Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

 

Past events in this series


Thu, 22 May 2025
16:00
Lecture Room 4

Mordell–Weil groups of elliptic curves — beyond ranks

Alex Bartel
(University of Glasgow)
Abstract

If $E/\mathbb{Q}$ is an elliptic curve, and $F/\mathbb{Q}$ is a finite Galois extension, then $E(F)$ is not merely a finitely generated abelian group, but also a Galois module. If we fix a finite group $G$, and let $F$ vary over all $G$-extensions, then what can we say about the statistical behaviour of $E(F)$ as a $\mathbb{Z}[G]$-module? In this talk I will report on joint work with Adam Morgan, in which we investigate the simplest non-trivial special case of this very general question. Our work has surprising connections to questions about frequency of failure of the Hasse principle for genus 1 hyperelliptic curves, and to work of Heath-Brown on 2-Selmer group distributions in quadratic twist families.

Thu, 05 Jun 2025
16:00
Lecture Room 4

TBA

Dominik Bullach
(University College London)
Thu, 12 Jun 2025
16:00
Lecture Room 4

TBA

Chris Williams
(University of Nottingham)
Thu, 19 Jun 2025
16:00
Lecture Room 4

TBA

Hanneke Wiersema
(University of Cambridge)