##### Department of Mathematics,

University of California San Diego

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### Math 211B - Group Actions Seminar

## Zvi Shem-Tov

#### Institute for Advanced Study

## Arithmetic Quantum Unique Ergodicity for 3-dimensional hyperbolic manifold

##### Abstract:

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 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.

Host: Brandon Seward

### March 9, 2023

### 10:00 AM

Zoom ID 967 4109 3409

Email an organizer for the password

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