Counting and Equidistribution in 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
This minicourse focuses on counting and equidistribution in homogeneous spaces. We will discuss results for rank-one settings in detail, while briefly surveying developments in the higher-rank case.
The first lecture explains how to derive Haar mixing from Bowen-Margulis-Sullivan mixing by analyzing transversal intersections, a technique developed by Roblin. The second lecture applies these mixing results to study the distribution of Jordan and Cartan spectra, which correspond to counting closed geodesics and orbit points, respectively.