Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Windings of closed geodesics around cusps of hyperbolic surfaces

Talk by Prof. Dr. Claire Burrin

**Date:** 11.04.22 **Time:** 14.05 - 15.05 **Room:** ETH HG G 43

In his 2006 ICM lecture, Ghys made the following observation. The winding of a closed geodesic around the cusp of the modular surface can be computed using a function from the theory of modular forms: the Rademacher function. In joint work with Flemming von Essen, we studied how and when Rademacher functions also encode the winding for closed geodesics around the cusps of hyperbolic surfaces. For certain families of surfaces, we use a Selberg trace formula argument to obtain precise statistical results on these winding numbers.