Mon, 08 Dec 2025

16:30 - 17:30
L5

Improved regularity for nodal sets of Abelian Yang-Mills-Higgs equations.

Dr. Shengwen Wang
(Queen Mary University of London)
Abstract
We consider Yang-Mills-Higgs equations with U(1) gauge group. There is a deep relation between the adiabatic limit of a sequence of this physical PDEs and geometric PDE of minimal submanifolds. It is known that the energy measures are converging to a codimension 2 stationary varifold and the energy functional is converging to the codimension 2 mass. When the ambient dimension is \leq 4 or the sequence is minimizing, we can improve the weak convergence above and obtain strong regularity for the nodal sets that they are converging to the limit minimal submanifold with uniform $C^{2,\alpha}$ bounds. This is joint work with Huy Nguyen. 


 

Thu, 20 Nov 2025

12:00 - 13:00
C5

Existence and weak-strong uniqueness of measure solutions to Euler-alignment/Aw-Rascle-Zhang model of collective behaviour

Ewelina Zatorska
(University of Warwick)
Abstract
I will discuss the multi-dimensional Euler–alignment system with a matrix-valued communication kernel, which is motivated by models of anticipation dynamics in collective behaviour. A key feature of this system is its formal equivalence to a nonlocal variant of the Aw–Rascle–Zhang (ARZ) traffic model, in which the desired velocity is modified by a nonlocal gradient interaction. The global-in-time existence of measure solutions to both formulations,  can be obtained via a single degenerate pressureless Navier–Stokes approximation. I will also discuss a weak–strong uniqueness principle adapted to the pressureless setting and to nonlocal alignment forces. As a consequence of these results we can rigorously justify the formal correspondence between the nonlocal ARZ and Euler–alignment models: they arise from the same inviscid limit, and the weak–strong uniqueness property ensures that, whenever a classical solution exists, both formulations coincide with it.


 

Computing multiple solutions of systems of nonlinear equations with deflation
 Farrell, P
Tue, 27 Jan 2026
12:30

TBA

Jasper Knox
Abstract

WCMB, University of Oxford and University of Bristol

Tue, 24 Feb 2026
12:30

TBA

Emma Bouckley
Abstract

University of Cambridge

Looking for Volunteers for London Outreach Initiative

Her-AI is a new after-school outreach initiative supported by Oxford University and based in South London. It is designed to inspire and equip girls in grades 9-11 from diverse backgrounds to explore pathways into artificial intelligence (AI) and computer science. The programme combines hands-on workshops, mentorship from Oxford students and researchers, and immersive experience days in Oxford.

Tue, 25 Nov 2025
16:00
L6

Random matrices & operator algebras

Jennifer Pi
((Mathematical Institute University of Oxford))
Abstract

I'll discuss some of the history of the use of random matrices for studying the structure of operator algebras, starting with Voiculescu's notion free independence. We'll see that the original notions of convergence of random matrix models to certain infinite-dimensional operators is actually fairly weak, and discuss the more recent "strong convergence" phenomenon and its applications to C*-algebras. Finally, I'll touch upon some ongoing work, joint with A. Shiner and S. White, for continuing to use random matrix tools to prove structural properties of C*-algebras.

Tue, 18 Nov 2025
16:00
L6

Matrix-product state skeletons in Onsager-integrable quantum chains

Imogen Camp
(Department of Physics)
Abstract

Matrix-product state (MPS) skeletons are connected networks of local one-dimensional quantum lattice models with ground states admitting an MPS representation with finite bond dimension. In this talk, I will discuss how such skeletons underlie certain families of models obeying the Onsager algebra, and how these simple ground states provide a route to explicitly computing correlation functions.

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