Automorphic forms study group

(Study group in Oxford, Hilary Term 2023)

This is a learning seminar mainly intended for masters and graduate students at Oxford, but everyone is welcome! If you have any questions, contact me or Zach. The goal is to cover the most important sections of Jayce Getz’s notes, and to develop the skills needed work with automorphic forms and representations.

Prerequisites:

We will assume few prerequisites beyond some knowledge of number fields and basic representation theory.

Schedule:

We will meet on Thursdays 13:30 in Room C5, which is the same time slot as the modularity lifting seminar last term.

Below is a tentative list of topics we intend to cover, although we’ll probably have to go beyond Hilary term if we want to cover all of them.

Topic	Speaker	Notes
1. Algebraic groups and adeles	Mick	notes
2. Non-archimedean theory of automorphic reps	Zach	notes
3. The Satake isomorphism	Håvard	notes
4. Local Langlands correspondence	Zach	notes
5. Archimedean theory of automorphic reps	James N.	notes
6. Automorphic representations	Alex	notes
7. The case of GL2/Q and modular forms	Arun	notes

A PDF containing all the notes so far can be found here. Comments, corrections and criticisms are most welcome!

Resources and references:

The main reference is Jayce Getz’s notes. Additionally, the following might be useful:

Bump’s classic book Automorphic Forms and Representations.
Getz and Hahn’s book An Introduction to Automorphic Forms (…).
Various notes and references from George’s seminar from last year might be useful.

Last updated: 19 November 2024