A. Zorich - Counting simple closed geodesics and volumes of moduli spaces (Part 2)

Anton Zorich (1) , Fanny Bastien (2)

1 UPMC - Université Pierre et Marie Curie - Paris 6 - UFR de Médecine Pierre et Marie Curie
2 IF - Institut Fourier

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.

Mots clés: Teichmüller dynamics mapping class groups and applications; simple closed geodesics; volumes of moduli spaces

Mots clés: eem2018; Grenoble; Counting

Domaines: Mathématiques [math]

Anton Zorich, Fanny Bastien. A. Zorich - Counting simple closed geodesics and volumes of moduli spaces (Part 2): Summer School 2018 - Teichmüller dynamics, mapping class groups and applications. 2018. ⟨medihal-01835742⟩