaki and Kidwai predicts particular values for these Donaldson--Thomas invariants for different types of finite-length trajectories, based on the output of topological recursion. The Donaldson--Thomas invariants produced by the category of Bridgeland and Smith do not always match these predictions. However, we show that if one replaces this category by the category recently studied by Christ, Haiden, and Qiu, then one does obtain the Donaldson--Thomas invariants matching the predictions. This is joint work with Omar Kidwai.
Dec 12	Tue	Ieke Moerdijk (Sheffield)	Topology Reading Group
12:00		(Co)homology of categories and functor (co)homology
		Hicks Seminar Room J11
Dec 12	Tue	TBA	Number Theory seminar
13:00
		Hicks Seminar Room J11 / Google Meet
Dec 13	Wed	Ana Alonso Serrano (AEI Potsdam)	Cosmology, Relativity and Gravitation
15:00		Thermodynamics as a tool for (quantum) gravitational dynamics
		Blackboard Collaborate
	Abstract: I present a review of concepts of thermodynamics of spacetime and the gravitational dynamics encoding in it, discussing also the recovery of Weyl transverse gravity instead of General Relativity. Then, I present a formalism to analyse low-energy quantum gravity modifications in a completely general framework based on the thermodynamics of spacetime. For that purpose, I consider quantum gravity effects via a parametrized modification of entropy by an extra logarithmic term in the area, predicted in most of the different approaches to quantum gravity. These results provide a general expression of quantum phenomenological equations of gravitational dynamics. Furthermore, I outline the application of the modified dynamics to particular models, such as cosmology and its predictions.
Dec 14	Thu	Simone Chierichini (Sheffield)	SP2RC/ESPOS seminar
10:00		A Bayesian approach to the drag-based modelling of ICMEs
		Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
	Abstract: Coronal Mass Ejections (CMEs) are huge clouds of magnetised plasma expelled from the solar corona that can travel towards the Earth and cause significant space weather effects.The Drag-Based Model (DBM) describes the propagation of CMEs in an ambient solar wind as analogous to an aerodynamic drag. The drag-based approximation is popular because it is a simple analytical model that depends only on two parameters, the drag parameter γ and the solar wind speed w. DBM thus allows us to obtain reliable estimates of CME transit time at low computational cost. Previous works proposed a probabilistic version of DBM, the Probabilistic Drag Based Model (P-DBM), which enables the evaluation of the uncertainties associated with the predictions. In this work, we infer the “a-posteriori” probability distribution functions (PDFs) of the γ and w parameters of the DBM by exploiting a well-established Bayesian inference technique: the Monte Carlo Markov Chains (MCMC) method. By utilizing this Bayesian method through two different approaches, an ensemble and an individual approach, we obtain specific DBM parameter PDFs for two ensembles of CMEs: those travelling with fast and slow solar wind, respectively. Subsequently, we assess the operational applicability of the model by forecasting the arrival time of CMEs. While the ensemble approach displays notable limitations, the individual approach yields promising results, demonstrating competitive performances compared to the current state-of-the-art, with a mean absolute error (MAE) of 9.86 ± 4.07 hours achieved in the best-case scenario.
Dec 14	Thu	Ieke Moerdijk (Sheffield)	Topology Reading Group
13:00		(Co)homology of categories and functor (co)homology
		Hicks Seminar Room J11
Dec 14	Thu	Simon Willerton (Sheffield)	Topology Seminar
16:00		Parametrized mates, or how I finally understood Fausk, Hu and May.
		Hicks Seminar Room J11
	Abstract: In various parts of mathematics such as algebraic geometry, homotopy theory and representation theory, you can encounter situations where you have a strong monoidal functor $f^*$ with an adjoint $f_+$. One automatically gets a comparison map between $f_+(a \times f^*b)$ and $f_+(a) \times b$ where $\times$ is the monoidal product. The projection formula is said to hold when this comparison map is an isomorphism. Fausk, Hu and May showed that the projection formula holds under various conditions, such as $f^*$ being a strong closed monoidal functor. I will show how a theory of mates for parametrized adjunctions (and my graphical version of it) has helped me understand their work.
Dec 14	Thu	Krzysztof Barczynski (ETH Zurich)	Plasma Dynamics Group
16:00		First high-resolution coordinated observations of an active region with Solar Orbiter and DKIST
		Google Meet
	Abstract: Active regions are the most dynamic structures in the solar disk. They contain numerous substructures with wide orders of sizes and lifetimes. The evolution of an active region with different time scales, the role of the small-scale structures in the active region, the mechanism triggering the transient phenomena, and the mechanism responsible for the plasma upflow at the active region border are still open issues. The main aim of the project is to focus on these open issues using high-resolution observation of the solar atmosphere obtained from different vantage points. The active region was observed during coordinated observations with Solar Orbiter and Daniel K. Inouye Solar Telescope (DKIST) on 18-21 October and 24 October 2022. Instruments onboard Solar Orbiter and DKIST provide unprecedented high-spatial and temporal simultaneous observation of the active region. Moreover, the Hinode and IRIS also focus on the same active region. We present the preliminary results of the coordinated observations from magnetic field, imaging and spectroscopy instruments.
Jan 18	Thu	Thomas Wagner (Helsinki)	Plasma Dynamics Group
16:00		Identifying and Tracking Coronal Flux Ropes
		Google Meet
	Abstract: To understand solar eruptions and the destabilization mechanism of the corresponding flux ropes, modelling the magnetic field in the solar corona in a time-dependent manner is commonly employed. However, identifying the field lines of solar flux ropes in simulation data is not trivial. We therefore developed a method for detecting and tracking flux ropes from modelling data. The extraction procedure uses a combination of some proxy map as input (for example the field line twist) and mathematical morphology algorithms, such as the morphological opening or the morphological gradient. The method is validated by applying it to time-dependent magnetofrictional model (TMFM) simulations of active regions AR11176 and AR12473. With full access to the flux rope field lines, we investigate the eruptivity and propagation of the flux ropes through the modelling domain. Finally, the methodology is also wrapped into a graphical user interface (GUI) to further simplify its application.
Jan 22	Mon	Dom Grainger
13:00
		Hicks Seminar Room J11
Jan 22	Mon	Dom Grainger (Sheffield)
14:00
		Hicks Seminar Room J11
Jan 24	Wed	Matteo Forconi (Rome)	Cosmology, Relativity and Gravitation
15:00		JWST’s Revelations and the Super-LCDM’s Promise
		Hicks Seminar Room J11
	Abstract: The recent observations by the James Webb Space Telescope (JWST) of massive galaxies at high redshifts (z ∼ 10) significantly challenge the Lambda Cold Dark Matter (ΛCDM) cosmological model. These observations suggest a higher stellar mass density than previously predicted, and raise questions about galaxy formation and matter distribution in the early universe. To reconcile these findings with standard predictions, an investigation one can look into potential systematics. If systematic errors are ruled out, one might also wonder whether this new anomaly is somehow originated from the same underlying issue as the Hubble tension, suggesting the need for a beyond-ΛCDM phenomenological explanation. One potential avenue is exploring the Dark Energy Sector. Another challenge to the standard ΛCDM model arises from allowing non-Gaussian fluctuations. Using the super sample signal, it is possible to promote the standard ΛCDM model to a more comprehensive Super-ΛCDM model. This model allows to study non-Gaussianity traces using only the power spectrum. The implications of this model extend to the field of neutrino physics, indicating that the traditional constraints on neutrino masses might need revision.
Jan 30	Tue	Nirmal Kotal (Chennai Mathematical Institute )
16:00		On Knutson Ideals and Polyomino
		Hicks Seminar Room J11
	Abstract: Consider a polynomial f with a square-free leading term with respect to some monomial ordering. Consider the smallest set of ideals such that the principal ideal (f) is in the set; the colon ideal I:J is in the set for any ideal I in the set and any arbitrary ideal J; and if I and J are in the set, then the sum I+J and the intersection I∩J are in the set. Conca-Varbaro and Seccia extensively studied this class of ideals and called the members of the set as "Knutson ideals," associated with f, as they were first studied by A. Knutson. In this discussion, we will explore many algebraic features of these ideals, such as the Grobner basis, radicality, F-splitting, etc. A polyomino is a set of unit squares on the plane that is made by joining the squares side by side. Qureshi associated an ideal generated by 2-minors with polyomino. This presentation will explore the application of Knutson's methodology in the analysis of polyomino ideals. This is an ongoing joint project with Mitra Koley and Dharm Veer.
Jan 31	Wed	Sebastian Schuster (Sheffield)	Cosmology, Relativity and Gravitation
15:00		What's Physical? A Space-Time Koan
		Hicks Seminar Room J11
	Abstract: Evaluating the physicality of a given space-time can prove difficult. Often, this is relegated to easy-to-check concepts: Absence of closed, time-like curves (vulgo: no time travel); validity of energy conditions (vulgo: mass/energy should be positive); geodesic completeness (vulgo: we shan't disappear); the related hole-freeness (vulgo: again, we shan't disappear); and more. The problem is that these are not necessarily mutually compatible with each other. Worse, as in the case of energy conditions, not all such concepts are either easy to justify or even fulfilled in known, physical situations. This talk will serve two purposes. The first is to make everyone queasy about the push-me-pull-you nature of physicality, as this allows us to critically examine which type of physicality may be more or less important in any given situation. Here, reverse-engineered metrics like warp drives and tractor beams will be in the spotlight. The second is to hone in on one particularly befuddling concept: Time travel. Fascinating as it is, in general relativity the space-time will either contain it or not. General relativity cannot explain why it might be there, or whether the confusion and contractions arising from it are due to the concept itself or from being in the wrong physical framework. Many arguments have to, at some point, wave their hands and allude to an unknown theory beyond it. To actually make this step beyond general relativity, I will present a very simple, quantum toy model of time travel with an emergent notion of time. While this first toy model will turn out to be not particularly illuminating, it still serves as a good starting point for more complicated toy models with richer structure.
Feb 7	Wed	Luca Marchetti (New Brunswick)	Cosmology, Relativity and Gravitation
16:00		Scalar cosmological perturbations from quantum-gravitational entanglement
		Hicks Seminar Room J11
	Abstract: A major challenge at the interface between quantum gravity and cosmology is to understand how cosmological structures can emerge from physics at the Planck scale. In this talk, I will discuss the main challenges associated with the understanding of such an emergence process and provide a concrete example of how they can be addressed by extracting the physics of scalar and isotropic cosmological perturbations from full quantum gravity, as described by a causally complete Barrett-Crane group field theory model. From the perspective of the underlying quantum gravity theory, cosmological perturbations will be associated with (relational) nearest-neighbor two-body entanglement, providing crucial insights into the potentially purely quantum-gravitational nature of cosmological perturbations. I will also show that at low energies the emergent relational dynamics of these perturbations are perfectly consistent with those of general relativity, while at trans-Planckian scales quantum effects become important. Finally, I will comment on the implications of these quantum effects for the physics of the early universe and outline future research directions.
Feb 8	Thu	Balazs Asztalos	SP2RC/ESPOS seminar
10:00		MHD Wave Propagation and Kelvin–Helmholtz Instability in Asymmetric Magnetic Slab Systems
Feb 8	Thu	PGR Lean Study Group
13:00
		Hicks Seminar Room J11
Feb 8	Thu	Sarah Whitehouse (Sheffield)	Topology Seminar
16:00		Homotopy theory of spectral sequences
		Hicks Seminar Room J11
	Abstract: For each r, maps which are quasi-isomorphisms on the r page provide a class of weak equivalences on the category of spectral sequences. The talk will cover homotopy theory associated with this setting. We introduce the category of extended spectral sequences and show that this is bicomplete by analysis of a certain presheaf category modelled on discs. We endow the category of extended spectral sequences with various model category structures. One of these has the property that spectral sequences is a homotopically full subcategory and so, by results of Meier, exhibits the category of spectral sequences as a fibrant object in the Barwick-Kan model structure on relative categories. We also note how the presheaf approach provides some insight into the décalage functor on spectral sequences. This is joint work with Muriel Livernet.
