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

In the first two lectures I will try to tell (or, rather, to give an idea) of how Maryam Mirzakhani has counted simple closed geodesics on hyperbolic surfaces. I plan to briefly mention her count of Weil-Peterson volumes and her proof of Witten's conjecture, but only on the level of some key ideas.In the last lecture I plan to show how ideas of Mirzakhani work in counting problems related to flat surfaces, namely, in computation of Masur-Veech volumes and in counting meanders