University of York Geometry, Analysis and Mathematical Physics seminar 2025-26

All are welcome to attend the seminar, which usually takes place at 2:30pm on Tuesdays in the Topos during term time. (Directions to the Topos)

Autumn Semester 2025

Date	Speaker	Title
23 September
30 September	Amihay Hanany (Imperial)	Symplectic singularities, Magnetic quivers, and Hasse diagrams
7 October	Jiajun Yan (Rice)	A gauge-theoretic construction of 4-dimensional hyperkähler ALE spaces
14 October	Derek Harland (Leeds)	The BF Lagrangian 1-form and the Hitchin system
4 November	Mathew Bullimore (Durham)	Symmetry and Solitons
11 November	Tom Bridgeland (Sheffield)	Joyce structures on spaces of quadratic differentials
18 November	Daan Janssen (York)	Quantum electromagnetism on manifolds with corners
24 November 3-4pm in CSE/202 (Topos) Note the date and time!	Yizhi Wang (York)	Homotopy Groups of Stable Loci through Transversality
2 December	Jason Lotay (Oxford)	Einstein manifolds, G2 geometry and geometric flows
4 December 10:30-11:30am in CSE/202 (Topos) Note the date and time!	Nuno Romao (Isaac Newton Institute)	Vortices as Fermionic Particles
9 December	Linden Disney-Hogg (Leeds)	Locations of JNR skyrmions

Spring Semester 2026

Date	Speaker	Title
3 February	Graeme Wilkin (York)	TBA
10 February
17 February
24 February
3 March
10 March	Laura Fredrickson (Oregon)	TBA
17 March
24 March
14 April
21 April
28 April

Previous years' seminars

2024-25
2023-24
2022-23
2021-22
2020-21
2019-20

Abstracts

30 September. Amihay Hanany (Imperial)
Title. Symplectic singularities, Magnetic quivers, and Hasse diagrams
Abstract. Symplectic singularities fall into classes of different types: Klein/duVal singularities, Moduli spaces of instantons, Nilpotent orbits, Intersection of orbits and Słodowy slices, Slices in the affine Grassmanian, and more. They are of interest in both mathematics and physics. Their construction could be

in algebraic settings, like in the study of nilpotent orbits.
Higgs branch of a supersymmetric gauge theory with 8 supercharges - this is sometimes called HyperKähler quotient, sometimes Hamiltonian reduction.
Coulomb branch of a 3d N=4 supersymmetric gauge theory - I prefer to call it magnetic quiver and drop the long name.

Quivers play a crucial role in the construction, going back to the work of Kraft and Procesi '79, proceeding with many contributions over the years. Many quivers appear naturally in superstring theory, with or without brane constructions. This leads to great physical insights on the behavior of symplectic singularities. Some of the phenomena go under the name "3d mirror symmetry" and "symplectic duality".

7 October. Jiajun Yan (Rice)
Title. A gauge-theoretic construction of 4-dimensional hyperkähler ALE spaces
Abstract. Non-compact hyperkähler spaces arise frequently in gauge theory. The 4-dimensional hyperkähler ALE spaces are a special class of complete non-compact hyperkähler spaces. They are in one-to-one correspondence with the finite subgroups of SU(2) and have interesting connections with representation theory and singularity theory, captured by the McKay Correspondence.
In this talk, we give a gauge-theoretic construction of these spaces, inspired by Kronheimer’s original construction via a finite-dimensional hyperkähler reduction. In the gauge-theoretic construction, we realize each ALE space as a moduli space of solutions to a system of equations for a pair consisting of a connection and a section of a vector bundle over an orbifold Riemann surface, modulo a hyperkähler gauge group action.

14 October. Derek Harland (Leeds)
Title. The BF Lagrangian 1-form and the Hitchin system
Abstract. Lagrangian multiform theory is a variational framework for integrable systems. It is a counterpoint to the more conventional hamiltonian framework. In this talk I will explain how to construct lagrangian 1-forms in a geometric way. I will then explain how applying this construction to Hitchin's integrable system produces a BF lagrangian. This connects lagrangian multiform theory with the work of Costello and others on gauge theory and integrability.

4 November. Mathew Bullimore (Durham)
Title. Symmetry and Solitons
Abstract. I will discuss how symmetries, including generalised and non-invertible symmetries, control the spectrum of solitons in quantum field theory, focussing on soliton particles in 1+1 dimensions and vortices in 2+1 dimensions.