Feb 9	Fri	Matt Lennard & Jake Saunders (Sheffield)
16:00
		Hicks Seminar Room J11
Feb 12	Mon	Dom Grainger (University of Sheffield)
15:00
		Hicks Seminar Room J11
Feb 13	Tue	Luis Santiago Palacios (Bordeaux)	Number Theory seminar
13:00		Geometry of the Bianchi eigenvariety at non-cuspidal points
		Hicks Seminar Room J11 / Google Meet
	Abstract: An important tool to study automorphic representations in the framework of the Langlands program, is to produce $p$-adic variation. Such variation is captured geometrically in the study of certain "moduli spaces" of p-adic automorphic forms, called eigenvarieties. In this talk, we first introduce Bianchi modular forms, that is, automorphic forms for $\mathrm{GL}_2$ over an imaginary quadratic field, and then discuss its contribution to the cohomology of the Bianchi threefold. After that, we present the Bianchi eigenvariety and state our result about its geometry at a special non-cuspidal point. This is a joint work in progress with Daniel Barrera (Universidad de Santiago de Chile).
Feb 13	Tue	Emmanouil Kalligeris (Sheffield)	Statistics Seminar
15:00		A Twisted Markov Switching Mechanism for the Modelling of Incidence Rate Data
		Hicks Seminar Room J11
	Abstract: Various time series models have been used over the years to capture the dynamic behaviour of significant variables in various scientific fields such as epidemiology, seismology, meteorology, finance, etc. In this work, a conditional mean Markov regime switching model with covariates is proposed and studied for the analysis of incidence rate data. The components of the model are selected by both penalised likelihood techniques in conjunction with the Expectation Maximisation algorithm, with the aim of achieving a high level of robustness with respect to modelling the dynamic behaviour of epidemiological data. In addition to statistical inference, changepoint detection analysis is used to select the number of regimes, reducing the complexity associated with likelihood ratio tests. [Kalligeris EN, Karagrigoriou A, Parpoula C. (2023): On Stochastic Dynamic Modeling of Incidence Data. Int J Biostat, 10.1515/ijb-2021-0134]
Feb 14	Wed	Robin Stephenson (Sheffield)	Probability seminar
16:00		Where do trees grow leaves?
		Hicks Seminar Room J11
	Abstract: We study a model of random binary trees grown ``by the leaves" in the style of Luczak and Winkler (2004). If $\tau_n$ is a uniform plane binary tree of size $n$, Luczak and Winkler, and later explicitly Caraceni and Stauffer, constructed a measure $\nu_{\tau_n}$ such that the tree obtained by adding a cherry on a leaf sampled according to $\nu_{\tau_n}$ is still uniformly distributed on the set of all plane binary trees with size $n+1$. It turns out that the measure $\nu_{\tau_n}$, which we call the leaf-growth measure, is noticeably different from the uniform measure on the leaves of the tree $\tau_n$. In fact we prove that as $n \to \infty$, with high probability it is almost entirely supported by a subset of only $n^{3 ( 2 - \sqrt{3})+o(1)} \approx n^{0.8038...}$ leaves. In the continuous setting, we construct the scaling limit of this measure, which is a probability measure on the Brownian Continuum Random Tree supported by a fractal set of dimension $ 6 (2 - \sqrt{3})$. We also compute the full (discrete) multifractal spectrum. This work is a first step towards understanding the diffusion limit of the discrete leaf-growth procedure.
Feb 15	Thu	Cora Uhlemann (Newcastle)	Cosmology, Relativity and Gravitation
11:00		Making dark matter waves - the cosmic web and wavelike dark matter
		Hicks Seminar Room J11
	Abstract: Despite the astonishing success of cosmological probes in constraining the LCDM model, the dark matter mass remains one of the least constrained physical parameters. Wavelike dark matter is an intriguing alternative to standard cold dark matter with key particle physics motivations (like the QCD axion or ultralight axion-like particles) and distinct astrophysical signatures. With a simple dynamical model for the evolution of the dark matter wavefunction, I will demonstrate how to predict the formation of destructive and constructive wave interference leading to topological defects and granules dressing the cosmic web of large-scale structure. Our wave-based formalism is a versatile tool to describe the complex phase-space dynamics of cold dark matter in position space; and the fundamental description for wavelike dark matter such as ultralight particles, leading to exciting and varied probing mechanisms bridging cosmology and astroparticle physics.
Feb 15	Thu	PGR Lean Study Group
13:00
		Hicks Seminar Room J11
Feb 20	Tue	Beth Romano (Kings College London)	Number Theory seminar
13:00		Epipelagic representations in the local Langlands correspondence
		Hicks Seminar Room J11 / Google Meet
	Abstract: The local Langlands correspondence (LLC) is a kaleidoscope of conjectures relating local Galois theory, complex Lie theory, and representations of p-adic groups. The LLC is divided into two parts: first, there is the tame or depth-zero part, where much is known and proofs tend to be uniform for all residue characteristics p. Then there is the positive-depth (or wild) part of the correspondence, where there is much that still needs to be explored. I will talk about recent results that build our understanding of this wild part of the LLC via epipelagic representations and their Langlands parameters. I will not assume background knowledge of the LLC, but will give an introduction to these ideas via examples.
Feb 21	Wed	João Paulo M Pitelli (Campinas State)	Cosmology, Relativity and Gravitation
15:00		Thermal effects on a global monopole with Robin boundary conditions
		Hicks Seminar Room J11
	Abstract: The quantum theory of a scalar field propagating on a spacetime with a naked singularity is not determined until we specify a boundary condition at the boundary. When this choice is not unique, any physical observable will depend on the particular choice of boundary condition. In this work we illustrate this explicit dependence by analyzing the transition rate of an Unruh-DeWitt detector coupled to a thermal state in the singular scenario of a global monopole. We show that the naked singularity manifests thermal effects with a non-trivial behavior with respect to the admissible boundary conditions. In particular, we show that the transition rate is finite at the singularity only for the Dirichlet boundary condition and that the divergence for the other possible (Robin) boundary conditions is consistent with the divergence of the thermal fluctuations.
Feb 22	Thu	Joseph Grant	Topology Seminar
16:00		Frobenius algebra objects in Temperley-Lieb categories at roots of unity
		Hicks Seminar Room J11
	Abstract: Frobenius algebras appear in many parts of maths and have nice properties. One can define algebra objects in any monoidal category, and there is a standard definition of when such an algebra object is Frobenius. But this definition is not satisfied by something which we'd like to think of as an algebra object in Temperley-Lieb categories at roots of unity. We will explore a more general definition of a Frobenius algebra object which covers this example, and will explore some of its properties. This is joint work with Mathew Pugh.
Feb 22	Thu	Renato Miotto (Unicamp, Brazil)	Plasma Dynamics Group
16:00		Bridging the gap between numerical simulations and experiments through computer vision and deep learning
		online / Google Meet
	Abstract: Several physics and engineering problems require knowledge of physical properties to be completely characterized. However, such properties cannot always be easily obtained experimentally, which means that numerical simulations are often necessary to study the problem in question. In the present work, we propose to leverage data from numerical simulations to extract relevant information from experimental visualizations of the flow field using deep learning. We uniquely treat the image semantic segmentation as an image-to-image translation task that infers semantic labels of structures from the input images in a supervised way. The present methodology exploits the semantic proximity between images from the numerical and experimental domains to translate any properties of interest between them. Example applications are shown for a moving airfoil as well as for predicting forces on a sand dune. Extrapolation and interpolation for different flow regimes never seen by the neural network are discussed.
Feb 26	Mon	Carina Dunlop (Surrey)	Mathematical Biology Seminar
13:00		What do cells and tissues feel? The integration of cell contractility, growth and adhesion in mechanosensing
		Hicks Seminar Room J11
Feb 27	Tue	Alexandros Groutides (Warwick)	Number Theory seminar
13:00		On integral structures in smooth $\mathrm{GL}_2$-representations and zeta integrals.
		Hicks Seminar Room J11 / Google Meet
	Abstract: We will discuss recent work on local integral structures in smooth ($\mathrm{GL}_2\times H$)-representations, where $H$ is an unramified maximal torus of $\mathrm{GL}_2$. Inspired by work of Loeffler-Skinner-Zerbes, we will introduce certain unramified Hecke modules containing lattices with deep integral properties. We'll see how this approach recovers a Gross-Prasad type multiplicity one result in this unramified setting and present an integral variant of it with applications to zeta integrals and automorphic modular forms. Finally, we will reformulate and answer a conjecture of Loeffler on integral unramified Hecke operators attached to the lattices mentioned above.
Feb 27	Tue	Prof. Robin Henderson (Newcastle University)	Statistics Seminar
15:00		Event History and Topological Data Analysis
		Hicks Seminar Room J11
	Abstract: Topological data analysis has become popular in recent years, though mainly outside the statistical literature. In this talk we review some of the elements of topological data analysis and we show links to event history and survival analysis. We argue that exploiting topological data as event history can be useful in the analysis of data in the form of images. We propose a version of the well-known Nelson-Aalen cumulative hazard estimator for the comparison of topological features of random fields and for testing parametric assumptions. We suggest a Cox proportional hazards approach for the analysis of embedded metric trees. The Nelson-Aalen method is illustrated on globally distributed climate data and on neutral hydrogen distribution in the Milky Way. The Cox method is used to compare vascular patterns in fundus images of the eyes of healthy and diabetic retinopathy patients.
Feb 28	Wed	Ozgur Bayindir (Queen Mary University of London)	Pure Maths Colloquium
14:00		Algebraic K-theory and chromatic redshift
		Hicks Seminar Room J11
	Abstract: I will begin with an introduction to algebraic K-theory, ring spectra and the chromatic redshift conjecture. After this, I will talk about our new proof of the redshift conjecture for Lubin-Tate spectra and our algebraic K-theory computations. This work is partially joint with Christian Ausoni and Tasos Moulinos.
Feb 29	Thu	Jack Romo (Leeds)	Topology Seminar
16:00		$(\infty, 2)$-Categories and their Homotopy Bicategories
		Hicks Seminar Room J11
	Abstract: Across the multitude of definitions for a higher category, a dividing line can be found between two major camps of model. On one side lives the ‘algebraic’ models where composition operations between morphisms are given, like Bénabou’s bicategories, tricategories following Gurski and the models of n-category of Batanin and Leinster, Trimble and Penon. On the other end, one finds the ‘non-algebraic’ models, where the space of possible composites is only guaranteed to be contractible. These include the models of Tamsamani and Paoli, along with quasicategories, Segal n-categories, complete n-fold Segal spaces and more. The bridges between these models remain somewhat mysterious. Progress has been made in certain instances, as seen in the work of Tamsamani, Leinster, Lack and Paoli, Cottrell, Campbell, Nikolaus and others. Nonetheless, the correspondence remains incomplete; indeed, for instance, there is no fully verified means in the literature to take an `algebraic’ homotopy n-category of any known model of $(\infty, n)$-category for general n. In this talk, I will present my contributions to the problem of taking algebraic homotopy bicategories of non-algebraic $(\infty, 2)$-categories. This talk also serves as an introduction to the model of $(\infty, 2)$-category I will be using, namely complete 2-fold Segal spaces. If time permits, I will discuss how to compute the fundamental bigroupoid of a topological space with this construction.
