DASOM Lecture Series

Beibei Liu (Ohio State University)

Date/Time: September 3 (Thu) 14:00–15:15, September 4 (Fri) 10:30–11:45 & 14:00–15:15

Place: Room 301, Building 129

Title: Geometrically infinite Kleinian groups

Abstract: A Kleinian group is a discrete subgroup of the isometry group of hyperbolic space. Geometrically finite Kleinian groups form an important class with particularly well-behaved geometric and dynamical properties, whereas geometrically infinite groups are considerably more mysterious and remain less well understood. In this series of talks, I will discuss several characterizations of geometric finiteness and infiniteness, with particular emphasis on the critical exponent and the Hausdorff dimension of the limit set. I will then describe methods for computing and estimating these quantities, together with some recent developments in the study of Kleinian groups. Finally, I will discuss gap phenomena for critical exponents arising from Kazhdan's Property (T) for more general Lie groups.