University of York Geometry, Analysis and Mathematical Physics seminar 2024-25

All are welcome to attend the seminar, which usually takes place at 2pm on Tuesdays in the Topos during term time. (Directions to the Topos)

Autumn Semester 2024

Date	Speaker	Title
15 October	Benoît Vicedo (York)	(Higher) operations in topological and conformal QFTs from factorisation
22 October	Graeme Wilkin (York)	The Morse complex for semiprojective varieties
5 November	Ian McIntosh (York)	The geometric Toda equations for noncompact symmetric spaces
12 November	Ian McIntosh (York)	Equivariant minimal surfaces in the complex hyperbolic plane
19 November 3-4pm in the Topos Note the time!	Inder Kaur (Glasgow)	A Lefschetz (1,1) theorem for singular varieties
26 November	Martin Kerin (Durham)	Isometric rigidity of Wasserstein spaces
3 December	Ben Lambert (Leeds)	Nonlocal estimates for volume preserving mean curvature flow

Spring Semester 2025

Date	Speaker	Title
14 January
21 January
4 February	Kasia Wyczesany (Leeds)	TBA
11 February
18 February	Francesca Tripaldi (Leeds)	TBA
25 February	Stefano Negro (York)	TBA
4 March	Josh Cork (Leicester)	TBA
11 March
18 March
25 March
1 April
22 April
29 April
6 May

Previous years' seminars

2023-24
2022-23
2021-22
2020-21
2019-20

Abstracts

15 October. Benoît Vicedo (York)
Title. (Higher) operations in topological and conformal QFTs from factorisation
Abstract. Prefactorisation algebras (PFAs) axiomatise the algebraic structure of observables in QFTs. In the case of locally constant PFAs, which correspond to topological QFTs, I will describe how the PFA induces a (higher) algebraic structure on the gauge invariant observables of the TQFT. This involves an ordinary associative, unital product but typically also "higher" operations known as Massey products. I will also discuss the case of holomorphic PFAs in one complex dimension, which correspond to 2d CFTs, and explain how in this setting the PFA encodes the vertex algebra structure of the CFT.

22 October. Graeme Wilkin (York)
Title. The Morse complex for semiprojective varieties
Abstract. Moduli spaces of Higgs bundles admit a natural \(\mathbb{C}^*\) action, which makes them examples of semiprojective varieties. In the first paper on the subject, Hitchin introduced the moment map associated to the action of \(S^1 \hookrightarrow \mathbb{C}^*\) and showed that this is a perfect Morse-Bott function. In this talk I will describe the cup product on the Morse complex for both this moment map as well as minus the moment map. This setup applies more generally to semiprojective varieties satisfying an additional transversality condition. I will spend some time explaining the case of rank \(2\) twisted Higgs bundles, where these constructions relate to questions from classical geometry.

5 November. Ian McIntosh (York)
Title. The geometric Toda equations for noncompact symmetric spaces
Abstract. Different forms of the Toda equations keep turning up both in surface theory and gauge theory. Everyone knows that they are really equations on something like the Cartan subgroup of a simple Lie group. While these have been well studied when the group is compact, the noncompact case has (surprisingly) not been given a general treatment. The aim of the talk is to explain a classification of these equations which fit the geometrical setting of minimal surfaces in noncompact symmetric spaces, and also discuss when methods from gauge theory (especially stability ideas) can be applied to provide spaces of solutions.

12 November. Ian McIntosh (York)
Title. Equivariant minimal surfaces in the complex hyperbolic plane
Abstract. Over a series of three papers, two with John Loftin (Rutgers-Newark), a clear picture has emerged for the structure of the moduli space of equivariant minimal surfaces in the complex hyperbolic plane through the link with PU(2,1)-Higgs bundles. In this talk I'll give a survey of the interesting features, focussing on what we can learn about the minimal surfaces from their Higgs bundles, and some remaining open questions.

19 November. Inder Kaur (Glasgow)
Title. A Lefschetz (1,1) theorem for singular varieties
Abstract. The Lefschetz (1, 1) theorem is a classical result that tells us that for any smooth projective variety, a rational (1, 1) Hodge class comes from a algebraic cycle of codimension 1. In 1994, Barbieri-Viale and Srinivas gave a counter-example to the obvious generalization of this result to singular varieties. Inspired by Totaro, in this talk, I will give a modification of the statement of Lefschetz (1, 1) and show that it is satisfied by several singular varieties such as those with ADE-singularities and rational singularities. In particular, this Lefschetz (1,1) statement is satisfied by the varieties considered by Barbieri-Viale and Srinivas.
This is joint work with A. Dan.

26 November. Martin Kerin (Durham)
Title. Isometric rigidity of Wasserstein spaces
Abstract. The Wasserstein spaces over a metric space X are sets of Borel probability measures on X which are equipped with metrics derived from optimal transport. In general, the Wasserstein spaces reflect properties of the underlying metric space X. In this context, it is natural to ask whether the isometries of the Wasserstein space are related to those of X. In this talk, I will discuss some work in this direction conducted together with Mauricio Che, Fernando Galaz-García and Jaime Santos-Rodríguez.

3 December. Ben Lambert (Leeds)
Title. Nonlocal estimates for volume preserving mean curvature flow
Abstract. The volume preserving mean curvature flow (VPMCF) is the gradient flow of the area functional under the fixed enclosed volume constraint, meaning that stationary solutions of this flow are hypersurfaces of constant mean curvature. However, the non-local term in this evolution means that the flow satisfies significantly different properties to mean curvature flow and many "standard" mean curvature flow methods simply don't work. In this talk I will discuss some progress on nonlocal estimates which, amongst other things, imply that the singularities of VPMCF are in fact modelled by the (better understood) ancient solutions of mean curvature flow.
This work is joint with Elena Maeder-Baumdicker.

4 February. Kasia Wyczesany (Leeds)
Title. TBA
Abstract. TBA

18 February. Francesca Tripaldi (Leeds)
Title. TBA
Abstract. TBA

25 February. Stefano Negro (York)
Title. TBA
Abstract. TBA

4 March. Josh Cork (Leicester)
Title. TBA
Abstract. TBA

Last updated 27 November, 2024