Mathematical Institute

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.

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Large deviations of the Schwarzian field theory

Losev, I The Annals of Probability volume 54 issue 3 (01 May 2026)

Could you be an OMMS buddy?

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.

Week 7 Student Bulletin

Paul Ouwerkerk - The Oxford Variations

It's the Week 7 Student Bulletin!

MPLS ED&I Awards 2026 - call for nominations

Nominations are now open to recognise staff and students in MPLS who have gone above and beyond in their efforts to advance Equality, Diversity and Inclusion

Oliver Smithies Lecture 2 @Balliol College

Mathematical constructions for minimal surfaces (soap films) - Nicolaos Kapouleas

18 June at 5.15 p.m., Balliol College

Short stories 2 - Who shaves the barber?

That Robin Wilson, he doesn't half go on.

To infinity in fact, the topic of Robin's eighteenth and final talk on the equations that made mathematics. With an irritating little paradox to whet your appetite below and the full talk here.

Short stories 1 - Can England win the World Cup?

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.

Paid undergraduate summer internships at the University of Plymouth

University of Plymouth logo Perhaps you are looking for some summer work. The University of Plymouth is looking for students of home fee status, and in their 2nd or 3rd year of their degree, to undertake funded summer internships on the following projects:

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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