Thu, 30 Apr 2026
16:00
Lecture Room 4

Propagating Langlands functoriality on eigenvarieties

Zachary Feng
((Mathematical Institute University of Oxford))
Abstract

A test case for the Langlands functoriality principle is the tensor product lifting of automorphic representations of $\mathrm{GL}(m) \times \mathrm{GL}(n)$ to automorphic representations of $\mathrm{GL}(mn)$. This has been established in several key instances: for $m=n=2$ by Ramakrishnan (2000), for $m=2$ and $n=3$ by Kim-Shahidi (2002), and more recently for $m=2$ and arbitrary $n$ over $\mathbb{Q}$ by Arias-de-Reyna-Dieulefait-Pérez (2025) under certain assumptions, including that the $\mathrm{GL}(2)$ factor has level 1. I will discuss some new results in the case of $\mathrm{GL}(2) \times \mathrm{GL}(n)$, as well as ideas for how to go further, when $m>2$, using a p-adic propagation technique introduced by Newton-Thorne (2021).

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Wed, 06 May 2026
17:00
Lecture Theatre 1

Space, time and Shakespeare - Paul Glendinning

Paul Glendinning
(University of Manchester)
Further Information

Shakespeare’s work provides a snapshot of how people made sense of the world around them: how they solved problems (how large is an opposing army?) and how they navigated a complex environment (does the sun rise in the east?).

In this talk Paul will explore how scientific and technological ideas are woven into Shakespeare’s plays and sonnets through actions, words and conversations between characters. He will mention Copernicus twice, once as an over-interpretation. His interest is in how we think within structures, not whether the structures are correct. Almanacs, mirrors and Dee’s vision of applied mathematics will be part of the story. He will also talk about nothing.

Paul Glendinning is the Beyer Professor of Applied Mathematics at the University of Manchester. His research is in applied dynamical systems and he has been President of the IMA (2022-2023) and Scientific Director of the International Centre for Mathematical Sciences in Edinburgh (2016-2021).

Please email @email to register to attend in person.

The lecture will be broadcast on the Oxford Mathematics YouTube Channel on Wednesday 27 May at 5-6 pm and any time after (no need to register for the online version).

The Oxford Mathematics Public Lectures are generously supported by XTX Markets.

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