Generalization of Selberg’s 3⁄16 theorem for convex cocompact thin subgroups of SO(n, 1)

Pratyush Sarkar (Yale University)

03-May-2021, 16:15-17:30 (3 years ago)

Abstract: Selberg’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.

dynamical systemsnumber theory

Audience: general audience


New England Dynamics and Number Theory Seminar

Organizers: Dmitry Kleinbock, Han Li*, Lam Pham, Felipe Ramirez
*contact for this listing

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