A p-adic approach to automorphic forms on Shimura curves. Computation and applications

The explicit computation of spaces of automorphic forms is a
very active and useful area of research in computational number
theory. Several authors have described algorithms to compute these
Hecke modules: to name a few, John Voight, Matt Greenberg and Lassina
Dembélé have described algorithms that work in different levels of
generality. In joint work with Cameron Franc, we propose a p-adic
approach to this problem, via understanding quotients of Bruhat-Tits
buildings.

In this talk we will give an introduction to this subject and explain
our approach to these explicit computations. If time permits we will
be able to see some Heegner point computations.