Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: An introduction to Patterson-Sullivan measures for Kleinian groups
Speaker: Ritwik Chakraborty, TIFR, Mumbai
Date: April 8, 2024
Time: 15:30:00 Hours
Venue: A-369
Abstract: A Kleinian group is a discrete group of orientation-preserving isometries of the $n$-dimensional hyperbolic space $H^n$, where n is at least 2. In this talk, given a convex, co-compact Kleinian group we will define a family of measures in the same measure class, called Patterson-Sullivan measures, on the boundary at infinity of $H^n$ supported on the limit set of the group. Key to defining these measures will be the study of the Poincare series associated with the group. We will aim to prove that for a convex, co-compact Kleinian group, the Patterson-Sullivan measure is proportional to the Hausdorff measure on the boundary at infinity of $H^n$ of dimension same as the radius of convergence of the Poincare series associated with the group.
Title of Talk: An introduction to Patterson-Sullivan measures for Kleinian groups
Speaker: Ritwik Chakraborty, TIFR, Mumbai
Date: April 8, 2024
Time: 15:30:00 Hours
Venue: A-369
Abstract: A Kleinian group is a discrete group of orientation-preserving isometries of the $n$-dimensional hyperbolic space $H^n$, where n is at least 2. In this talk, given a convex, co-compact Kleinian group we will define a family of measures in the same measure class, called Patterson-Sullivan measures, on the boundary at infinity of $H^n$ supported on the limit set of the group. Key to defining these measures will be the study of the Poincare series associated with the group. We will aim to prove that for a convex, co-compact Kleinian group, the Patterson-Sullivan measure is proportional to the Hausdorff measure on the boundary at infinity of $H^n$ of dimension same as the radius of convergence of the Poincare series associated with the group.