Mar 4	Mon	Michael Clerx (Nottingham)	Mathematical Biology Seminar
13:00		Estimating parameters for biological time-series models: lessons learned from a deep dive into ion channel modelling
		Hicks Seminar Room J11
Mar 4	Mon	Lea Bottini	The Sheffield Geometry and Physics Seminar
14:00		Gapped phases and phase transitions from the SymTFT
		Hicks Seminar Room J11
	Abstract: In this talk, I will introduce the concept of Symmetry Topological Field Theory (SymTFT); this is a (d+1)-dimensional topological theory associated to a d-dimensional theory T, which neatly encodes its symmetry properties and has emerged as a key tool to study generalized symmetries. In particular, I will show how the SymTFT can be used to determine gapped infra-red phases of 2d theories that have a symmetry S described in general by a fusion category. This approach gives concrete computational tools to extract information on the gapped phase, such as the symmetry breaking pattern, the number of vacua, and the action of the symmetry on such vacua. Moreover, I will introduce a generalization of the usual SymTFT framework that allows us to characterize phase transitions between such gapped phases. The SymTFT also manifestly encodes the order parameters for the phases, thus providing a generalized version of the Landau paradigm for symmetries that go beyond the standard group-like case.
Mar 4	Mon	Franco Rota	The Sheffield Geometry and Physics Seminar
15:00		Non-degeneracy invariants of Enriques surfaces
		Hicks Seminar Room J11
	Abstract: Every Enriques surface Y has an elliptic pencil, and every elliptic pencil on Y has two multiple fibers, whose reduced support is called a half-fiber. The non-degeneracy invariant of an Enriques surface is defined to be the maximum number of half-fibers meeting each other at exactly one point. This invariants influences the projective geometry of Y, as well as the structure of its derived category. In collaboration with R. Moschetti and L. Schaffler, we study techniques to compute non-degeneracy. These mix computer algebra and classical geometric methods. I'll illustrate our results in a few examples and I'll outline future directions.
Mar 5	Tue	Lewis M Combes	Number Theory seminar
13:00		Period polynomials of level 1 Bianchi modular forms
		Hicks Seminar Room J11 / Google Meet
	Abstract: The period polynomial of a classical modular form encodes important arithmetic information about the form itself, being made out of critical L-values and connecting to congruences via Haberland's formula. In this talk, we report on work to generalise these connections to the setting of Bianchi modular forms---those over an imaginary quadratic field. We demonstrate explicit congruences between various types of Bianchi modular form, and show how to detect them using a pairing on period polynomials.
Mar 6	Wed	Simon Willerton (Sheffield)	Pure Maths Colloquium
14:00		Instantaneous dimension of metric spaces via spread and magnitude
		Hicks Seminar Room J11
	Abstract: Some spaces seem to have different dimensions at different scales. A long thin strip might appear one-dimensional at a distance, then two-dimensional when zoomed in on, but when zoomed in on even closer it is seen to be made of a finite array of points, so at that scale it seems zero-dimensional. I will present a way of quantifying this phenomenon using a couple of measures of the size of metric spaces, namely magnitude and spread. I will show lots of examples for finite metric spaces.
Mar 6	Wed	William Giare (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Do we need to rethink inflation?
		Hicks Seminar Room J11
	Abstract: I will discuss some arguments that have led me to question whether we need to reassess our understanding of cosmic inflation. Large-scale CMB temperature and polarization measurements from the Planck satellite and the BICEP/Keck collaboration have established stringent constraints on the amplitude of primordial gravitational waves (r < 0.036) and the spectral index of scalar modes (ns = 0.9649 ± 0.0044). In contrast, small-scale CMB data from the Atacama Cosmology Telescope yield divergent predictions, pointing towards a scale-invariant spectrum (ns = 1.008 ± 0.015). This leads to an overall disagreement regarding the inflationary potential as inferred by CMB experiments probing different angular scales in the sky. The well-known Hubble tension further compounds the challenge. Solutions involving new physics at early times may reshape the predictions for inflation based on large-scale measurements to align with trends observed in small-scale data. As a result, with inflation, we find ourselves between the known and the unknown.
Mar 7	Thu	Ryan Campbell (Queen's University Belfast, United Kingdo)	SP2RC/ESPOS seminar
10:00		DKIST's view of quiet photospheric magnetism and application of neural networks to the characterisation of Stokes profiles
	Abstract: A new era of solar physics commences with observations of the quiet Sun using the 4-metre Daniel K. Inouye Solar Telescope/Visible Spectropolarimeter (DKIST/ViSP). We present full-Stokes observations taken during DKIST’s cycle 1, in the Fe I 630.1/630.2 nm lines, allowing us to examine small-scale magnetism in the photosphere. We use the Stokes Inversion based on Response functions (SIR) code to invert the Fe I line pair. We reveal the existence of a serpentine magnetic element for the first time. A statistical analysis is undertaken, comparing inversions of DKIST data with Hinode data. A novel machine learning technique is used to characterise and contrast the shapes of circular polarisation signals found in the ground-based and space-based data, and synthetic observations produced from MANCHA simulations are used to aid our understanding of the differences between datasets.
Mar 7	Thu	Nadia Mazza (Lancaster)	Topology Seminar
16:00		Endotrivial modules for finite groups of Lie type
		Hicks Seminar Room J11
	Abstract: Let G be a finite group and k a field of positive characteristic p diving the order of G. An endotrivial kG-module is a finitely generated kG-module which is "invertible" in some suitable sense. Since the late 70s, these modules have been intensely studied in modular representation theory. In this talk, we review the essential background on endotrivial modules, and present some results about endotrivial modules for finite groups of Lie type, obtained jointly with Carlson, Grodal and Nakano.
Mar 8	Fri	Fabrizio del Monte (Sheffield)
11:00
Mar 8	Fri	Stefano Gariazzo (IFT Madrid)	Cosmology, Relativity and Gravitation
15:00		Relic neutrinos: decoupling and direct detection perspectives
		Hicks Seminar Room J11
	Abstract: A background radiation of relic neutrinos, originated during the early phases of the Universe expansion, is predicted by the standard cosmological model, but has never been confirmed by a direct measurement. In this seminar, I will review some of the theoretical and phenomenological aspects of relic neutrino decoupling, present indirect evidence of their existence and discuss proposed techniques and ongoing experimental efforts for attempting the first direct detection of the neutrino background.
Mar 8	Fri	Andrew Neate (Sheffield)
16:00
		Hicks Seminar Room J11
Mar 11	Mon	Alex Fletcher (Sheffield)	Mathematical Biology Seminar
13:00
		Hicks J11
Mar 12	Tue	Andrea Dotto (Cambridge)	Number Theory seminar
13:00		Some consequences of mod p multiplicity one for Shimura curves
		Hicks Seminar Room J11 / Google Meet
	Abstract: The multiplicity of Hecke eigenspaces in the mod p cohomology of Shimura curves is a classical invariant, which has been computed in significant generality when the group is split at p. This talk will focus on the complementary case of nonsplit quaternion algebras, and will describe a new multiplicity one result, as well as some of its consequences regarding the structure of completed cohomology. I will also discuss applications towards the categorical mod p Langlands correspondence for the nonsplit inner form of GL_2(Q_p). Part of the talk will comprise a joint work in progress with Bao Le Hung.
Mar 13	Wed	Evgeny Shinder (Sheffield)	Pure Maths Colloquium
14:00		Gromov's cancellation question in birational algebraic geometry
		Hicks Seminar Room J11
	Abstract: I explain some cancellation and non-cancellation phenomena in algebraic geometry and relate them to the structure of the Grothendieck ring of varieties and to the groups of birational self-maps of algebraic varieties, in particular the Cremona groups.
Mar 13	Wed	Eemeli Tomberg (Lancaster)	Cosmology, Relativity and Gravitation
15:00		Primordial black holes and stochastic inflation
		Hicks Seminar Room J11
	Abstract: Quantum fluctuations from cosmic inflation give rise to the macroscopic structures of the universe. The strongest fluctuations collapse into primordial black holes, a dark matter candidate and a possible source of gravitational waves. Stochastic inflation is a tool to compute the fluctuation statistics non-perturbatively, needed for accurate black hole predictions. I discuss recent progress in these computations, their numerical implementation and analytical approximations, and the implications for black hole abundance in single-field models of inflation.
Mar 14	Thu	Giannis Dakanalis (National Observatory of Athens)	Plasma Dynamics Group
16:00		Swirling motions in the lower solar atmosphere: detection, statistics and profile analysis from multi-wavelength observations
		LT6 (Hicks Building)
	Abstract: Ubiquitous vortical motions in the solar atmosphere have been recently revealed by high resolution observations from both space-borne and ground-based observatories in quiet, as well as, in active regions. In chromospheric observations obtained in spectral lines, such as the Halpha and Ca II IR, they manifest themselves as swirling dark spiral- and circular-shaped patches known as “chromospheric swirls”. Their suggested contribution to the channeling of energy, mass and momentum from the sub-photospheric to the higher layers of the solar atmosphere places them amongst potential candidates for atmospheric heating. In this context, their detection and statistical information concerning their population and several significant physical parameters and properties are of vital importance. To overcome the drawbacks of the detection methods based on visual inspection or on the Local Correlation Tracking (LCT) techniques, we have developed a novel automated detection method, which is purely based on their morphological characteristics. We will be presenting a brief description of the algorithm and the results from its application on high- resolution observations obtained with the CRisp Imaging SpectroPolarimeter (CRISP) of the Swedish 1-m Solar Telescope (SST) in three chromospheric spectral lines, namely, the Halpha, Ca II IR and Ca II K lines. The results include several statistical parameters such as their number, spatial distribution and temporal evolution, as well as significant physical parameters, such as radii and lifetimes. Specifically, for the estimation of the mean lifetime, apart from the usual approaches, the statistical method of survival analysis was implemented. This approach, which estimates more accurately the mean lifetime of a population, although common in several other scientific fields, is scarcely used in solar physics/astrophysics. We will finally be focusing on co-spatially detected swirling structures in all three chromospheric lines and the profile analysis performed to derive significant physical parameters, such as line-of-sight velocities, FWHM and equivalent widths.
Mar 15	Fri	Noemi Zsamberger (Sheffield)	SP2RC/ESPOS seminar
13:00		Non-parallel wave propagation in an asymmetric magnetic slab
		Google meet link: https://meet.google.com/ciq-zovu-rzm
	Abstract: Interactions between the highly dynamic atmosphere of our Sun and the magnetic fields permeating its atmosphere give rise to a wide variety of magnetohydrodynamic (MHD) wave phenomena. Combining observations of MHD waves with an applied mathematical description of the waveguides has allowed researchers to determine elusive physical quantities of the solar atmosphere using the methods of solar magneto-seismolgy. The ‘classical’ models utilised in this discipline describe straight, symmetrical MHD waveguides (slabs or flux tubes). A recent direction of research has focused on wave propagation in asymmetric slab waveguides, where the direction of propagation was strictly parallel to the magnetic field lines within the slab. Here, some further results are presented in the case when a magnetic slab is embedded in a non-magnetic, asymmetric environment, and the direction of propagation is allowed to deviate from the internal magnetic field lines of the slab. We describe this non-parallel wave propagation in various analytical approximations relevant to solar atmospheric waveguides (thin and wide slabs, low-beta plasmas) and present numerical solutions to the full dispersion relation to expand on our findings.
Mar 18	Mon	Philip Pearce (UCL)	Mathematical Biology Seminar
13:00		Some consequences of phenotypic heterogeneity in living active matter
		Hicks Seminar Room J11
Mar 18	Mon	Qaasim Shafi (Birmingham)	The Sheffield Geometry and Physics Seminar
14:00		Refined curve counts on surfaces with descendants
		Hicks Seminar Room J11
	Abstract: An old theorem of Mikhalkin says that the number of rational plane curves of degree d through 3d-1 points is equal to a count of tropical curves, combinatorial objects which are more amenable to computations. One can try to generalise this result in two directions, either by allowing for higher genus curves or allowing for different conditions than solely passing through points. I’ll discuss a generalisation which does both, using intersection theory on the moduli space of curves and integrable hierarchies, as well as ongoing work connecting this thread to quantum scattering diagrams coming from log Calabi-Yau surfaces. This is joint work with Patrick Kennedy-Hunt and Ajith Urundolil Kumaran.
