Nicolas Templier

We present the uniform distribution of roots of quadratic congruences on the unit circle. Several proofs have been rediscovered over the years. I will review some of the very different methods involved -- ergodic theory, exponential sums, automorphic...

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...