11 November. Tom Bridgeland (Sheffield)
Title. Joyce structures on spaces of quadratic differentials
Abstract. A Joyce structure on a complex manifold involves a one-parameter family of flat, non-linear, symplectic connections on the tangent bundle. It gives rise to a hyperkähler structure on the total space of this bundle. This is new terminology for old mathematics: writing the definition in local co-ordinates gives a system of p.d.e.s known as Plebanski's heavenly equations which date back to 1975. These geometries have received renewed interest recently due to (so far conjectural) relations with Donaldson-Thomas (DT) invariants. In this talk I will introduce the definition of a Joyce structure, and explain how to construct a class of non-trivial examples. This involves moduli spaces of vector bundles on algebraic curves equipped with both a connection and a Higgs field.

18 November. Daan Janssen (York)
Title. Quantum electromagnetism on manifolds with corners
Abstract. Inspired by a geometric perspective on the phase space of classical gauge theories on manifolds with boundaries and corners, we adapt a construction of pure electromagnetism as an (algebraic) quantum field theory to such manifolds. We include from the outset observables sensitive to boundary behaviour (so-called semi-local observables) in our theory, which allow us to discuss quantum analogues of phase space (Poisson) foliations and gluing procedures. We shall furthermore highlight the role of Hodge theory on manifolds with boundaries in the quantisation and analysis of this theory.

24 November. Yizhi Wang (York)
Title. Homotopy Groups of Stable Loci through Transversality
Abstract. We investigate the homotopy groups of stable loci in affine Geometric Invariant Theory (GIT), arising from linear actions of complex reductive algebraic groups on complex affine spaces. Our approach extends the infinite-dimensional transversality framework of Daskalopoulos-Uhlenbeck and Wilkin to this general GIT setting. Central to our method is the construction of a G-equivariant holomorphic vector bundle over the conjugation orbit of a one-parameter subgroup (1-PS), whose fibres are precisely the negative weight spaces determining instability. A key proposition establishes that a naturally defined evaluation map is transverse to the zero section of this bundle, implying that generic homotopies avoid all unstable and strictly semistable strata under certain dimensional inequalities. The framework will be illustrated with several examples during the seminar.

2 December. Jason Lotay (Oxford)
Title. Einstein manifolds, G2 geometry and geometric flows
Abstract. There are infinitely many positive Einstein metrics in dimension 7 and many can be encoded through G2 geometry. It is natural to ask about the stability of the associated G2 geometry with respect to natural geometric flows of G2 structures. I will report on joint works with A. Kennon and J. Stein that address this question, particularly for Einstein metrics with symmetries, demonstrating cases of both stability and instability.

4 December. Nuno Romao (Isaac Newton Institute)
Title. Vortices as Fermionic Particles
Abstract. I will revisit some of the surprising facts supporting the viewpoint that vortices quantise as fermionic (rather than bosonic) particles. One of such facts is an analogue of Sen’s conjecture, for which a complete proof exists in the simplest setting of vortices in line bundles.

9 December. Linden Disney-Hogg (Leeds)
Title. Locations of JNR skyrmions
Abstract. Skyrmions, topological solitons arising in nonlinear sigma models, have long been proposed as effective models for atomic nuclei. While exact solutions remain unknown, a variety of approximations, often inspired by better understood solitons such as monopoles and instantons, have been developed. In particular, Sutcliffe recently introduced a novel approximation using an ultra-discrete computation of the holonomy of a JNR instanton. In this talk, I will outline the mathematical framework behind this construction, before focusing particularly on the constituent locations of the resulting Skyrmions. I will present new theoretical and computational tools for analysing these locations, reveal their connections to classical geometry, and discuss their potential implications for future research.
Based on joint work with Josh Cork.

Introductory talk abstract. I will give a short overview of instantons and the ADHM construction, which is a backbone of the Atiyah-Manton approximation of skyrmions. In doing so, I will touch upon the recurring features and motivations that arise in the story of many topological solitons.

3 February. Graeme Wilkin (York)
Title. TBA
Abstract. TBA

10 March. Laura Fredrickson (Oregon)
Title. TBA
Abstract. TBA

Last updated 9 December, 2025