Mar 19	Tue	Yoon Jae Nho	The Sheffield Geometry and Physics Seminar
10:00		Spectral networks and Floer theory
		Hicks Seminar Room J11
	Abstract: In this talk, I will give a brief introduction to the theory of spectral networks on a marked Riemann surface. I will describe how the GMN non-abelianization map can be understood in terms of Lagrangian Floer theory of the spectral curve in the cotangent bundle of the Riemann surface, for the quadratic differentials case. If time permits, I will describe one way to generalize this to the higher rank situation.
Mar 19	Tue	Jake Saunders (Booking room for online talk at Southampton PGR Seminar)
12:00
		Hicks Seminar Room J11
Mar 20	Wed	Emine Yildirim (University of Leeds)	Pure Maths Colloquium
14:00		Why the Return to Pictures in Algebra?
		Hicks Seminar Room J11
	Abstract: In ancient Greece, geometry was about points, lines, circles, and communicated through pictures. The 17th Century marked a transformative shift, connecting geometry with algebra, and lead to working with equations over visual representations. Algebraic geometry emerged as a magical blend of geometric intuition and algebraic methods. Commutative algebra, mainly the study of polynomial rings and their ideals, dominated the field for an extensive period. Then with the emergence of noncommutative algebras, such as matrix algebras, our unstoppable geometric intuition hit an immovable wall. The solution? A return to pictures as representations. In this expository talk, I will introduce a visual perspective on algebras, exploring path algebras and their captivating connections to different fields.
Mar 20	Wed	Aindriú Conroy (Charles U Prague)	Cosmology, Relativity and Gravitation
15:00		Unruh-DeWitt Particle Detectors in Bouncing Cosmologies
		Hicks Seminar Room J11
	Abstract: There is no well-defined notion of a particle in quantum field theory in curved spacetime due to the lack of global symmetries. The standard procedure in quantum field theory is to treat fields rather than particles as the fundamental object of interest. Nevertheless, in a seminal 1976 paper by W. G. Unruh, an operational meaning was given to the particle concept by examining the absorption and emission of field quanta by a two-level atom. This is the so-called Unruh-DeWitt detector and, in this operational sense, we say a particle is what a particle detector detects! In this talk, we begin by formulating an analytic model of a non-singular bouncing cosmology, the bounce phase of which receives a correction inspired by loop quantum cosmology. We then study the semi-classical particle production associated with spacetime within the Unruh-DeWitt particle detector framework, analysing the rate of particle detection with the aim of (a) understanding quantum effects at early times; (b) identify relics of pre-bounce physics; and (c) highlighting signatures of non-singular theories.
Mar 21	Thu	Július Koza (Astronomical Institute, Slovak Academy of Sciences, Slovakia)	SP2RC/ESPOS seminar
10:00		Data-driven model of temporal evolution of the solar Mg II h and k profiles over the solar cycle
		Zoom
	Abstract: The solar radiation in the cores of the Mg II h & k spectral lines strongly correlates with solar magnetic activity and global variations of magnetic fields with the solar cycle. This work provides a data-driven model of temporal evolution of the solar full-disk Mg II h & k profiles over the solar cycle. Based on selected 76 IRIS near-UV full-Sun mosaics covering almost the full solar cycle 24, we find the parameters of double-Gaussian fits of the disk-averaged Mg II h & k profiles and a model of their temporal evolution parameterized by the Bremen composite Mg II index. The Markov Chain Monte Carlo algorithm implemented in the IDL toolkit SoBAT is used in modeling and predicting temporal evolution of the Mg II h & k peak-to-center intensity ratio and the Bremen Mg II index. The relevant full-disk Mg II h & k calibrated profiles with uncertainties and spectral irradiances are provided as an online machine-readable table. To facilitate utilization of the model corresponding routines, written in IDL, are made publicly available at GitHub. Co-authors: Stanislav Gunár (The Czech Academy of Sciences, Czech Republic), Pavol Schwartz (Slovak Academy of Sciences, Slovakia), Petr Heinzel (The Czech Academy of Sciences, Czech Republic; University of Wrocław, Poland), Wenjuan Liu (The Czech Academy of Sciences, Czech Republic) Web announcement: https://espos.stream/2024/03/21/Koza/ Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
Mar 21	Thu	Andy Baker (Glasgow)	Topology Seminar
16:00		Endotrivial modules for the quaternion group and iterated Jokers in chromatic homotopy theory
		Hicks Seminar Room J11
	Abstract: The Joker is a famous very singular example of an endotrivial module over the 8-dimension subHopf algebra of the mod 2 Steenrod algebra generated by $\operatorname{Sq}^1$ and $\operatorname{Sq}^2$. It is known that this can be realised as the cohomology of two distinct Spanier-Whitehead dual spectra. Similarly, the double and iterated double are also realisable, but then the process stops.
Apr 4	Thu	Daniel Nóbrega-Siverio (Instituto de Astrofísica de Canarias —IAC, Spain)	SP2RC/ESPOS seminar
10:00		Deciphering solar coronal heating: Energizing small-scale loops through surface convection
		Zoom
	Abstract: The solar atmosphere is filled with clusters of hot small-scale loops commonly known as Coronal Bright Points (CBPs). These ubiquitous structures stand out in the Sun by their strong X-ray and/or extreme-ultraviolet (EUV) emission for hours to days, which makes them a crucial piece when solving the solar coronal heating puzzle. Here we present a novel 3D numerical model using the Bifrost code that explains the sustained CBP heating for several hours. We find that stochastic photospheric convective motions alone significantly stress the CBP magnetic field topology, leading to important Joule and viscous heating concentrated around the CBP’s inner spine at a few megameters above the solar surface. We validate our model by comparing simultaneous CBP observations from SDO and SST with observable diagnostics calculated from the numerical results for EUV wavelengths as well as for the Halpha line using the Multi3D synthesis code. Co-authors: Fernando Moreno-Insertis, Klaus Galsgaard, Kilian Krikova, Luc Rouppe van der Voort, Reetika Joshi, and Maria Madjarska Web announcement: https://espos.stream/2024/04/04/Nobrega-Siverio/ Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
Apr 15	Mon	Francesca Scarabel (Leeds)	Mathematical Biology Seminar
13:00		Structured population models
		Hicks Seminar Room J11
Apr 15	Mon	Johannes Walcher (Heidelberg)	The Sheffield Geometry and Physics Seminar
14:00		Exponential networks for linear partitions
		Hicks Seminar Room J11
	Abstract: Previous work has given proof and evidence that BPS states in local Calabi-Yau 3-folds can be described and counted by exponential networks on the punctured plane, with the help of a suitable non-abelianization map to the mirror curve. This provides an appealing elementary depiction of moduli of special Lagrangian submanifolds, but so far only a handful of examples have been successfully worked out in detail. In this talk, I will present an explicit correspondence between torus fixed points of the Hilbert scheme of points on C^2\subset C^3 and anomaly free exponential networks attached to the quadratically framed pair of pants. This description realizes an interesting, and seemingly novel, "age decomposition'' of linear partitions. We also provide further details about the networks' perspective on the full D-brane moduli space.(Joint work with Sibasish Banerjee, Mauricion Romo, Raphael Senghaas)
Apr 16	Tue	Dominic Grainger and Dr Ben Wigley (Sheffield)	Statistics Seminar
15:00		Dominic: The Efficient Modelling of Individual Animal Movement in Continuous Time; Ben: Stressing over shape: A Procrustean investigation of dental fluctuating asymmetry.
		Hicks Seminar Room J11
Apr 17	Wed	Tony Samuel (University of Birmingham)	Pure Maths Colloquium
14:00		Complexity and geometry of aperiodic systems
		Hicks Seminar Room J11
	Abstract: Aperiodic sequences and sequence spaces form prototypical mathematical models of quasicrystals. The most quintessential examples include subshifts of Sturmian words and substitutions, which are ubiquitous objects in ergodic theory and aperiodic order. Two of the most striking features these shift spaces have, are that they have zero topological entropy and are uniquely ergodic. Random substitutions are a generalisation of deterministic substitutions, and in stark contrast to their deterministic counterparts, subshifts of random substitutions often have positive topological entropy and exhibit uncountably many ergodic measures. Moreover, they have been shown to provide mathematical models for physical quasicrystals with defects. We will begin by talking about subshifts generated by Sturmian words and ways to measure their complexity beyond topological entropy, and show how this measure of complexity can be used to build a classification via Jarník sets. We will then build a bridge between these subshifts and subshifts of random substitutions. We will conclude with some recent dynamical results on subshifts of random substitutions and ways to visualise these subshifts. Namely, we will present a method to build a new class of Rauzy fractals.
Apr 18	Thu	Giulio Del Zanna (University of Cambridge)	SP2RC/ESPOS seminar
10:00		Thoughts on measuring elemental abundances in the solar atmosphere
		Zoom
	Abstract: I briefly review some methods and measurements of elemental abundances in the solar atmosphere, with emphasis on the transition region and corona. Some limitations in the methods, in the modelling of the spectral line intensities, and in the observations are discussed. Examples from the X-rays, the EUV, the UV, the visible and near-infrared are presented. A significant improvement in the modelling some of the ions is being made available with CHIANTI version 11. All the observations indicate that the solar corona has photospheric abundances and that the hot 3 MK active region cores have stable enhancements of a factor of about 3.2 in the ratios of low to high-FIP elements. A lot of uncertainties and puzzles still exist, requiring further analyses and, more importantly, future instrumentation.
Apr 18	Thu	Briony Eldridge (Southampton)	Topology Seminar
16:00		Loop Spaces of Polyhedral Products Associated with Substitution Complexes
		Hicks Seminar Room J11
	Abstract: Polyhedral products are a topological space formed by gluing together ingredient spaces in a manner governed by a simplicial complex. They appear in many areas of study, including toric topology, combinatorics, commutative algebra, complex geometry and geometric group theory. A fundamental problem is to determine how operations on simplicial complexes change the topology of the polyhedral product. In this talk, we consider the substitution complex operation. We obtain a description of the loop space associated with some substitution complexes, and use this to build a new family of simplicial complexes such that the homotopy type of the loop space of the moment angle complex is a product of spheres and loops on spheres.
Apr 18	Thu	José Juan González Avilés (Universidad Nacional Autónoma de México)	Plasma Dynamics Group
16:00		Global MHD simulations of solar wind streams in the inner heliosphere using sunRunner3D
		online / Google Meet
	Abstract: Understanding the large-scale three-dimensional structure of the inner heliosphere, while important in its own right, is crucial for space weather applications, such as forecasting the time of arrival and propagation of coronal mass ejections (CMEs). This study uses sunRunner3D (SR3D), a 3-D MHD model, to simulate solar wind (SW) streams and generate background states. SR3D employs the boundary conditions generated by CORHEL and the PLUTO code to compute the plasma properties of the SW with the magnetohydrodynamic (MHD) approximation up to 1.1 AU in the inner heliosphere. We demonstrate that SR3D reproduces global features of Corotating Interaction Regions (CIRs) observed by Earth-based spacecraft (OMNI) and STEREO-A for a set of Carrington rotations that cover a period that lays in the late declining phase of solar cycle 24. Additionally, we demonstrate that the model solutions are valid in the corotating and inertial frames of references. Moreover, a comparison between SR3D simulations and in-situ measurements shows reasonable agreement with the observations, and our results are comparable to those achieved by Predictive Science Inc.'s MAS code and SWASTi-SW framework.
