Seminars this semester

13:00

Hicks Seminar Room J11 / Google Meet

Sep 28

Thu

Muralikrishnan Gopalakrishnan Meena (Oak Ridge National Laboratory)

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)

13:00

Hicks Seminar Room J11

Oct 3

Tue

TBA

13:00

Hicks Seminar Room J11 / Google Meet

Oct 3

Tue

TBA

14:30

Hicks Seminar Room J11

Oct 4

Wed

Tyler Kelly (Birmingham)

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)

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)

13:00

Hicks Seminar Room J11

Oct 10

Tue

Ju-Feng Wu (University of Warwick)

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

14:30

Hicks Seminar Room J11

Oct 11

Wed

Markus Szymik (Sheffield)

14:00

Hicks Seminar Room J11

Oct 11

Wed

Marco de Cesare (Naples)

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)

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)

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

10:00

Hicks Seminar Room J11

Oct 16

Mon

TBA

11:30

Hicks Seminar Room J11

Oct 16

Mon

Alex Best (Journal Club) (Sheffield)

13:00

Hicks Seminar Room J11

Oct 17

Tue

TBA

13:00

Hicks Seminar Room J11 / Google Meet

Oct 17

Tue

TBA

Black History Month Colloquium

14:30

Hicks Seminar Room J11

Oct 18

Wed

Lassina Dembele (King's College London)

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)

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)

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)

13:00

Hicks Seminar Room J11

Oct 24

Tue

Neil Strickland (Sheffield)

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

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

14:30

Oct 25

Wed

Reem Yassawi (Queen Mary University of London)

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)

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))

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)

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

10:00

Hicks Seminar Room J11

Oct 30

Mon

TBA

11:30

Hicks Seminar Room J11

Oct 30

Mon

TBC

13:00

Hicks Seminar Room J11

Oct 31

Tue

Robert Kurinczuk (Sheffield)

13:00

Blocks for classical p-adic groups

Hicks Seminar Room J11

Oct 31

Tue

TBA

14:30

Hicks Seminar Room J11

Nov 1

Wed

Eli Hawkins (University of York)

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)

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)

13:00

Hicks Seminar Room J11

Nov 7

Tue

Neil Strickland (Sheffield)

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)

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

14:30

Hicks Seminar Room J11

Nov 8

Wed

Daniel Graves (University of Leeds)

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)

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

10:00

Hicks Seminar Room J11

Nov 13

Mon

TBA

11:30

Hicks Seminar Room J11

Nov 13

Mon

Alexandria Volkening (Purdue/Cambridge)

13:00

Hicks Seminar Room J11

Nov 14

Tue

Dan Graves (Leeds)

09:00

Background from stable homotopy theory

Hicks Seminar Room J11

Nov 14

Tue

TBA

13:00

Hicks Seminar Room J11 / Google Meet

Nov 14

Tue

TBA

14:30

Hicks Seminar Room J11

Nov 15

Wed

Emre Özülker (Istanbul Tech U.)

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)

13:00

(Co)homology of categories and functor (co)homology

Hicks Seminar Room J11

Nov 16

Thu

Callum Reader (Sheffield)

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)

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)

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)

12:00

(Co)homology of categories and functor (co)homology

Hicks Seminar Room J11

Nov 21

Tue

Robert Rockwood (Kings)

13:00

Hicks Seminar Room J11 / Google Meet

Nov 21

Tue

TBA

14:30

Hicks Seminar Room J11

Nov 22

Wed

Paul Johnson (Sheffield)

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)

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)

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 )

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)

13:00

(Co)homology of categories and functor (co)homology

Hicks Seminar Room J11

Nov 23

Thu

Yuqing Shi (MPIM Bonn)

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)

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

10:00

Hicks Seminar Room J11

Nov 27

Mon

TBA

11:30

Hicks Seminar Room J11

Nov 27

Mon

Lewis Bartlett (Georgia)

13:00

Hicks Seminar Room J11

Nov 28

Tue

TBA

09:00

TBA

Hicks Seminar Room J11

Nov 28

Tue

Ieke Moerdijk (Sheffield)

12:00

(Co)homology of categories and functor (co)homology

Hicks Seminar Room J11

Nov 28

Tue

Johannes Girsch (Sheffield)

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

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)

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)

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)

13:00

(Co)homology of categories and functor (co)homology

Hicks Seminar Room J11

Nov 30

Thu

Fiona Torzewska (Bristol)

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

TBC

13:00

Hicks Seminar Room J11

Dec 5

Tue

Ieke Moerdijk (Sheffield)

12:00

(Co)homology of categories and functor (co)homology

Hicks Seminar Room J11

Dec 5

Tue

Chris Birkbeck (UEA)

13:00

Hicks Seminar Room J11 / Google Meet

Dec 5

Tue

TBA

14:30

Hicks Seminar Room J11

Dec 7

Thu

Ieke Moerdijk (Sheffield)

13:00

(Co)homology of categories and functor (co)homology

Hicks Seminar Room J11

Dec 7

Thu

Lukas Brantner (Oxford)

16:00

Hicks Seminar Room J11

Dec 11

Mon

Ivan Tulli (Sheffield)

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)

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)

12:00

(Co)homology of categories and functor (co)homology

Hicks Seminar Room J11

Dec 12

Tue

TBA