Number Theory Seminar: On the sup-norm of Maass forms of large level

We discuss the question of quantitative bounds on the sup-norm of automorphic cusp forms. We present an improvement on a recent result by Blomer-Holowinski on Hecke-Maass forms on $X_0(N)$ with large level $N$. Analogous results are then established for all compact arithmetic surfaces by a geometric approach.