Families of p-adic automorphic forms on unitary groups

We will start with an introduction to p-adic automorphic forms and then discuss a variant of the q-expansion
principle (called the Serre-Tate expansion principle) for p-adic automorphic forms on unitary groups of arbitrary
signature. We outline how this can be used to produce p-adic families of automorphic forms on unitary groups,
which has applications to the construction of p-adic L-functions. This is done via an explicit description of the
action of certain differential operators on the Serre-Tate expansion.

The talk is based on joint work with Ana Caraiani, Ellen Eischen, Elena Mantovan and Ila Varma.