Philadelphia Area Number Theory Seminar

Wednesday, March 1, 2023 - 3:30pm

Zvi Shem-Tov

Institute for Advanced Study

The Quantum Unique Ergodicity conjecture of Rudnick and Sarnak says that eigenfunctions of the Laplacian on a compact manifold of negative curvature become equidistributed as the eigenvalue tends to in nity. In the talk I will discuss a recent work on this problem for arithmetic quotients of the three dimensional hyperbolic space. I will present a rather detailed proof of our key result that these eigenfunctions cannot concentrate on certain proper submanifolds. Joint work with Lior Silberman.