Séminaire - Avril (annulé)
Le séminaire aura lieu un mercredi par mois de 14h à 15h à l'Institut Henri Poincaré à Paris. Pour télécharger l'affiche du mois: avril.pdf.
- 01/04/2020 - Francisco Arana-Herrera (Stanford University) - salle 05
Titre: Counting
square-tiled surfaces with prescribed real and imaginary foliations.
Resumé:
Let X be a closed, connected, hyperbolic surface of genus 2. Is it more
likely for a simple closed geodesic on X to be separating or
non-separating? How much more likely? In her thesis, Mirzakhani gave
very precise answers to these questions. One can ask analogous
questions for square-tiled surfaces of genus 2 with one horizontal
cylinder. Is it more likely for such a square-tiled surface to have
separating or non-separating horizontal core curve? How much more
likely? Recently, Delecroix, Goujard, Zograf, and Zorich gave very
precise answers to these questions. Surprisingly enough, their answers
were exactly the same as the ones in Mirzakhani’s work. In
this talk we explore the connections between these counting problems,
showing they are related by more than just an accidental coincidence.