Devika Sharma (Weizmann Institute)
Congruent modular forms

We introduce congruences in modular forms, and see how they lead to the notion of a Hida family. We also review the theory of deformations of Galois representations. We use these concepts to understand the (local) behavior of the p-adic Galois representation attached to a (p-ordinary) modular form. 
Dirichlet's theorem in function fields (06/12/2017)