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| Oct 8 |
Wed |
Farbod Sayyed Rassouli (Nottingham) |
Cosmology, Relativity and Gravitation |
| 15:00 |
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Hicks Seminar Room J11 |
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| Oct 13 |
Mon |
Thorsten Schimannek (Utrecht) |
Theoretical High Energy Physics Seminar |
| 15:00 |
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Counting the curves for fun and profit
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Hicks Seminar Room J11 |
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Abstract:
After giving a brief introduction to Calabi-Yau manifolds and classical mirror symmetry, I will focus on some of the special properties arising for torus fibered CY 3-folds. My first goal is to describe how mirror symmetry can be used to obtain "Gopakumar-Vafa polynomials", that capture the multiplicities of singular fibers in terms of the Chern classes of bundles that determine the structure of the torus fibration. This will lead us to conjecture subtle constraints on the possible multiplicities that, from a physical perspective, are related to the cancellation of Dai-Freed anomalies in six-dimensional supergravity. I will outline how these constraints connect to cobordism groups, to the APS eta-invariant on lens spaces and a quadratic refinement of the corresponding torsion pairing in cohomology.
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| Oct 22 |
Wed |
Debnandini Mukherjee (Birmingham) |
Cosmology, Relativity and Gravitation |
| 15:00 |
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Hicks Seminar Room J11 |
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| Oct 29 |
Wed |
David Hume (Birmingham) |
Topology Seminar |
| 14:00 |
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Coarse geometry of groups and spaces
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Hicks Seminar Room J11 |
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Abstract:
A helpful method of understanding a group is to look at geometric objects that it acts on. One natural construction of such a geometric object is a Cayley graph equipped with a shortest path metric, which has the disadvantage of depending on a choice of generating set. For groups that admit a finite generating set, all of the Cayley graphs are quasi-isometric (an equivalence relation on metric spaces which generalises isometry). In geometric group theory, and more recently coarse graph theory, a major target is uncovering and computing properties of groups and graphs which are invariant under quasi-isometry.
In his thesis, Ashley focuses on a generalisation of quasi-isometry called coarse homotopy, which has the advantage that it may be defined for a more general class of objects - coarse spaces in the sense of Roe. Ashley proves that some quasi-isometry invariants fail to be coarse homotopy invariants (such as asymptotic dimension) and embarks on a programme of defining new coarse homotopy invariants and calculating them in certain cases.
In this talk, I will describe a different generalisation to a notion of coarse inclusion (regular embeddings) which generalise subgraph inclusions among bounded degree graphs and subgroup inclusions among finitely generated groups. Most quasi-isometry invariants do not behave well with respect to regular embeddings, but two that do are asymptotic dimension and the growth function. I will explain these two invariants and show how they may be combined to create a world of new invariants. Then, I will explain how to compute them in an interesting collection of cases (products of real hyperbolic and Euclidean spaces) and raise many open questions.
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| Oct 29 |
Wed |
Sam Collingbourne (Edinburgh) |
Cosmology, Relativity and Gravitation |
| 15:00 |
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Hicks Seminar Room J11 |
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| Nov 5 |
Wed |
Vlad Bavula (Sheffield) |
Pure Maths Colloquium |
| 14:00 |
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Analogue of the Galois Theory for normal fields and B-extensions (characteristic free approach)
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Hicks Seminar Room J11 |
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Abstract:
By definition, a Galois field extension is a separable and normal field extension and the Galois Theory is about Galois field extensions. For a long time it was an open question to produce a `Galois Theory' for normal (but not necessarily separable) field extensions. Examples are all purely inseparable field extensions but normal field extensions are a larger class. The last time when progress was made are the classical results on `Galois Theory' of Jacobson (1937, 1944) for purely inseparable field extensions of exponent one and its generalizations for modular extensions by Sweedler (1968), and Gerstenhaber and Zaromp (1970). In my talk, I will present an analogue of the Galois Theory for normal field extensions which is based on two of my recent papers.
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| Nov 24 |
Mon |
Matijn François (Geneva) |
Theoretical High Energy Physics Seminar |
| 15:00 |
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From open topological strings to eigenfunctions
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Hicks Seminar Room J11 |
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Abstract:
The topological string/spectral theory correspondence establishes a precise, non-perturbative duality between topological strings on local Calabi–Yau threefolds and the spectral theory of quantized mirror curves. This duality has been rigorously formulated for the closed string sector, but the open string sector is less understood. In this talk, I will explain how one can use open-string partition functions to construct true eigenfunctions for the quantized mirror curves of local F₀ and the Y(N,0) geometries more generally. We will then discuss the four-dimensional limit, underlining the implications of the topological string/spectral theory correspondence for spectral problems relating four-dimensional supersymmetric gauge theories to the quantization of their Seiberg–Witten curves. This will give us exact, analytic solutions for a deformation of the usual Schrödinger equation.
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| Nov 26 |
Wed |
Mohammad Akhond (Rome Tor Vergata) |
Theoretical High Energy Physics Seminar |
| 14:00 |
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On brane systems with O+ planes
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Hicks Seminar Room J11 |
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Abstract:
I will present recent results on the Higgs branches of field theories with 8 supercharges in 5 and 6 dimensions, focusing on theories realised on brane systems in Type II with an Op+ plane. Exploiting accidental isomorphisms of lie algebras at low rank, allows one to conjecture a recipe to extract the magnetic quivers. The main consequence of the presence of the orientifold is that it renders the magnetic quiver to be non-simply-laced. From the magnetic quivers, we compute Hasse diagrams and highest weight generating functions for the Higgs branches, enabling us to identify the global form of the flavour symmetry for several families of 5d SQFTs; among them Bhardwaj’s rank-1 theory. For 6d theories realised on a −4 curve, we observe the appearance of an additional D4 slice on top of the phase diagram as one goes to the tensionless limit.
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| Dec 1 |
Mon |
Tommaso Pedroni (SISSA) |
Theoretical High Energy Physics Seminar |
| 15:00 |
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Blowing-up the edge: connection formulae and stability chart of the Lamé equation
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Hicks Seminar Room J11 |
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Abstract:
Connections between different areas of physics often provide new perspectives on difficult
problems and suggest guiding principles for their solutions. In this work, we show how
the correspondence between 4d N = 2 supersymmetric gauge theories, 2d conformal field
theories and quantum integrable systems can be used to study periodic spectral problems,
with a particular focus on the Lam´e equation.
After introducing the key ingredients, we use 2d CFT techniques to solve the connection
problem of the Lam´e equation in terms of semiclassical Virasoro blocks. We then analyze
their analytic structure, showing how apparent poles turn into branch points through
a partial resummation that combines the AGT correspondence—relating 2d conformal
blocks to 4d Nekrasov partition functions—with a specific limit of the C2 blow-up equa-
tions satisfied by these functions. Finally, we apply these results to the study of the
periodic spectral problems of the Lam´e equation, highlighting the new insights gained
from this perspective.
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| Dec 8 |
Mon |
Marina Moleti (SISSA) |
Theoretical High Energy Physics Seminar |
| 15:00 |
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Hicks Seminar Room J11 |
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