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
8 January	Simon Donaldson (Imperial)	Multiple facets of multi-valued functions
3 February	Graeme Wilkin (York)	Loop groups, Brieskorn's theorem and ALE spaces
10 February	Ian McIntosh (York)	Understanding the moduli space of equivariant minimal surfaces in real hyperbolic space using Higgs bundles
17 February
24 February	Martin Guest (Waseda)	Geometry of the spaces of monodromy data for the four real forms of the radial Tzitzeica equation
3 March
10 March	Laura Fredrickson (Oregon)	The asymptotics of hyperkähler metrics from Gaiotto-Moore-Neitzke's conjecture
17 March	Christiane Klein (York)	Teukolsky scalars on Kerr black holes and their quantization
24 March	Arya Yae (Oregon)	Metric Convergence from Parabolic Higgs Bundle Moduli Spaces to Hyperpolygon Spaces
14 April	Riccardo Ontani (Imperial)	Jeffrey-Kirwan localisation
5 May	Robert Hanson (Imperial)	TBA
6 May Joint seminar with Mathematical Physics	Lionel Mason (Oxford)	TBA
12 May	Richard Thomas (Imperial)	TBA
19 May
26 May
9 June
16 June

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.

8 January. Simon Donaldson (Imperial)
Title. Multiple facets of multi-valued functions
Abstract. Over the past decade "multi-valued" solutions of elliptic PDE have entered in a variety of areas in differential geometry. By multi-valued we mean that there is a singular set of codimension 2 and the solutions have a non-trivial monodromy around the singular set. The classical example is the square root in complex function theory. In higher dimensional situations an interesting feature from the point of view of analysis is that the singular set is not determined a priori but is part of the solution, similar to free boundary problems. In the first part of the talk we will explain this background and indicate some of the areas in which these objects have arisen (gauge theory, calibrated geometry, exceptional holonomy). In the last part of the talk we will describe some explicit solutions found using classical integral representation formulae, related to twistor theory.

3 February. Graeme Wilkin (York)
Main Talk Title. Loop groups, Brieskorn's theorem and ALE spaces
Abstract. Gravitational instantons are classified by the asymptotic behaviour of their metric near the boundary. In the first part of the talk I will describe joint work with Rafe Mazzeo, where we study partial compactifications of ALE gravitational instantons that have the same underlying complex manifold as the ALG gravitational instantons constructed by Hein and recently classified by Chen and Chen. The asymptotically locally Euclidean (ALE) instantons have a beautiful classification (due to Kronheimer) in terms of affine ADE Dynkin diagrams and in the last part of the talk I will describe work in progress to put the above construction in a more general framework and give a gauge-theoretic construction of these spaces in type A using loop groups and Brieskorn's theorem.

Introductory Talk Title. Introduction to Kleinian singularities and their deformations
Abstract. Klein's study of quintic polynomial equations in the 1880s led him to investigate quotients \(\mathbb{C}^2 / \Gamma\), where \(\Gamma \subset \mathsf{SU}(2)\) is a finite subgroup. Moving forward to the 1970s and 1980s, the McKay correspondence connects the representation theory of the group \(\Gamma\) with the topology of the resolutions and deformations of these quotients and work of Kronheimer shows that they admit the structure of a hyperkähler gravitational instanton. In this talk I will give an overview of these results with a focus on the type A example where everything can be done explicitly.

10 February. Ian McIntosh (York)
Title. Understanding the moduli space of equivariant minimal surfaces in real hyperbolic space using Higgs bundles
Abstract. Over a series of papers (some joint with John Loftin, Rutgers-Newark) we developed a way of parametrising minimal surfaces in real and complex hyperbolic spaces by using nonabelian Hodge theory to identify them with certain kinds of Higgs bundles. This talk will describe the real hyperbolic space case, since this is the most straightforward, and explain what information we can deduce about minimal surfaces using this approach.

The pre-talk will be an introduction to the "fundamental theorem of submanifold theory" for homogeneous spaces and present the Gauss-Codazzi-Ricci equations in this context.

