Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Shrinking rates of horizontal gaps for generic translation surfaces

Talk by Dr. Samantha Fairchild

Speaker invited by: Prof. Dr. Claire Burrin

**Date:** 17.10.22 **Time:** 13.30 - 14.30 **Room:** Y27H28

A translation surface is given by polygons in the plane, with sides identified by translations to create a closed Riemann surface with a flat structure away from finitely many singular points. Understanding geodesic flow on a surface involves understanding saddle connections. Saddle connections are the geodesics starting and ending at these singular points and are associated to a discrete subset of the plane. To measure the behavior of saddle connections of length at most R, we obtain precise decay rates as R goes to infinity for the difference in angle between two almost horizontal saddle connections. This is based on joint work with Jon Chaika.