On the Quantum Unique Ergodicity Conjecture for Hyperbolic Arithmetic Manifolds

We will discuss recent results towards the quantum unique ergodicity conjecture of Rudnick and Sarnak, concerning the distribution of Hecke--Maass forms on hyperbolic arithmetic manifolds. The conjecture was resolved for congruence surfaces by Lindenstrauss and we focus on manifolds of higher dimension, where substantial new difficulties arise. Based on joint works with Alexandre de Faveri and Lior Silberman.