Title: Short geodesics and small eigenvalues on random hyperbolic punctured spheres
We study the geometry and spectral theory of random genus 0 hyperbolic surfaces with n cusps as n tends to infinity. In particular, we are interested in the number of "short" closed geodesics and "small" Laplacian eigenvalues for surfaces sampled with Weil-Petersson probablity. Inspired by the work of Mirzakhani and Petri (in the case of large genus compact surfaces), we demonstrate Poisson statistics for the number of closed geodesics on surfaces with n cusps whose lengths are on scales 1/sqrt(n). Using similar ideas we show that with high probability, a random genus 0 surface with n cusps has polynomially (in n) many small eigenvalues as n tends to infinity.
This is joint work with Joe Thomas (Durham).
Bei Interesse an einer online-Teilnahme den Teilnahmelink bitte bei Tobias Weich erfragen.