Seminar: Analytic families of p-adic modular forms in level 1

Dino Destefano will give a talk on Analytic families of p-adic modular forms in level 1.

Abstract: The results of Coleman allow to embed classical modular forms into p-adic analytic families. This gives us a powerful tool to study congruences between classical modular forms. The study of the radius of analytic families passing through an eigenform  of fixed, finite slope is a difficult task: even computational examples are rare in the literature.

I will give an overview of the subject, introducing the p-adic modular forms and presenting the relevant problems. If time permits, I will show how one can obtain results for fixed primes.

The lecture is part of the ALG/NCG/TOP Ph.D. students' seminar.