Geometry MMA Seminar: The geometry of random hyperbolic subsurfaces

Speaker:   Francisco Arana Herrera, UMD

Title:   The geometry of random hyperbolic subsurfaces

Abstract:  Cutting a hyperbolic surface along a simple closed geodesic yields a hyperbolic subsurface with totally geodesic boundary. For a given hyperbolic surface, what is the expected geometry of these subsurfaces? We discuss recent joint work with Aaron Calderon showing that these subsurfaces look like random metric ribbon graphs in the sense of Kontsevich. In particular, the limiting law does not depend on the initial choice of hyperbolic surface. This result strengthens Mirzakhani’s famous counting results for simple closed geodesics on hyperbolic surfaces. 

Time: Monday, February 19, 2024 – 10:30am-11:30am

Place: Exploratory Hall, Room 4106