Geodesics and Brownian motion on hyperbolic surfaces

Talk by Prof. Dr. Yilin Wang

Date: 04.03.26  Time: 13.30 - 14.30  Room: ETH HG F 26.3

There are intimate relations between the geodesic flow and Brownian motion on hyperbolic surfaces (for instance, Hopf-Tsuji-Sullivan theorem and the expression of harmonic measure). In this talk, I will show how we can use Brownian motion to express the lengths of closed geodesics, length of orthogeodesics, zeta-regularized determinant of the Laplace-Beltrami operator of a hyperbolic surface. This gives a tool to study the length spectra of a hyperbolic surface and we obtain a new identity between the length spectrum of a hyperbolic surface and that of the same surface with an arbitrary number of additional cusps. This is mainly based on a joint work with Yuhao Xue (IHES).