Geometry and Topology Seminar: Counting geodesics on random hyperbolic surfaces

Speaker: Benjamin Dozier from Cornell University

Host: Xiaolong Hans Han

Abstract: There are several natural models of random hyperbolic surfaces: random covers of a fixed surface, random gluings of ideal triangles, and Weil-Petersson measure. The study of these is often motivated by a fruitful analogy with random regular graphs, which becomes stronger as the genus/number of vertices goes to infinity. I will discuss the problem of counting closed geodesics on these objects, and in particular the “birthday paradox”, which concerns the length scale at which closed geodesics become very likely to self-intersect. A key tool is effective mixing of the geodesic flow and its relation to spectral gap of the Laplace operator. Based on joint work with Jenya Sapir.

Time: 4/17 Thursday, 8am

Location: Join Zoom Meeting ID: 961 6068 8897 (Passcode: 829231)