Abstract:
Let X be a hyperbolic surface. In this talk, I will begin by discussing the intersection number of closed geodesics on X. When X is compact, I will explain a bound on the intersection number in terms of the lengths of the geodesics and the geometry of X. Next, I will describe the equidistribution of intersection points on X in the finite-volume setting. Finally, I will show how random simple closed geodesics provide a new perspective on the study of Teichmüller space.