Large-genus asymptotics for translation surfaces

Vortrag von Prof. Dr. Anja Randecker

Sprecher eingeladen von: Prof. Dr. Rémi Abgrall

Datum: 01.10.25  Zeit: 13.30 - 14.30  Raum: Y27H28

Translation structures on surfaces can be obtained in many different ways: as suspensions of interval exchange transformations, from holomorphic differentials, as cotangent vectors to Teichmüller space, or by unfolding polygonal billiards. We ask how such translation surfaces generically look like for large genus.

In the talk, I will introduce translation surfaces through their connections to dynamical systems and give an overview on the question of large-genus asymptotics. The focus will be on a recent joint result with Howard Masur and Kasra Rafi on the distribution of the number of short saddle connections.