Sie haben Javascript deaktiviert!
Sie haben versucht eine Funktion zu nutzen, die nur mit Javascript möglich ist. Um sämtliche Funktionalitäten unserer Internetseite zu nutzen, aktivieren Sie bitte Javascript in Ihrem Browser.

Info-Icon This content is not available in English
Show image information
Tuesday, 31.01.2023 | 14.15 Uhr - 15.30 Uhr | D 1 320

Oberseminar "Geometrische Analysis und Zahlentheorie": William Hide (hybrid)

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.

The University for the Information Society