Learning Seminar: p-adic modular forms

Spring 2020

Time and Place

Mondays 12-1:30p in 1 Illini Hall

Seminar info

Our goal for this semester is to learn about the theory of p-adic modular forms. We are mostly going to focus on Katz's moduli-theoretic interpretation of p-adic modular forms, though we will review the classical theory and Serre's approach to p-adic modular forms.

Schedule

You can find a tentative schedule here. If there is a topic you would like to volunteer to talk about, just email Dominic or Patrick Allen.

References

Below you can find some of the main references we will use in this seminar.

Katz's p-adic properties of p-adic moduli schemes and modular forms.
Gouvea's "Arithmetic of p-adic modular forms." This is available through the university's library system.
Serre's Formes modulaires et fonctions zeta p-adique.
Katz's paper on p-adic L-functions arising from moduli of elliptic curves.

Here are some expository papers on the subject that you may also find useful.

Calegari's lecture notes on Congruences between modular forms.
These notes by William Chen here