Fri, 28 Nov 2025
12:00
Quillen Room N3.12

Character theory of fusion systems

Tom Lawrence
(University of Loughborough)
Abstract

Fusion systems are a generalisation of finite groups designed in a way to capture local structure at a prime motivated by the existence of "exotic" fusion systems; local structures that do not appear in any finite group. In this talk I will give a brief introduction to fusion systems with emphasis on how they relate to groups. I will then discuss recent work done on fusion invariant character theory, concluding with a short excursion into biset functor theory to state a character value formula for "induction" between fusion systems and a Frobenius reciprocity analogue.

Fri, 13 Feb 2026
12:00
Quillen Room N3.12

Small essential 2-subgroups in fusion systems

Joshua Bridges
(University of Birmingham)
Abstract

A (saturated) fusion system on a p-group P contains data about conjugacy within P, the typical case being the system induced by a group on its Sylow p-subgroup. Fusion systems are completely determined by looking at their essential subgroups, which must admit an automorphism of order coprime to p. For p=2, we describe two new methods that address the question: given an essential subgroup $E<P$ of a fusion system on P, what can we say about P? In particular, one method gives us sufficient conditions to deduce that $E\triangleleft P$, while the other explores cases where we have strong control over the normaliser tower of E in P.

Fri, 30 Jan 2026
12:00
Quillen Room N3.12

Three realisations of theta functions via the Heisenberg representation

Allan Perez Murillo
(University of Bristol)
Abstract
The classical theta functions appear throughout number theory, geometry, and physics, from Riemann’s zeta function to the projective geometry of abelian varieties. Despite these appearances, theta functions admit a unifying description under the lens of representation theory.
 
In this talk, I will explain how the Heisenberg representation, together with the Stone–von Neumann–Mackey theorem, provides a framework that
identifies three equivalent realizations of theta functions:
  • as holomorphic functions on certain symplectic spaces
  • as matrix coefficients of the Heisenberg (and metaplectic) representation,
  • as sections of line bundles on abelian varieties.
I will describe how these perspectives fit together and, if time permits, illustrate the equivalence through concrete one-dimensional examples. The
emphasis will be on ideas rather than technicalities. I will aim to make the talk self-contained, assuming familiarity with complex geometry and representation theory; background in Lie theory and harmonic analysis will be helpful but not essential.

Everyone is invited to join Mathematrix and the Mirzakhani Society for the launch party of the Oxford Women and Non-binary People in Mathematics Day (28 February). We’ll be in the South Mezzanine from 3 pm on Friday Jan 30 (following the official launch during Fridays@2) with coffee, tea, and sweet treats. Come along for a break and to learn all about OxWIM Day 2026.

Registrations for OxWIM Day is open. Find out more here.

THE FBSDE APPROACH TO SINE–GORDON UP TO 6π
Gubinelli, M Annals of Probability

The key lesson from the digital age is don't leave the best bit of your song or film until the end. In which case the Stone Roses would have had no chance. Standing Here is far from their best song (it was a B-Side) but the outro from 3.07 turns it in to gold. Skip the first 3.06 if you wish though it ain't so bad.

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