# Winter 2024

The Seminar runs on *Tuesdays from 15:00 to 16:00* at **STRAND BLDG S4.29**

16 January, 15:00-16:00, STRAND BLDG S4.29

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23 January, 15:00-16:00, STRAND BLDG S4.29

Speaker: **Cheuk Yu Mak** (University of Southampton)

Title: Loop group action on symplectic cohomology

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.

30 January, 15:00-16:00, STRAND BLDG S4.29

Speaker: **Andrew Dancer** (University of Oxford)

Title: Implosion, contraction and nonreductive quotients

Abstract: We describe the constructions of implosion and contraction for complex-symplectic or hyperkahler manifolds. Implosions are examples of nonreductive quotients in geometric invariant theory. We can interpret both constructions in terms of a generalisation of the Moore-Tachikawa category that was introduced in physics.

6 February, 15:00-16:00, STRAND BLDG S4.29

Speaker: **Liana Heuberger** (University of Bath)

Title: Applications of Laurent inversion to K-moduli

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 toric Fano 3-fold X of anticanonical volume 28 which smooths to a Fano threefold of Picard rank 4, we combine a local study of its singularities with the global deformation provided by Laurent inversion, and conclude that the K-moduli space is rational around X. This is joint work with Andrea Petracci.

13 February, 15:00-16:00, STRAND BLDG S4.29

Speaker: **Vlad Markovic** (University of Oxford)

Title: Distribution of random quasifuchsian surfaces in 3-manifolds

Abstract: I will discuss the distribution of geometrically and topologically nearly geodesic random surfaces in a closed hyperbolic 3-manifold $M$, and describe the resulting $\mathrm{PSL}(2,\mathbb{R})$ invariant measures on the Grassmann bundle of $M$. (Joint work with J. Kahn and I. Smilga.)

20 February, 15:00-16:00, STRAND BLDG S4.29

Speaker: **Clement Dupont** (Université de Montpellier)

Title: How to compute divergent integrals using logarithmic geometry

Abstract: One is sometimes faced with the task of assigning finite values to divergent integrals in a consistent and meaningful way. Since differential forms and integrals play a central role in geometry, how to think about divergent integrals in geometric terms? The goal of this talk will be to answer this question in the case of logarithmic divergences (such as the integral of 1/x near x=0). The idea is to pass from manifolds to slightly more general objects called manifolds with log corners. They are the differential geometer’s version of logarithmic varieties in algebraic geometry. A key ingredient of our construction is a new notion of morphism between manifolds with log corners (or logarithmic varieties) which is more flexible than the obvious one and faithfully records the geometric information needed to regularize divergent integrals. This is joint work with Erik Panzer and Brent Pym.

27 February, 15:00-16:00, STRAND BLDG S4.29

Speaker: **Richard Webb** (The University of Manchester)

Title: An equator theorem for the 2-sphere

Abstract: In this talk, we will focus on the group of Hamiltonian diffeomorphisms (and area-preserving homeomorphisms) of the 2-sphere. A tremendous amount of progress has been made in the study of these groups in the last few years, but many problems remain, including the Equator Conjecture. An equator on the 2-sphere is a simple closed curve whose complementary components have equal area. The Equator Conjecture predicts that for any positive K, there are pairs of equators such that any Hamiltonian diffeomorphism sending one equator to the other must have Hofer norm larger than K. We will prove an alternative conjecture, by replacing “Hofer norm” with “quantitative fragmentation norm”. To prove this, we construct new quasimorphisms defined on all area-preserving homeomorphisms on the 2-sphere, coming from methods inspired from mapping class groups and geometric group theory. Joint work with Yongsheng Jia.

5 March, **11:00-12:00**, STRAND BLDG **S3.31***

***Note non-standard time and location**

Speaker: **Dario Beraldo** (University College London)

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12 March, 15:00-16:00, STRAND BLDG S4.29

Speaker: **Marta Mazzocco** (University of Birmingham)

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19 March, 15:00-16:00, STRAND BLDG S4.29

Speaker: **Marie-Amélie Lawn** (Imperial College London)

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26 March, 15:00-16:00, STRAND BLDG S4.29

Speaker: **Michael Wemyss** (University of Glasgow)

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