15:30
Closed geodesics on surfaces: topology; geometry, arithmetic
Abstract
The study of closed geodesics on hyperbolic surfaces is a subject that shares deep connections with many areas of mathematics. We survey classic and recent results in the subject, emphasizing the relations between three different perspectives: topology, geometry, and arithmetic. In particular, we discuss recently discovered connections with mapping class groups and Teichmüller dynamics. The talk assumes no previous knowledge on the subject.