##### Department of Mathematics,

University of California San Diego

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### Math 211 B00 - Group Actions Seminar

## Pratyush Sarkar

#### Yale University

## Generalization of Selberg's 3/16 theorem for convex cocompact thin subgroups of SO(n, 1)

##### Abstract:

Selbergâ€™s 3/16 theorem for congruence covers of the modular surface is a beautiful theorem which has a natural dynamical interpretation as uniform exponential mixing. Bourgain-Gamburd-Sarnak's breakthrough works initiated many recent developments to generalize Selberg's theorem for infinite volume hyperbolic manifolds. One such result is by Oh-Winter establishing uniform exponential mixing for convex cocompact hyperbolic surfaces. These are not only interesting in and of itself but can also be used for a wide range of applications including uniform resonance free regions for the resolvent of the Laplacian, affine sieve, and prime geodesic theorems. I will present a further generalization to higher dimensions and some of these immediate consequences.

Host: Brandon Seward

### October 21, 2021

### 12:00 PM

Zoom ID 967 4109 3409 (email an organizer for the password)

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