Apr 19	Fri	Adrià Gómez Valent (Barcelona)	Cosmology, Relativity and Gravitation
14:00		Is there still room for low-z solutions to the Hubble tension?
		Hicks Seminar Room J11
	Abstract: The ∼5\sigma mismatch between the value of the Hubble parameter measured by SH0ES and the one inferred from the inverse distance ladder (IDL) constitutes the biggest tension afflicting the standard model of cosmology, which could be pointing to the need of physics beyond LCDM. In this talk I will review the background history required to solve the H0 tension if we consider standard prerecombination physics, paying special attention to the role played by the data on baryon acoustic oscillations (BAO) employed to build the IDL. I will show that the anisotropic BAO data favor an ultra-late-time (phantom-like) enhancement of H(z) at z<0.2, accompanied by a transition in the absolute magnitude of supernovae of Type Ia M(z) in the same redshift range. The effective dark energy (DE) density must be smaller than in the standard model at higher redshifts. Instead, when angular BAO data (claimed to be less subject to model dependencies) is employed in the analysis, the increase of H(z) must start at much higher redshifts, typically in the range z= 0.5-0.8. In this case, M(z) could experience also a transition (although much smoother) and the effective DE density becomes negative at z\sim 2. Both scenarios require a violation of the weak energy condition, but leave an imprint on completely different redshift ranges and might also have a different impact on the perturbed observables. They allow for the effective crossing of the phantom divide. I will put the accent on the utmost importance of the choice of the BAO data set in the study of the possible solutions to the H0 tension.
Apr 22	Mon	TBC	Mathematical Biology Seminar
13:00
		Hicks F41
Apr 22	Mon	Cheuk Yu Mak (Southampton)	The Sheffield Geometry and Physics Seminar
14:00		Loop group action on symplectic cohomology
		Hicks Seminar Room J11
	Abstract: For a compact Lie group G, its massless Coulomb branch algebra is the G-equivariant Borel-Moore homology of its based loop space. This algebra is the same as the algebra of regular functions on the BFM space. In this talk, we will explain how this algebra acts on the equivariant symplectic cohomology of Hamiltonian G-manifolds when the symplectic manifolds are open and convex. This is a generalization of the closed case where symplectic cohomology is replaced with quantum cohomology. Following Teleman, we also explain how it relates to the Coulomb branch algebra of cotangent-type representations. This is joint work with Eduardo González and Dan Pomerleano.
Apr 22	Mon	Cyril Closset (Birmingham)	The Sheffield Geometry and Physics Seminar
15:00		Topologically twisted indices for any G
		Hicks Seminar Room J11
	Abstract: We consider the A-model obtained by a partial topological twist of a 3d N=2 supersymmetric gauge theory. The twisted indices are the Witten indices over the Hilbert space of the 3d theory compactified on a closed Riemann surface, which generalise the Verlinde formulae. (In the special case of pure Chern-Simons theories – that is, 3d gauge theory without matter--, they give us the number of conformal blocks of the corresponding WZW model on the Riemann surface.) Previous physical methods only computed the twisted indices for a gauge group G that is simply connected and/or unitary. We generalise the supersymmetric computation to G any real compact Lie group, using the notion of higher-form symmetries. I will give a pedagogical presentation of our results. [Work to appear with Elias Furrer and Osama Khlaif.]
Apr 23	Tue	Johannes Droschl	Number Theory seminar
13:00		On modular representations of $GL_n$ over a p-adic field
		Hicks Seminar Room J11 / Google Meet
	Abstract: The Godement-Jacquet L-function is a classical invariant attached to irreducible representations of $GL_n$. Minguez extended their definition to representations over fields of characteristic $\ell\neq p$. In this talk we will finish the computation of these L-functions for modular representations and check that they agree with the L-function of their respective C-parameter defined by Kurinczuk and Matringe. We approach the problem by extending the theory of square-irreducible representations, and their derivatives, of Lapid and Minguez to modular representations and applying it to our setting.
Apr 24	Wed	Catherine Meusburger (University of Erlangen)	Pure Maths Colloquium
14:00		Dijkgraaf-Witten theory with defects
		Hicks Seminar Room J11
	Abstract: We use 3d defect TQFTs to give a gauge theoretical formulation of (untwisted) Dijkgraaf-Witten TQFT with defects. This leads to a simple description in terms of embedding quivers, groupoids and their representations. Defect Dijkgraaf-Witten TQFTs is then formulated in terms of spans of groupoids and representations of spans. This is work in progress with João Faría-Martins, University of Leeds.
Apr 24	Wed	Elsa Teixeira (Montpellier)	Cosmology, Relativity and Gravitation
15:00		Exploring Signatures of the Dark Sector through Fluid Approximations
		Hicks Seminar Room J11
	Abstract: The persistent discrepancy between theoretical predictions of the standard cosmological model and precision measurements from diverse observational probes remains a pressing challenge in modern cosmology. Over the past decade, mounting evidence for persistent discrepancies in the inferred values of cosmological parameters derived from both model-dependent and -independent methodologies has motivated the proposal of alternatives to the standard paradigm. In this seminar, I will focus on the exploration of potential missing physics within the standard model, focusing on the enigmatic dark sector comprising dark matter and dark energy, and any potential interactions between them. Leveraging on fluid approximations for the physical nature of the dark sector and its underlying dynamics, we assess the viability of various models in reconciling the observed cosmological tensions.
Apr 26	Fri	Thomas Montandon (Montpellier)	Cosmology, Relativity and Gravitation
15:00		Relativistic matter bispectrum of cosmic structure
		Hicks Seminar Room J11
	Abstract: Upcoming surveys of cosmic structures will probe scales ranging from the nonlinear regime to scales close to the cosmological horizon. This opens up the possibility of probing the ΛCDM model, as well as early universe scenarios with non-Gaussianity. Modeling the galaxy bispectrum is challenging, as it involves general relativity, radiation, and large nonlinearities. In this talk, I will present the latest developments we have achieved in the numerical and theoretical modeling of the matter angular bispectrum on the light cone, including relativistic and radiation effects. This is a crucial step towards modeling the observable bispectra, i.e., the galaxy number count bispectrum and the weak lensing bispectrum.
Apr 29	Mon	Enrico Dell'Arra (Sheffield)	Mathematical Biology Seminar
13:00
		Hicks J11
Apr 29	Mon	Sukjoo Lee (Edinburgh)	The Sheffield Geometry and Physics Seminar
14:00		Hodge number duality for orbifold Clarke mirror pairs via tropical geometry.
		Hicks Seminar Room J11
	Abstract: Hodge number duality is one of the most fundamental phenomena in mirror symmetry. In the 1990s, Batyrev and Borisov introduced a combinatorial mirror construction for nef toric complete intersections of Calabi-Yau varieties, verifying Hodge number duality for these cases. Clarke has recently expanded this construction, broadening its scope to include a wide range of examples of mirror pairs. In this talk, I will discuss ongoing work with Andrew Harder, where we establish Hodge number duality for a large class of orbifold Clarke mirror pairs. We achieve this by developing a new tropical geometric tool to compute Hodge numbers. Our results not only confirm the result of Batyrev and Borisov but also lead to a proof of a conjecture by Katzarkov, Kontsevich, and Pantev for orbifold toric complete intersections. If time permits, I will also describe several applications, including the functoriality in Fano mirror symmetry and mirror symmetry for singular varieties.
Apr 29	Mon	Dylan Butson (Oxford)	The Sheffield Geometry and Physics Seminar
15:00		W-algebras, Yangians, and Calabi-Yau threefolds
		Hicks Seminar Room J11
	Abstract: I'll recall some basics about Slodowy slices, generalized slices in the affine Grassmannian, and quantizations thereof called W-algebras and Yangians, respectively, as well as their analogues for affine Lie algebras which are naturally described using the theory of vertex algebras. Then I'll explain a construction of vertex algebras associated to divisors in toric Calabi-Yau threefolds, which include affine W-algebras in type A for arbitrary nilpotents, and outline a dictionary between the geometry of the threefolds and the representation theory of these algebras. I'll also explain the physical interpretation of these results, as an example of twisted holography for M5 branes in the omega background.
Apr 30	Tue	Bence Hevesi (Kings College London)	Number Theory seminar
13:00		Local-global compatibility at l=p for torsion automorphic Galois representations
		Hicks Seminar Room J11 / Google Meet
	Abstract: Some ten years ago, Scholze proved the existence of Galois representations associated with torsion eigenclasses appearing in the cohomology of locally symmetric spaces for GL_n over imaginary CM fields. Since then, the question of local-global compatibility for these automorphic Galois representations has been an active area of research motivated by applications towards new automorphy lifting theorems. I will report on my work on local-global compatibility at l=p in this direction, generalising the results of the celebrated 10-author paper and Caraiani—Newton.
May 1	Wed	David Corfield (University of Kent)	Pure Maths Colloquium
14:00		Homotopy type theory and its modal variants
		meet.google.com/cxn-dnca-zci
	Abstract: Over the past decade or so, homotopy type theory (HoTT) has emerged as a novel foundation for mathematics. Rather than taking sets as the basic entities of mathematics, HoTT provides us with a synthetic theory of structures, expressing naturally notions of structural equivalence. These structures are infinity-groupoids, or what Peter Scholze has called ‘anima’. Evidence that the underlying dependent type theory is well-suited to present mainstream mathematics comes from the success of Kevin Buzzard’s program to use Lean as an automated proof assistant to verify contemporary results. In HoTT itself it is possible to develop what is called ‘synthetic homotopy theory’. But mathematicians also treat further varieties of structure, such as cohesion, smooth structure, equivariance and linear structure. It turns out that these may all be treated synthetically by the addition of ‘modalities’ to HoTT. With the close relationship between HoTT and computation, it appears that Linear HoTT has things to say about quantum computation. In this talk I shall be giving a gentle introduction to these ideas.
May 2	Thu	Sanja Danilovic (Institute for Solar Physics, Stockholm University, Sweden)	SP2RC/ESPOS seminar
10:00		An overview of last October's SST-SolO observational campaign
		Zoom
	Abstract: We present the results of coordinated observations of the Swedish 1-m Solar Telescope with Solar Orbiter that took place from October 12th to 26th 2023. The campaign resulted in 7 datasets of various quality. The observational programs were adjusted to the seeing conditions. The observations cover two active regions and a coronal hole. We focus on the morphology and evolution of several targets that are observed from two vantage points. We share the lessons we learned and give an outline of our plans for October this year and the support we could give during remote sensing windows 16 and 17. Web announcement: https://espos.stream/2024/05/02/Danilovic/ ——————————————————— Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
May 2	Thu	Ehud Meir (Aberdeen)	Topology Seminar
16:00		Invariants that are covering spaces and their Hopf algebras
		Hicks Seminar Room J11
	Abstract: Different flavours of string diagrams arise naturally in studying algebraic structures (e.g. algebras, Hopf algebras, Frobenius algebras) in monoidal categories. In particular, closed diagrams can be realized as scalar invariants. For a structure of a given type the closed diagrams form a commutative algebra that has a richer structure of a self dual Hopf algebra. This is very similar, but not quite the same, as the positive self adjoint Hopf algebras that were introduced by Zelevinsky in studying families of representations of finite groups. In this talk I will show that the algebras of invariants admit a lattice that is a PSH-algebra. This will be done by considering maps between invariants, and realizing them as covering spaces. I will then show some applications to subgroup growth questions, and a formula that relates the Kronecker coefficients to finite index subgroups of free groups.
