** Valentin Blomer** (Toronto)

*Bounding sup-norms of cusp forms*

Given an L^{2}-normalized cusp form f on a modular curve X_{0}(N), what can be
said about pointwise bounds for f? For Hecke eigenforms, we will prove the
first non-trivial bound in terms of the level N as well as hybrid bounds in
terms of the level and the Laplacian eigenvalue. Similar techniques work for
functions on other spaces, e.g. quotients of quaternion algebras.
This is joint work with R. Holowinsky.