UVic Dynamics and Probability Seminar: Vaughn Climenhaga

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.