24 February. Martin Guest (Waseda)
Title. Geometry of the spaces of monodromy data for the four real forms of the radial Tzitzeica equation
Abstract. There are four real forms of the Tzitzeica equation. They are distinguished from each other by their geometrical interpretations, as well as by their analytic properties. We focus on the special case of radial solutions, which can be regarded as real solutions of a version of the Painleve III equation, and hence correspond to monodromy data of a linear isomonodromic system. The spaces of monodromy data are explicitly computable smooth surfaces in three-dimensional space. We discuss the interplay between the geometrical properties of the monodromy data and the analytic properties of solutions.

The pre-talk will be about Stokes data with the goal of "de-mystifying the Stokes data".

10 March. Laura Fredrickson (Oregon)
Title. The asymptotics of hyperkähler metrics from Gaiotto-Moore-Neitzke's conjecture
Abstract. Hitchin's equations are a system of gauge theoretic equations on a Riemann surface that are of interest in many areas including representation theory, Teichmüller theory, and the geometric Langlands correspondence. The Hitchin moduli space carries a natural hyperkähler metric, a rich and rigid geometric structure. An intricate conjectural description of its asymptotic structure appears in the work of Gaiotto-Moore-Neitzke. I will discuss some recent and less-recent results using tools coming out of geometric analysis which are well-suited for verifying these extremely delicate conjectures. This strategy often stretches the limits of what can currently be done via geometric analysis, and simultaneously leads to new insights into these conjectures.

17 March. Christiane Klein (York)
Title. Teukolsky scalars on Kerr black holes and their quantization
Abstract. Perturbations of rotating black holes play an important role in the measurement of black holes. However, studying these perturbations is a non-trivial problem, and this becomes even more prominent when one is interested in quantum perturbations. One of the tools to tackle this problem are the Teukolsky scalars. In fact, these scalars do not only help with the classical problem, but they may also serve as a stepping stone towards understanding linearized quantum gravity in rotating black holes. In this talk, I will describe how the Teukolsky scalars arise from the metric perturbation and how they can be quantized. I construct a physically motivated state for the quantum theory which can serve as a starting point for exploring linear quantum gravity effects in rotating black holes.
This talk is based on joint work with Dietrich Häfner.

24 March. Arya Yae (Oregon)
Title. Metric Convergence from Parabolic Higgs Bundle Moduli Spaces to Hyperpolygon Spaces
Abstract. The moduli space of parabolic Higgs bundles on a Riemann sphere \(\mathbb{P}^1\) with n marked points is a hyperkähler manifold with a rich geometric structure, bearing close ties to character varieties, integrable systems, and Teichmüller spaces. Points in the moduli space correspond to solutions to Hitchin's equations, which arise via dimensional reduction of the Yang-Mills equations. On certain submanifolds, the solutions correspond to Kähler-Einstein connections, and on others they correspond to uniformization metrics on \(\mathbb{P}^1\) with conical singularities at the n marked points; in general, solutions are very hard to find.

We show that under a fine-tuned degeneration of the moduli parameters, the hyperkähler metric on the moduli space converges pointwise to that of an embedded Nakajima quiver variety called hyperpolygon space. The proof uses a construction of model solutions to Hitchin's equations near the marked points, a delicate gluing procedure, and an application of the analytic implicit function theorem in the degenerate limit to perturb the approximate solution to an actual solution. This talk is based on joint work with Laura Fredrickson.

14 April. Riccardo Ontani (Imperial)
Title. Jeffrey-Kirwan localisation
Abstract. Computing integrals on moduli spaces is a central problem in enumerative geometry. I will recall a powerful technique for computing such integrals, inspired by an idea of Witten and established by Jeffrey and Kirwan using methods from symplectic geometry. Their approach requires the moduli spaces under consideration to be sufficiently smooth. I will then report on joint work with Richard Thomas, in which we show that the formula continues to hold for singular moduli spaces M, where integrals are replaced by intersection products and the fundamental class [M] is replaced by a "virtual" fundamental class [M]^vir.

Introductory talk title. Equivariant cohomology and ABBV localisation
Abstract. I will give a brief introduction to the localisation formula of Atiyah-Bott-Berline-Vergne, which expresses integrals on a manifold X with a torus action in terms of local data at the fixed locus X^T.

5 May. Robert Hanson (Imperial)
Title. TBA
Abstract. TBA

6 May. Lionel Mason (Oxford)
Title. TBA
Abstract. TBA

12 May. Richard Thomas (Imperial)
Title. TBA
Abstract. TBA

Last updated 22 April, 2026