91影视破解版

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Mathematics Institute

2026-27

Location: Zeeman B3.02.

Organisers: Giuseppe Cannizzaro, Harini Desiraju, Lukas Gr盲fner, Fabian H枚fer, and Nikolaos Zygouras

The probability seminar takes place on Wednesday afternoons at 4.00pm.

Term 1

  • 07 October 2026: Kostantinos Kavvadias (Courant Institute of Mathematical Sciences NYU):

 Title: The Conformally Invariant metric on $\mathrm{CLE}_4$

Abstract: Here. Link opens in a new window

  • 14 October 2026: Vincent Bansaye (脡cole Polytechnique):

Title: Replication in Archaea cells and branching within branching

Abstract: We consider particles following a branching process and living inside cells which divide. The division of a cell does not impact the dynamics of particles. First, we will focus on the biological motivation and the replication of chromosomes in archaea cells. The replication starts from several sites and a high variability in the number of chromosomes per cell is observed. Second, I will consider a constant cell division rate and look at the repartition of chromosomes within the cells. The associated first-moment semigroup now exhibits a family of positive eigenfunctions, and thus a family of spines. This is reminiscent of what happens for growth-fragmentation with exponential growth and a constant fragmentation rate [Doumic, Escobedo 15, & Bertoin, Watson 18]. In particular, in an intermediate regime, the size-biased particle goes to infinity while a uniform cell goes to 0 asttends to infinity. Finally, I will consider a division rate which depends on the number of particles. I will focus on a very simple model of exponential growth with fragmentation rate. This allows us to understand the intermediate regime for a non-constant while bounded division rate. We prove in that case a (surprising?) non-Malthusian behavior and show an analogy with weakly subcritical branching processes in random environments. This talk is based on collaborations within the HALOMATHS project and a work in progress with Aurelien Velleret.

Title: Construction of the 2D non-Abelian Yang-Mills-Higgs measure via stochastic quantisation

Abstract: In this talk, I will discuss the construction of the Yang-Mills-Higgs measure on the two-dimensional torus. In the 1980s, Parisi and Wu proposed a dynamical approach to constructing such measure via the corresponding Langevin dynamics, aiming to sidestep the difficulty of fixing a global gauge. Our result carries out this program rigorously and provides the first construction of the measure in 2D. I will begin by introducing the Yang-Mills-Higgs model and explaining Parisi and Wu's idea, and will then discuss the new ingredients needed to implement this approach rigorously, including a dynamical way of gauge fixing, covariant heat kernel estimates, and the exploitation of the instability of two-dimensional Yang-Mills connections.

This is based on joint work in preparation with Bjoern Bringmann, Sky Cao and Martin Hairer.

  • 04 November 2026: R茅mi Rhodes (Aix-Marseille Universit茅):
Title: H3 WZW model and the Liouville correspondence
Abstract: I will present a probabilistic construction of the three-dimensional hyperbolic Wess–Zumino–Witten (H鈧� WZW) model, starting directly from its path integral. Even though this construction works on arbitrary closed Riemann surfaces, in the presence of smooth background gauge fields, I will focus on the simple case of the Riemann sphere with trivial bundle. Within this framework, I will establish a rigorous correspondence between correlation functions of the H鈧� WZW model and those of Liouville conformal field theory, extending formulas by Ribault–Teschner and Hikida–Schomerus. A consequent part of the talk will be devoted to context and motivations.
This is joint work with Colin Guillarmou and Antti Kupiainen.
  • 11 November 2026: Jiawei Li (University of Edinburgh):

Title: Probabilistic well-posedness of dispersive PDEs beyond variance blowup

Abstract: In this talk, we use the fourth moment theorem to investigate a possible extension of probabilistic well-posedness theory of nonlinear dispersive PDEs with random initial data beyond variance blowup. As a model equation, we study the Benjamin-Bona-Mahony equation (BBM) with Gaussian random initial data. By introducing a suitable vanishing multiplicative renormalization constant on the initial data, we show that solutions to BBM with the renormalized Gaussian random initial data beyond variance blowup converge in law to a solution to the stochastic BBM forced by the derivative of a spatial white noise. I will also briefly discuss the results on 2D wave equation.

Based on the joint works with Guopeng Li (BIT), Shao Liu (Bonn), Tadahiro Oh (Edinburgh) and Nikolay Tzvetkov (ENS Lyon).

  • 18 November 2026: Mikhail Basok (Aalto University):
  • 25 November 2026: Julie Tourniaire (Universit茅 de Franche-Comt茅):
  • 02 December 2026: Thomas Mountford (脡cole Polytechnique Federale de Lausanne):
  • 09 December 2025: Juan Carlos Pardo Mill谩n (Centro de Investigati贸n en Matem谩ticas):

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