Colloquium-Counting geodesics

Date and Time: November 5th, 2021, 1-2pm;

Place: Zoom
Zoom link:

Speaker: Prof. Vaughn Climenhaga (University of Huston) 

Title: Counting geodesics

Abstract: For negatively curved Riemannian manifolds, various natural geometric quantities grow exponentially quickly: the volume of a ball in the universal cover; the number of "distinguishable" geodesics of a given length; the number of closed geodesics with length below a given threshold. Margulis gave very precise asymptotic estimates in this setting. After surveying the general background and history of Margulis-type results, I will describe joint work with Gerhard Knieper and Khadim War in which we obtain Margulis asymptotics for surfaces without conjugate points.