May 2	Thu	Ellie Mcclure (Sheffield)	Plasma Dynamics Group
16:00		Vortex Community Detection
		Room E39 (Hicks Building)
	Abstract: Vortical plasma motions are present in the solar atmosphere at different spatial and temporal scales and act as natural channels of energy from the lower to upper layers. Over the past decade, considerable attention has been devoted to uncovering the physical properties of various vortical motions within magnetic flux tubes, with the aim of understanding their ability to generate and sustain magnetohydrodynamic waves, instigate instabilities, and concentrated energy. While much focus has been placed on investigating individual vortical structures across varying scales, recent advancements in magneto-convection simulations and high-resolution observations have revealed that vortices exist not in isolation but rather as communities. A precise understanding of the intricate interplay among plasma vortices within their communities and the analysis of interactions between different communities in the presence of magnetic fields are essential for a deeper understanding of the plasma dynamics that underlie significant solar atmospheric phenomena and facilitate energy transport from the lower to upper atmosphere. In this talk, we present the first analysis on solar vortex communities and an overview of their properties and time evolution.
May 7	Tue	Jay Taylor (Manchester)	Number Theory seminar
13:00
		Hicks Seminar Room J11 / Google Meet
May 8	Wed	Gabriele Barca (Rome/Sheffield)	Cosmology, Relativity and Gravitation
15:15		Cut-Off Physics Effects on the Primordial Universe
		Hicks Seminar Room J11
	Abstract: Cosmological singularities represent the limit of predictability of General Relativity, but in the high-energy regimes close to the singularity quantum effects are expected to play an important role. I will present some alternative quantization procedures constructed to introduce different kinds of cut-offs. They will be implemented on various cosmological models, both in an effective semiclassical description and on a pure quantum level, with the aim of studying the fate of singularities. These alternative quantization procedures can be powerful for their easy implementation to various systems and for the possible derivation of phenomenological signatures.
May 8	Wed	Alessandro Chiarini (OIST, Okinawa, Japan)	Fluid Dynamics Seminar
16:00		Finite-size inertial spherical particles in homogeneous isotropic turbulence
		Diamond LT2
	Abstract: We use direct numerical simulations to study the fluid-solid interaction of non-dilute suspensions of spherical particles in homogeneous isotropic turbulence. I will discuss how finite-size inertial spherical particles modulate turbulence, and how they preferentially accumulate in specific regions of the flow. In particular, we observe that particles of different size and density modulate the flow in a different way. For small and heavy particles, the classical energy cascade is inhibited, and the energy transfer across scales is essentially driven by the fluid-solid interaction. We also find that particles of different size and density have a different level of clustering. I will discuss their collective motion and preferential location in relation with properties of the carrier flow.
May 9	Thu	Georg Struth (Sheffield)	Topology Seminar
16:00		Single-set Cubical Categories and Their Formalisation with a Proof Assistant
		Hicks Seminar Room J11
	Abstract: Cubical sets and cubical categories are widely used in mathematics and computer science, from homotopy theory to homotopy type theory, higher-dimensional automata and, last but not least, higher-dimensional rewriting, where our own interest in these structures lies. To formalise cubical categories with the Isabelle/HOL proof assistant along the path of least resistance, we take a single-set approach to categories, which leads to new axioms for cubical categories. Taming the large number of initial candidate axioms has relied essentially on Isabelle's proof automation. Yet we justify their correctness relative to the standard axiomatisation by Al Agl, Brown and Steiner via categorical equivalence proofs outside of Isabelle. In combination, these results present a case study in experimental mathematics with a proof assistant. In this talk I will focus on the formalisation experience -- lights and shadows -- and conclude with some general remarks about formalised mathematics. This is joint work with Philippe Malbos and Tanguy Massacrier (Université Claude Bernard Lyon 1).
May 13	Mon	Paul Blackwell/ Journal Club	Mathematical Biology Seminar
13:00
		Hicks J11
May 15	Wed	Álvaro Álvarez Domínguez (Madrid)	Cosmology, Relativity and Gravitation
15:15		Black holes from light?
		Hicks Seminar Room J11
	Abstract: General Relativity theoretically allows the formation of black holes through the gravitational collapse of purely electromagnetic radiation. However, this scenario would involve electromagnetic strengths surpassing the critical Schwinger limit, resulting in the generation of electron-positron pairs. This quantum phenomenon counteracts the collapse, with the created particles scattering out of the collapsing region, carrying their energy. Here, we show that this dissipative effect alone is enough to prevent the formation of black holes from light in the non-classical regime. arXiv:2405.02389
May 16	Thu	Ben Snow (University of Exeter)	SP2RC/ESPOS seminar
10:00		Partially ionised mixing with collisional and radiative ionisation and recombination
	Abstract: Turbulence is a fundamental process that drives mixing and energy redistribution across a wide range of astrophysical systems. For warm (T ≈ 10^4K) plasma, the material is partially-ionised, consisting of both ionised and neutral species. The interactions between ionised and neutral species are thought to play a key role in heating (or cooling) of partially-ionised plasmas. Here mixing is studied in a two-fluid partially-ionised plasma undergoing the shear-driven Kelvin-Helmholtz instability to evaluate the thermal processes within the mixing layer. 2D numerical simulations are performed using the open-source (PIP) code that solves for a two-fluid plasma consisting of a charge-neutral plasma and multiple excited states of neutral hydrogen. Both collisional and radiative ionisation and recombination are included. In the mixing layer, a complex array of ionisation and recombination processes occur as the cooler layer joins the hotter layer, and vice-versa. In localised areas of the mixing layer, the temperature exceeds the initial temperatures of either layer with heating dominated by collisional recombinations over turbulent dissipation. The mixing layer is in approximate ionisation-recombination equilibrium, however the obtained equilibrium is different to the Saha-Boltzmann LTE equilibrium. The dynamic mixing processes may be important in determining the ionisation states, and with that intensities of spectral lines, of observed mixing layers.
May 16	Thu	Gong Show	Topology Seminar
15:30
		Hicks Seminar Room J11
May 16	Thu	Samuel Skirvin (Sheffield)	Plasma Dynamics Group
16:00		Modelling the connection between propagating disturbances and solar spicules
	Abstract: Propagating (intensity) disturbances (PDs) have been reported throughout the solar atmosphere in coronal loops, plumes and recent links with spicular activity. However, despite being reported in observations, they are yet to be studied in depth from a modelling point of view. In this work, we present results from 3D MHD numerical simulations where features with striking characteristics to those of detected PDs arise as a result of the transition region dynamics. Furthermore, the PDs can be interpreted as slow magnetoacoustic pulses propagating along the magnetic field carrying sufficient energy flux to at least partially heat the lower coronal plasma. Using forward modelling, we demonstrate the similarities between the PDs in the simulations and those reported in observations from IRIS and SDO/AIA. These results may have important implications in the context of providing a source for mass and energy in powering the (fast) solar wind.
May 16	Thu	Gong Show	Topology Seminar
16:30
		Hicks Seminar Room J11
May 17	Fri	Matteo Sacchi (Oxford)	The Sheffield Geometry and Physics Seminar
11:00		Symmetries, anomalies, and compactifications in QFT
		Hicks Seminar Room J11
	Abstract: Anomalies and symmetries play key roles in understanding quantum field theories (QFTs) by allowing us to constrain their dynamics. Compactification, which relates theories in different spacetime dimensions, offers valuable insights as well. In this talk, I will first give a review of some of these topics. Then, I will discuss the recent understanding of some aspects of the behaviour of anomalies and generalized symmetries under compactification. In particular, how the anomalies of the higher and the lower dimensional theories can be related by integration over the compact space, and the fate of various generalized symmetry structures (2-group and non-invertible symmetries) in 4d models upon compactification on a 2-sphere. These structures tend to trivialize in 2d, but they can still leave an imprint in terms of ’t Hooft anomalies or symmetry breaking patterns. While tested in supersymmetric models, these concepts are applicable to non-supersymmetric theories too.
May 17	Fri	Phillip Engel (Bonn)	The Sheffield Geometry and Physics Seminar
14:00		Compact moduli of K3 and Enriques surfaces
		Hicks Seminar Room J11
	Abstract: Due to Torelli theorems, moduli spaces of surfaces of Kodaira dimension 0 are orthogonal Shimura varieties. In the 60’s-80’s, compactifications of such varieties were constructed by Baily-Borel, Ash-Mumford-Rapaport-Tai, and Looijenga. But are any of these “semitoroidal” compactifications distinguished, in the sense that they parameterize some stable K3 or Enriques surfaces? Work on the Minimal Model Program from the 80’s-00’s by Kollar-Shepherd-Barron-Alexeev proved that an ample divisor on a Calabi-Yau variety defines a notion of stability, leading to compact moduli spaces. I will describe joint work with Alexeev, relating the Hodge-theoretic and MMP approaches to compactification, via the notion of a “recognizable divisor”.
May 20	Mon	Juan Morales (Glasgow)	Mathematical Biology Seminar
14:00
		Hicks Seminar Room J11
May 21	Tue	Owen Patashnick (Kings College London)	Number Theory seminar
13:00		Aut we to act? a mod p story.
		Hicks Seminar Room J11 / Google Meet
	Abstract: In this talk, we will show that an analogy for a result about the action of the automorphism group on the mod p points of the Markoff surface is true for a certain class of K3 surfaces as well, namely, the Kummer of the square of an elliptic curve without CM.
May 23	Thu	Nika Shakiba (British Columbia)	Mathematical Biology Seminar
11:00		TBC
		Hicks Seminar Room J11
May 24	Fri	Clare Rees-Zimmerman (University of Oxford)	SIAM-IMA Chapter Seminar
16:00		Modelling paint drying: controlling particle arrangement with diffusiophoresis
		Hicks Seminar Room J11
	Abstract: Stratification in drying films – how a mixture of differently-sized particles arranges itself upon drying – is examined. Being able to control this would allow the design of coating formulations which self-assemble during drying to give a desired structure. Potential applications are across a range of industries, from a self-layering car paint, to a biocidal coating in which the biocide stratifies to the top surface, where it is required. Diffusiophoresis is the migration of particles along a concentration gradient of a different solute species. Diffusiophoresis can be caused by different mechanisms, two of which are investigated here: excluded volume and electrolyte-driven diffusiophoresis. A continuum hydrodynamic model is derived, and the resulting partial differential equations solved numerically. Asymptotic solutions are found for high evaporation rate. It is found that the final film structure is governed by the relative magnitudes of the diffusive and diffusiophoretic terms. The diffusiophoretic term promotes small-on-top stratification, and so may account for experimental observations of accumulated small particles at the top surface of dried films. In the case of electrolyte-driven diffusiophoresis, two methods are discovered to control the resulting stratification: (i) setting the surface charge on the particles, and (ii) setting the background salt concentration.
May 29	Wed	Lucia Menendez-Pidal (Madrid)	Cosmology, Relativity and Gravitation
15:00		The measurement problem and Quantum Cosmology
		Hicks Seminar Room J11
	Abstract: If, according to most theories of Quantum Gravity, the Universe started as a quantum system, there must have been a quantum-to-classical transition fairly early in its history. However, explaining the emergence of Classical Mechanics from Quantum Mechanics is not an easy task, and one is faced with the so called "measurement problem". Intuitively, the measurement problem can be understood as the difficulties in defining what exactly is a measurement in Quantum Mechanics. How does one measure if everything is quantum? How do we distinguish between measuring device and system? These are some of the questions that appear when talking about measurements. If one wants to consider the entire Universe as a quantum system, this problem is exacerbated. There are several proposals to solve this conundrum, but all of them change our perspective about Quantum Mechanics. This shift in perspective has consequences, in particular regarding the canonical interpretation of Quantum Gravity. In this talk, I will first give an accessible introduction to the measurement problem and present two modifications to Quantum Mechanics that have been proposed to resolve it, namely Bohmian Mechanics and Spontaneous Collapse Models. I will then dive deeper in Spontaneous Collapse Models, introducing the principal choices of Collapse Operators. Additionally, I will show how Spontaneous Collapse terms can be implemented in Quantum Cosmology and how these new terms allow the Universe to transition from a fully quantum state to a classical state using a simple toy model as an example. Finally, I will briefly present the shortcomings and prospects of the application of Spontaneous Collapse Models in Quantum Gravity and Quantum Cosmology.
