Wed, 04 Feb 2026

11:00 - 13:00
L4

Scaling limit of a weakly asymmetric simple exclusion process in the framework of regularity structures

Prof. Hendrik Weber
(University of Münster)
Abstract
We prove that a parabolically rescaled and suitably renormalised height function of a weakly asymmetric simple exclusion process on a circle converges to the Cole-Hopf solution of the KPZ equation. This is an analogue of the celebrated result by Bertini and Giacomin from 1997 for the exclusion process on a circle with any particles density. The main goal of this article is to analyse the interacting particle system using the framework of regularity structures without applying the Gärtner transformation, a discrete version of the Cole-Hopf transformation which linearises the KPZ equation. 
 
Our analysis relies on discretisation framework for regularity structures developed by Erhard and Hairer [AIHP 2019] as well as estimates for iterated integrals with respect to jump martingales derived by Grazieschi, Matetski and Weber [PTRF 2025]. The main technical challenge addressed in this work is the renormalisation procedure which requires a subtle analysis of regularity preserving discrete convolution operators. 
 
Joint work with R. Huang (Münster / now Pisa) and K. Matetski (Michigan State).


 

Wed, 21 Jan 2026

16:00 - 17:00
L4

Outer automorphism groups and the Zero divisor conjecture

Andrew Ng
(Bonn)
Abstract

I will report on ongoing joint work with Sam Fisher on showing that the mapping class group has a finite index subgroup whose group ring embeds in a division ring. Our methods involve p-adic analytic groups, but no prior knowledge of this will be assumed and much of the talk will be devoted to explaining some of the underlying theory. Time permitting, I will also discuss some consequences for the profinite topology for the mapping class group and potential extensions to Out(RAAG).

Mon, 19 Jan 2026

16:30 - 17:30
L4

Towards Computational Topological (Magneto)Hydrodynamics: long term computation of fluids and plasma

Kaibo Hu
((Mathematical Institute University of Oxford))
Abstract
From Kelvin and Helmholtz to Arnold, Khesin, and Moffatt, topology has drawn increased attention in fluid dynamics. Quantities such as helicity and enstrophy encode knotting, topological constraints, and fine structures such as turbulence energy cascades in both fluid and MHD systems. Several open scientific questions, such as corona heating, the generation of magnetic fields in astrophysical objects, and the Parker hypothesis, call for topology-preserving computation. 
 
In this talk, we investigate the role of topology (knots and cohomology) in computational fluid dynamics by two examples: relaxation and dynamo. We investigate the question of “why structure-preservation” in this context and discuss some recent results on topology-preserving numerical analysis and computation. Finite Element Exterior Calculus sheds light on tackling some long-standing challenges and establishing a computational approach for topological (magneto)hydrodynamics.

 
Mon, 02 Feb 2026
14:15
L4

Non-generic neck pinching in Lagrangian mean curvature flow

Spandan Ghosh
((Mathematical Institute University of Oxford))
Abstract
Lagrangian mean curvature flow (LMCF) is a way to deform a Lagrangian submanifold inside a Calabi--Yau manifold according to the negative gradient of the area functional. There are influential conjectures about LMCF due to Thomas--Yau and Joyce, describing the long-time behaviour and singularities of the flow. By foundational work of Neves, Type I singularities are ruled out under mild assumptions, so it is important to construct examples of Type II singularities with a given blow-up model. In this talk, we describe a general method to construct examples of Lawlor neck pinching in LMCF in complex dimension at least 3. We employ a P.D.E. based approach to solve the problem, as an example of 'parabolic gluing'. The main technical tool we use is the notion of manifolds with corners and a-corners, as introduced by Joyce following earlier work of Melrose. Time permitting, we will discuss how one may construct examples of generic neck pinching.
Mon, 09 Feb 2026
14:15
L4

Biharmonic maps on conformally compact manifolds

Marco Usula
((Mathematical Institute University of Oxford))
Abstract

In this talk, I will present a result proved in my recent paper arXiv:2502.13580. I will discuss biharmonic maps between (and submanifolds of) conformally compact manifolds, a large class of complete manifolds generalizing hyperbolic space. After an introduction to conformally compact geometry, I will discuss one of the main results of the paper: if S is a properly embedded sub-manifold of a conformally compact manifold (N,h), and moreover S is transverse to the boundary and (N,h) has non-positive curvature, then S must be minimal. This result confirms a conjecture known as the Generalized Chen’s Conjecture, in the conformally compact context.

Mon, 19 Jan 2026
14:15
L4

Quantitative symplectic geometry of disk tangent bundles

Johanna Bimmerman
((Mathematical Institute University of Oxford))
Abstract

Symplectic capacities are symplectic invariants that measure the “size” of symplectic manifolds and are designed to capture phenomena of symplectic rigidity.

In this talk, I will focus on symplectic capacities of fiberwise convex domains in cotangent bundles. This setting provides a natural link to the systolic geometry of the base manifold. I will survey current results and discuss the variety of techniques used to compute symplectic capacities, ranging from billiard dynamics to pseudoholomorphic curves and symplectic homology. I will illustrate these techniques using disk tangent bundles of ellipsoids as an example.

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