Geometry of homogeneous spaces
Introductory Workshop: Topological and Geometric Structures in Low Dimensions & Geometry and Dynamics for Discrete Subgroups of Higher Rank Lie Groups January 26, 2026 - January 30, 2026
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
The topic of this minicourse is the geometry of the higher rank real semisimple Lie groups, their subgroups and their homogeneous spaces. We will focus on concrete examples like the group of real unimodular matrices. We will explain the classical structure theorems for these groups and their subgroups.
As an application, we will introduce various natural exponents, like the relative exponential growth or the decorrelation speed, associated to such homogeneous spaces. We will see that these exponents are always equal. This is a joint result with Siwei Liang that solves questions raised by Kobayashi and extends previous results of Patterson, Sullivan, Corlette, Leuzinger, Edwards-Oh and Lutsko-Weich-Wolf.