May 30	Thu	Llŷr Dafydd Humphries (Aberystwyth University)	SP2RC/ESPOS seminar
10:00		Detection and in-depth analyses of quiet-Sun IRIS Bright Points
	Abstract: Observations of small-scale brightenings in the low solar atmosphere can provide valuable constraints on possible heating and heat transport mechanisms. We present a method for the detection and analysis of bright points (BPs), and demonstrate its application to time-series imagery of the Interface Region Imaging Spectrograph (IRIS) in the extreme ultraviolet. The method is based on spatio-temporal band-pass filtering, adaptive thresholding and centroid tracking, and records an event’s spatial position, duration, speed, total brightness, maximum brightness, and intrinsic brightness. Spatial area, brightness, and position are also recorded as functions of time throughout the event’s lifetime. Detected brightenings can fragment, or merge, over time – thus the number of distinct regions constituting a brightening event is recorded over time, and the maximum number of regions recorded as Nfrag, which is a simple measure of an event’s coherence or spatial complexity. The method is first tested on synthetic data based on Poisson statistics before being applied to real IRIS data. We present statistical characteristics of brightenings from the application of this method to 1330, 1400, and 2796 Å IRIS slit-jaw image time series. Several thousand events are recorded that coexist in all three channels, giving high confidence that they are real. Finally, we will also present continuing applications of this detection method to analyse a large set of BPs and their characteristics – over 12,000 BPs in total – and compare those that are found within ‘Active’ and ‘Quiet’ domains within a QS region, as well as possible future applications of the detection method. Zoom link: https://zoom.us/j/165498165 (Meeting ID: 165 498 165)
May 30	Thu	Statistics UQ Reading group	Statistics Seminar
14:00
		Hicks Seminar Room J11
May 31	Fri	Antreas Tsiapalis	SP2RC seminar
13:00		Non-Parallel Wave Propagation in an Asymmetric Magnetic Slab
		Google Meet
	Abstract: Theoretical and numerical analysis of solar atmospheric structures have a vital role in understanding the behaviour of magnetohydrodynamic (MHD) waves, especially when looking at the plasma-dynamics of the Sun. As a result, the developing branch of magneto-helioseismology is indebted to the insight granted by the assessment of simple magnetic slabs with variance to the conditions within the slab and its environment. This study examines the analytic approach of deriving the dispersion relation of the propagating MHD waves in a uniform magnetic slab, surrounded by non-magnetic atmospheres of different densities and consider the case of oblique wave propagation. Similar to the strictly parallel case, a plethora of modes emerges that can be classified into quasi-kink and quasi-sausage, body and surface, fast and slow waves. The slab itself can be categorised as thin or wide as seen in predating works, but now it can also be categorised as short and long, which is the analogue of the thin and wide classification in the non-parallel direction, expanding our established knowledge regarding the propagating MHD waves in magnetic slabs. In addition, the variance of the wavenumber along the non-parallel dimension brings to light many interesting features such as modes changing character with the change in the angle of the wave vector while the propagation speed is the same. Further new information is provided by the newly derived classification limits, which act as a form of generalised Alfvén and sound speeds in the dispersion relation.
Jun 3	Mon	Swarnendu Banerjee (Amsterdam)	Mathematical Biology Seminar
13:00
		Hicks Seminar Room J11
Jun 5	Wed	Jake Saunders (Booking room for meeting with UGRI student)
13:00
		Hicks Seminar Room J11
Jun 5	Wed	Jake Saunders (Booking room for meeting with UGRI student)
14:00
		Hicks Seminar Room J11
Jun 5	Wed	Ethan James German (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Adiabatic inspirals under electromagnetic radiation reaction on Kerr spacetime
		Hicks Seminar Room J11
	Abstract: Consider an electrically charged particle orbiting a spinning black hole, described by the Kerr spacetime. As the charged particle moves, it undergoes a radiation-reaction process, driven by the electromagnetic force which causes it to lose orbital energy and angular momentum. Consequently, it inspirals towards the black hole until the final plunge. In this work we calculate how the orbital parameters for eccentric orbits change along the inspiral, by applying flux-balance laws. We make comparisons to inspirals driven by gravitational waves, and to non-relativistic Keplerian approximations based on the Abraham-Lorentz force law. We find that the electromagnetic inspirals circularize less efficiently than gravitational inspirals, and we quantify the effect of the black hole spin. I will also describe work in progress on calculating the local self-force acting on the particle, which includes a conservative part that cannot be found through the flux-balance approach.
Jun 6	Thu	Stanley Strawbridge (Cambridge)	Mathematical Biology Seminar
10:00		Pushy guests: interrogating cell-fate specification in the early embryo through chimeras and computation
		Hicks LT9
Jun 11	Tue	Dr Zexun Chen (Edinburgh)	Statistics Seminar
15:00		Peer-induced Fairness: A Simple Causal Approach for Algorithmic Bias Discovery in Credit Approval
	Abstract: In today's world, where AI and automation increasingly shape decision-making processes, ensuring algorithmic fairness is paramount. While much attention has been given to fairness concepts like statistical parity and equal opportunity, practical challenges in detecting and addressing bias remain. Traditional methods often involve embedding fairness metrics into algorithms, which can compromise their accuracy. In this seminar, I will introduce a fundamental shift in tackling algorithmic bias by presenting our novel "peer-induced fairness" framework. This approach leverages counterfactual fairness and advanced causal inference techniques, including the Single World Intervention Graph, to detect bias at the individual level through peer comparisons and hypothesis testing. Focusing on the context of credit approval, our framework addresses common issues such as data scarcity and imbalance, and operates independently of specific decision-making methodologies, such as classifier selection. It provides explainable feedback to individuals who receive adverse decisions, distinguishing between algorithmic bias, discrimination, and the capabilities of the subjects involved. Our framework has been validated using a dataset of SMEs, demonstrating its effectiveness in identifying unfair practices and suggesting practical interventions. The results show that 'peer-induced fairness' not only improves fairness in algorithmic decisions but also serves as a flexible, transparent, and adaptable tool for diverse applications. Finally, if time allows, I will present some of my working ideas around Gaussian process modelling, including multivariate Gaussian processes and constrained Gaussian processes.
Jun 12	Wed	Michael Krivelevich (Tel Aviv)	External seminars
14:00		Fast construction on a restricted budget
		LT2, Sir Henry Stephenson Building, Mappin St
	Abstract: (This is a Computer Science seminar, potentially of interest to mathematicians.) We will discuss a model of a controlled random graph process. In this model, the edges of the complete graph $K_n$ are ordered randomly and then revealed, one by one, to a player called Builder. He must decide, immediately and irrevocably, whether to purchase each observed edge. The observation time is bounded by parameter $t$, and the total budget of purchased edges is bounded by parameter $b$. Builder's goal is to devise a strategy that, with high probability, allows him to construct a graph of purchased edges possessing a target graph property $P$, all within the limitations of observation time and total budget. We analyze this model in the context of several graph theoretic properties such as minimum degree, Hamiltonicity, and the containment of fixed-size trees and cycles. Joint work with Alan Frieze and Peleg Michaeli.
Jun 12	Wed	Luis Escamilla (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Reconstructing the Dark Energy
		Hicks Seminar Room J11
	Abstract: One of the biggest challenges in Cosmology is the lack of understanding of the underlying nature of the Dark Sector, which includes Dark Matter and Dark Energy. To address this problem, several approaches can be considered: assuming that the standard model is incomplete or incorrect, questioning the data, etc. An alternative approach to explore possible solutions or at least give weight to favorable ones involves the so-called "reconstructions". In this talk, I will review my research on using the reconstruction method to study Dark Energy. I will discuss different types of reconstructions, their mechanisms, and the results I obtained during my PhD. The focus will be on "model-independent reconstructions" and their applications to the equation of state, the density parameter of Dark Energy, and the interaction kernel in an Interacting Dark Sector scenario.
Jun 13	Thu	Charlotte Proverbs (Lancashire, UK)	SP2RC/ESPOS seminar
10:00		Automatic Identification and Tracking of Sunspots
		Zoom
	Abstract: t is well understood that the dynamics of sunspots lead to energy being transferred to the solar atmosphere and stored in the coronal magnetic field. This provides a surplus of energy that may be released in solar eruptions. The driving mechanisms for this energy transfer may include sunspot rotations, both within individual sunspots and between sunspot pairs. Calculation of the rotations of individual sunspots have been carried out by several authors, but studies of the rotation of sunspot pairs has been less systematically investigated. Calculation of rotations in either case rely on careful tracking of the sunspots from observation to observation. Identification and tracking of sunspots is therefore essential to understanding the energies in play that lead up to solar eruptions. To date, this has predominantly been done manually which has restricted many studies to being a small number of case studies rather than large statistical samples. In order to construct large samples, the careful tracking of sunspots must be automated. We present a fully automatic method to identify and track sunspots in long sequences of data from the Solar Dynamics Observatory Helioseismic and Magnetic Imager (SDO/HMI) at a high temporal resolution. This includes registering the splitting and merging of sunspots, and allocating sunspots to active regions. This information can be fed into algorithms to measure the rotation of individual sunspots or used to calculate the relative motion of sunspots with respect to each other (including co-rotation). The method is applied to a four-month data set that has previously been analysed using a semi-automatic method where the basic sunspots were identified by eye, and the results are compared to determine any differences between the methods. From this data, sunspot dynamics such as sunspot rotation, shearing and merging are calculated, alongside sunspot pair interactions. Case studies of successfully tracked sunspots will be presented, showing examples of the individual sunspot rotations and some initial results involving sunspot pair interactions with correlations to solar activity.
Jun 14	Fri	SLB	Maths Knowledge Exchange Hub Triage Workshops
10:00		Physics Informed Surrogate Models for Nonlinear Partial Differential Equations with Variable Coefficients
		https://newton.us21.list-manage.com/track/click?u=1f88d1ca28e2385959c2201f0&id=99c3ff5224&e=cfdba87233
	Abstract: Background Partial Differential Equations (PDEs) are ubiquitous in modelling physical phenomena across various scientific disciplines and solving them accurately can be computationally expensive and challenging, especially for complex systems. Physics Informed Machine Learning (PIML) bridges this gap by incorporating the underlying physical laws and constraints into machine learning algorithms. This approach not only accelerates the modelling process but also enhances the robustness and interpretability of machine learning models, making it a transformative tool for tackling complex problems in science and engineering. There are certain limitations around using this technology. The network is used to compute the partial derivatives for the PDE using automatic differentiation in order to setup the loss function. This has shown to work for a set of PDEs but not much work has been published on PDEs containing discrete variable coefficients that are nonlinear in the state variable. In addition, it is complicated to resolve all the constitutive physics and chemistry that is used in the numerical simulators. The Challenge In this workshop, we will look at a problem around modelling fluid flow in heterogeneous porous media. A method is introduced in which a commercial fluid flow simulator can be used to compute the loss function while training a PIML model. The aim is to compute the loss function accurately using the physical implementation available within the numerical simulator without explicitly coding any physical constraints in the network. The challenge is to converge the gradient descent iterations while training the network only using the gradients coming from the numerical simulator for an ensemble of model descriptions.
