: École d’Été 2018 - Teichmüller dynamics, mapping class groups and applications

Mathematicians have long understood periodic trajectories on the square billiard table. In the present work, we describe periodic trajectories on the regular pentagon – their geometry, symbolic dynamics, and group structure. Some of the periodic trajectories exhibit a surprising "dense but not equidistributed" behavior. I will show pictures of periodic trajectories, which are very beautiful. This is joint work with Samuel Lelièvre and Barak Weiss