Arithmetic Quantum Unique Ergodicity for 3-dimensional hyperbolic manifolds

Group Actions, Geometry and Dynamics
Event time: 
Monday, March 6, 2023 - 4:00pm
Zvi Shem-Tov
Speaker affiliation: 
Event description: 

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 infinity.
In the talk I will discuss a recent work on this problem for arithmetic quotients of the three dimensional hyperbolic space. I will discuss our key result that Hecke eigenfunctions cannot concentrate on certain proper submanifolds. Joint work with Lior Silberman.