Number Theory Seminar

Speaker: Samuel Edwards (Yale)

Title: Exponential mixing of the geodesic flow on geometrically finite hyperbolic manifolds.

Abstract: Fundamental work by Duke-Rudnick-Sarnak and Eskin-McMullen connects orbital counting problems for discrete subgroups of Lie groups with equidistribution problems on homogeneous spaces. A key ingredient in obtaining the required equidistribution statements is mixing for diagonal flows on the underlying homogeneous space. I will discuss joint work with Hee Oh in which we obtain mixing with an exponential error term in the special case of the geodesic flow on geometrically finite hyperbolic manifolds with large enough critical exponent. Patterson-Sullivan densities and Burger-Roblin measures, the Lax-Phillips spectral gap for the Laplace operator on infinite volume geometrically finite hyperbolic manifolds, and complementary series representations are all involved in both the statement and proof of our result, and I will try to explain how these different objects are related in this setting.

The talk will take place on Zoom. If you would like to receive the Zoom link and are not part of our current NT Seminar mailing list, please contact the organizer.