Jun 19	Wed	Eleonora Di Valentino (Sheffield)	Cosmology, Relativity and Gravitation
15:00		Anomalies and Tensions in Cosmological Data: Challenges and Insights
		Hicks Seminar Room J11
	Abstract: The standard Lambda Cold Dark Matter cosmological model has been incredibly successful in explaining a wide range of observational data, from the cosmic microwave background radiation to the large-scale structure of the universe. However, recent observations have revealed a number of inconsistencies among the model's key cosmological parameters, which have different levels of statistical significance. These include discrepancies in measurements of the Hubble constant, the S8 tension, and the CMB tension. While some of these inconsistencies could be due to systematic errors, the persistence of such tensions across various probes suggests a potential failure of the canonical LCDM model. I will examine these inconsistencies and discuss possible explanations, including modifications to the standard model, that could potentially alleviate them. However, I will also discuss the limitations of these proposed solutions and note that none of them have successfully resolved the discrepancies.
Jun 21	Fri	Yudong Ye (Planetary Environmental and Astrobiological Research Laboratory (PEARL) Sun Yat-sen University, Zhuhai)	SP2RC seminar
10:00		Mass Ejection: From Stars to Planets
		LT 11 / Google Meet
	Abstract: This groundbreaking study presents direct evidence of explosive mass ejections from the Martian ionosphere, triggered by magnetic reconnections. While such phenomena are well-documented on the Sun and other stars, this research highlights their occurrence on a partially magnetized planet like Mars. Utilizing data from the Mars Atmosphere and Volatile EvolutioN (MAVEN) mission, we identified three significant events of mass ejection. These findings suggest that strong localized magnetic fields above the Martian exobase are crucial for such explosive activities, challenging previous assumptions that global magnetic fields are necessary for mass ejections. This study not only enhances our understanding of Martian atmospheric dynamics but also has broader implications for planetary science and space weather phenomena.
Jun 26	Wed	Paul Fontana (Seattle University)	Fluid Dynamics Seminar
15:00		Thermodynamics of state transitions in non-equilibrium systems, with application to laminar-turbulent transitions in pipe flows
		F20
	Abstract: In equilibrium thermodynamics, the direction of a spontaneous reaction or state change is predicted by considering the free energy difference between the equilibrium states, which corresponds to the maximum useful work that could be extracted from the system during the transition. Open systems with non-equilibrium steady states also undergo transitions, but predicting their direction is more difficult due to the omnipresence of dissipation and the lack of reversible processes. In this talk I will discuss how the idea of maximum useful work can be generalized to non-equilibrium state transitions. Work is underway to test the theory on the laminar-to-turbulent transition in pipe flows.
Jun 27	Thu	Angelos Valentino (CfMPA, KU Leuven)	SP2RC/ESPOS seminar
10:00		Modeling of non-radially propagating halo CMEs and forecasting their arrival time at Earth
		Zoom
	Abstract: The prediction of geomagnetic storms is becoming more and more important, with the aim to take effective measures for avoiding the possible damage from the extreme events. One of the important parameters when modeling CMEs and CME-driven shocks, is their arrival time at Earth. We present a study of several halo CMEs with the propagation direction which significantly deviated from the Sun-Earth line and as a result, CMEs impacted Earth as flank-encounters. We modeled selected events with the default-setup of EUHFORIA and the Cone model for the CMEs. The aim of our study is to better understand the importance of the CME’s direction of propagation in the input parameters of the Cone model and improve the modeled arrival time at Earth. We selected events that were propagating strongly non-radialy in the low corona, in order to understand how important are the effects of the deflections in the low corona, in the direction of propagation. Our results show that, when the data from the DONKI database are used, the modeled arrival time has the largest discrepancy(≥10h) when compared with observations. When the input parameters are taken employing the GCS fitting technique though, up to the height of 12 Ro (solar radii), the accuracy of the modeled arrival time improves, shifting closer to the observed ones. This result reflects the characteristic that, up to the heights of about 10 Ro, CMEs experience all the low coronal deflections and have taken their final direction of propagation.
Jun 28	Fri	Various	Maths Knowledge Exchange Hub Triage Workshops
09:30		ESGI180: European Study Group with Industry Finale Livestream
		https://bham-ac-uk.zoom.us/j/87031560651?pwd=1CvsVhsPFTf6ndsiSFEQNvXTVcGYnS.1
	Abstract: Livestream of the closing session of the ESGI, featuring an outline of each problem and summary of the team's progress for each of the challenges addressed.
Jul 1	Mon	Statistics UQ Reading group	Statistics Seminar
15:00
		Hicks Seminar Room J11
Jul 3	Wed	Alina Donea (Monash)	Plasma Dynamics Group
16:00		An ultrasound scan of large sunspots: from birth to death
		Room J11 (Hicks Building)
	Abstract: Sunspots emerge, evolve and then "die". Some sunspots can move fast, some are slow, some decay faster than others and the magnetic fragmentation proves this. I will analyse the acoustic properties of a few interesting giant sunspots. Standard local helioseismic diagnostics of large sunspots show the signature of anomalously strong compact scatterers of p-modes within about a Mm beneath their photospheres. These "strong acoustic scatterers" appear in both umbrae and inner penumbrae, but in a sunspot whose umbra is large enough to accommodate several of them, they show a decided affinity for the boundary separating the two. This work helps understanding the flux emergence of active regions, which leads to a better understanding of the development of large active regions, which produce solar flares and coronal mass ejections, all relevant for space weather processes near Earth. Also: ample discussions about other research related to flux emergence and ML
Jul 5	Fri	Wansoo Kim (Sheffield)	SP2RC seminar
13:00		MHD waves in 3-dimensional slab modelling - Solar applications
		Google Meet
	Abstract: Our Sun’s atmosphere shows structuring on various scales due to the presence of e.g. inhomogeneously distributed magnetic fields. Using magnetohydrodynamic (MHD) theory, we investigate wave propagation of MHD waves in a magnetic slab system representing a simple waveguide model applicable to a wide range of solar phenomena. After reviewing a recent advances of slab models including various sources of asymmetry in the background parameters (such as plasma parameters, magnetic field strengths and flow speeds), we focus on a case where the plasma slab is permeated by a homogeneous magnetic field directed along the slab, and this central slab is embedded in a plasma environment made up of different homogeneous regions on all sides. In this expansion of the slab model, as a first step, the external regions were left symmetric, filled with the same homogeneous plasma and not subject to a background magnetic field. In previous approaches, the MHD waves were described with inhomogeneity in a single direction of structuring perpendicular to the direction of the background magnetic field, while the configuration was left semi-infinite in the third direction perpendicular both to the structuring and the magnetic field. Expanding upon this model, our study delved into all three dimensions of the problem. While we still focused on waves propagating along the magnetic field, we closed the slab in both directions perpendicular to the background magnetic field and left it open only in the direction parallel to the field lines. We worked on deriving the system of new governing equations of this complex and generalised problem and on matching the solutions to these equations to obtain a dispersion relation modelling MHD wave propagation in a 3D slab applicable to solar phenomena such as e.g., magnetic bright points, light bridges, or prominences.
Jul 11	Thu	Matthew Lennard and Lauren McClure (Sheffield)	Plasma Dynamics Group
16:00
		Room J11 (Hicks Building)
Jul 12	Fri	easyJet (https://www.kehubmaths.co.uk/triage-workshops/)	Maths Knowledge Exchange Hub Triage Workshops
10:00		Strategic standby aircraft allocation for enhanced network efficiency
		https://newton.us21.list-manage.com/track/click?u=1f88d1ca28e2385959c2201f0&id=22f0b431cb&e=cfdba87233
	Abstract: Background Standby aircraft are essential for maintaining operational continuity in the face of unforeseen disruptions. Traditionally, airlines designate a portion of their fleet as standby aircraft, ensuring that replacement planes are available in the event of mechanical issues, adverse weather, or other delays. Currently, we have 14 aircraft designated as standby 3 days ahead of operations, and 11 on the day of operations. This approach, while providing a buffer for unforeseen disruptions, contributes to inefficiencies by sidelining a significant portion of our fleet. The challenge lies in finding the balance between having readily available standby aircraft and achieving maximum fleet utilisation. The aim of this project is to develop a dynamic standby aircraft allocation strategy to optimise the placement and utilisation of standby aircraft across the network. This strategy will distribute standby capacity throughout the fleet by mathematically scheduling breaks in the flight schedule across different aircraft and times of the day. Such an approach will ensure that the entire fleet is utilised to its maximum potential while still maintaining the flexibility to respond to operational disruptions. By integrating this dynamic allocation strategy, we can transform how standby aircraft are utilised, moving away from the traditional model of keeping specific aircraft idle towards a more fluid and efficient model that enhances both operational flexibility and fleet efficiency.
Jul 16	Tue	Jeremy Oakley (Sheffield)	Statistics Seminar
15:00		Reading group: Auto-Encoding Variational Bayes (Kingma and Welling, https://arxiv.org/pdf/1312.6114)
		Hicks LTD
Jul 17	Wed	Nils Albin Nilsson (IBS Daejeon)	Cosmology, Relativity and Gravitation
15:00		Radiation fields and gravitational-wave observables with spacetime-symmetry breaking
		Hicks Seminar Room J11
	Abstract: Presently, interest in tests of the underlying principles of fundamental physics is high, both in theory and experiment. This is motivated by a search for a unifying theory encompassing both GR and QFT, for example quantum gravity. In the literature, it has been suggested that the underlying spacetime symmetries could be broken in small but detectable ways in some approaches to quantum gravity. To this end, a generic effective-field theory has been in use for decades, and many strong constraints exist. In this talk, I will introduce the state of the art in the search for spacetime-symmetry breaking in gravity, with special focus on gravitational-wave solutions and observables. I will show how extra polarisations appear at the generation stage and how the propagation properties are altered, as well as constraints available from LVK data. Finally, I will discuss plans for the future with next-generation detectors such as LISA.
Jul 23	Tue	Jeremy Oakley (Sheffield)	Statistics Seminar
14:00		Reading group: Auto-Encoding Variational Bayes (Kingma and Welling, https://arxiv.org/pdf/1312.6114) - Continued!
		Hicks Seminar Room J11
Jul 26	Fri	Dstl (https://www.kehubmaths.co.uk/triage-workshops/)	Maths Knowledge Exchange Hub Triage Workshops
10:00		Generating data for graph machine learning
		https://newton.us21.list-manage.com/track/click?u=1f88d1ca28e2385959c2201f0&id=529330050b&e=cfdba87233
	Abstract: Background With the world becoming ever more connected and our reliance on this connectivity increasing, Dstl have an enduring need to efficiently analyse and interpret network structured data. Graph machine learning (ML) techniques have been popular in the data science community and have promise in several tasks such as link prediction and node classification. However, like all ML techniques, they rely on copious amounts of quality labelled data to perform well. Dstl need to devise a strategy for generating synthetic training data for these ML tasks. By generating synthetic and representative data, pitfalls like overfitting can be avoided and models can be applied to unseen data. This workshop’s challenge is to discuss ideas for an approach to scalable and efficient data generation for network analysis tasks. Dstl’s scenario models networks in one domain where they are scale-free, directed, large (up to 106 nodes), with a pre-specified degree distribution, and with node attributes. Specifically, generating network topologies which match a specified degree distribution lowers the quality of synthetic data as it fails to reproduce other characteristics of the real networks. One should consider the generation technique, its cost in terms of time and computer (memory) resource, and its format.
Oct 2	Wed	Mariana Carrillo González (Imperial College London)	Cosmology, Relativity and Gravitation
15:30
		Hicks Seminar Room J11
Oct 9	Wed	Tiziano Schiavone (GGI Firenze)	Cosmology, Relativity and Gravitation
15:00
		Hicks Seminar Room J11
Oct 16	Wed	Enrico Specogna (Sheffield)	Cosmology, Relativity and Gravitation
15:00
		Hicks Seminar Room J11
Oct 23	Wed	Rishav Roshan (Southampton)	Cosmology, Relativity and Gravitation
15:00
		Hicks Seminar Room J11
Oct 30	Wed	Shiladitya Porey (Novosibirsk State U.)	Cosmology, Relativity and Gravitation
15:00
		Blackboard Collaborate