Title: Arithmetic quantum unique ergodicity 
Abstract:
Let $M$ be a compact hyperbolic $d$-manifold. A basic problem of harmonic analysis on $M$ is understanding the asymptotic behaviour of eigenfunctions of the Laplace operator in the large eigenvalue limit. 
The quantum unique ergodicity, or QUE conjecture of Rudnick and Sarnak predicts that for any orthonormal basis $u_j$ of Laplace eigenfunctions the measures $|u_j|^2 dm$ become equidistributed as $j \to \infty$. 
A well-studied special case of the problem, known as arithmetic QUE, is when the manifold is arithmetic and the eigenfunctions $u_j$ are common eigenfunctions of the Laplacian and the Hecke operators. 
AQUE was obtained by Lindenstrauss for hyperbolic surfaces. In this talk we will discuss recent results, for manifolds of higher dimension. We will present some of the main ideas of the proofs, focusing on "escape from subvarieties".
Livestream/Recording: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=e8f26f21-6507...