MI

 

It's the Week 1 Student Bulletin!

We hope the first week back of teaching has gone well, and you've settled back into university life. 

Read on for next week's Fridays@2, a paid summer maths counsellor opportunity, and more of your favourite shorts!

Generalised multilevel Picard approximations
Giles, M Jentzen, A Welti, T IMA Journal of Numerical Analysis
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).


 

An Algebro-geometric Higher Szemeredi Lemma
Hrushovski, E ZAG Handbook of Algebraic Geometry 349-350 (28 Oct 2025)
ARCH-COMP25 Category Report: Stochastic Models
Abate, A Akbarzadeh, O Blom, H Haesaert, S Hassani, S Lavaei, A Mathiesen, F Misra, R Nejati, A Niehage, M Ørum, F Remke, A Samari, B Wang, R Wisniewski, R Wooding, B Zaker, M Epic Series in Computing volume 108 122-151 (01 Jan 2025)
Wed, 11 Feb 2026
15:00
L6

The distribution of zeroes of  modular forms 

Zeev Rudnick
Abstract

I will discuss old and new results about the distribution of zeros of modular forms, and relation to Quantum Unique Ergodicity. It is known that a modular form of weight k has about k/12 zeros in the fundamental domain . A classical question in the analytic theory of modular forms is “can we locate the zeros of a distinguished family of modular forms?”. In 1970, F. Rankin and Swinnerton-Dyer proved that the zeros of the Eisenstein series all lie on the circular part of the boundary of the fundamental domain. In the beginning of this century, I discovered that for cuspidal Hecke eigenforms, the picture is very different - the zeros are not localized, and in fact become uniformly distributed in the fundamental domain. Very recently, we have investigated other families of modular forms, such as the Miller basis (ZR 2024, Roei Raveh 2025, Adi Zilka 2026), Poincare series (RA Rankin 1982, Noam Kimmel 2025) and theta functions (Roei Raveh 2026),  finding a variety of possible distributions of the zeroes.

Further Information

Joint seminar with Number Theory.

Tue, 17 Feb 2026

14:00 - 15:00
C3

Approximating Processes on Complex Networks

George Cantwell
(University of Cambridge)
Abstract
Graphs are an attractive formalism because, despite over-simplification, they seem capable of representing the rich structure we see in complex dynamical systems. 
Mean-field style approximations can be highly effective at describing equilibrium systems. In this talk, we will begin by reviewing such methods and showing how to make systematic corrections to them via spatial expansions. Adapting the methods for dynamic systems is an ongoing project. Through two simple case studies -- the random walk and the SIS model -- we make a start on this. In both case studies non-trivial predictions are made.



 

Tue, 10 Mar 2026
14:00
C3

TBA

Márton Pósfai
(Central European University)
Tue, 03 Mar 2026

14:00 - 15:00
C3

Explaining order in non-equilibrium steady states

Dr. Jacob Calvert
(Sante Fe Institute)
Abstract
Statistical mechanics explains that systems in thermal equilibrium spend a greater fraction of their time in states with apparent order because these states have lower energy. This explanation is remarkable, and powerful, because energy is a "local" property of states. While non-equilibrium steady states can similarly exhibit order, there can be no local property analogous to energy that explains why, as Landauer argued 50 years ago. However, recent experiments suggest that a broad class of non-equilibrium steady states satisfy an approximate analogue of the Boltzmann distribution, with tantalizing possibilities for basic and applied science.
 
I will explain how this analogue can be viewed as one of several approximations of Markov chain stationary distributions that arise throughout network science, random matrix theory, and physics. In brief, this approximation "works" when the correlation between a Markov chain's effective potential and the logarithm of its exit rates is high. It is therefore important to estimate this correlation for different classes of Markov chains. I will discuss recent results on the correlation exhibited by reaction kinetics on networks and dynamics of the Sherrington–Kirkpatrick spin glass, as well as highly non-reversible Markov chains with i.i.d. random transition rates. (Featuring joint work with Dana Randall and Frank den Hollander.)
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