Mon, 15 Jun 2026
16:00
C3

Eigenvarieties and p-adic rigidity for GSp4

Charlotte Clare-Hunt
((Mathematical Institute University of Oxford))
Abstract

There has been substantial progress in the construction of eigenvarieties and $p$-adic families of automorphic forms, and their relationship with Selmer groups and ($p$-adic) $L$-functions. In this talk I will introduce some of these constructions, starting with modular forms, and the concept of complete $p$-adic rigidity: the non-existence of nontrivial $p$-adic deformations. I will explain some of the techniques used to study the geometry of eigenvarieties, and how these specialise to show that certain noncuspidal 'Saito—Kurokawa' points are completely $p$-adically rigid. If time permits, I will also briefly outline how similar strategies may be used to construct $p$-adic families through cuspidal, nonholomorphic Saito—Kurokawa points and to produce nontrivial Selmer classes predicted by the Bloch—Kato conjecture. 

Large deviations of the Schwarzian field theory
Losev, I The Annals of Probability volume 54 issue 3 (01 May 2026)

As you may know, the MSc in Mathematical Sciences (OMMS) is a standalone MSc which runs parallel with Part C. To help the MSc students feel welcomed to the department, we have a buddy system where our OMMS students are paired with current Part B students who will be staying on to Part C and they can communicate over the summer if they choose. A buddy would be someone the MSc student could ask informal questions (a bit like a college parent). MSc students and buddies would then be free to decide when to meet during the academic year.

The World Cup is almost here and everyone has an opinion about likely winners. But being mathematicians, we have insisted on looking at the data, and we think we have found the secret to predicting results.

Josh Bull is our analyst in the studio.

Tue, 16 Jun 2026

12:00 - 13:00
C5

Global existence for a cross diffusion system with different mobilities

Charles Elbar
(Université Claude Bernard Lyon 1)
Abstract

We consider a cross diffusion system of two populations, often called the Busenberg-Travis system. The two species are transported by the same pressure gradient with Darcy’s law, modeling overcrowding effect (populations tend to move away from regions of high pressure). However, their mobility is different: the first species moves with mobility 1, whereas the second moves with mobility \nu. The difficulty to prove existence is to prove strong compactness of each densities, which we achieve with a variant of the div-curl lemma applied to evolution PDEs.

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