| Orateur(s) | Elise Goujard - Bordeaux,
|
| Titre | Number of components of a random multicurve |
| Date | 02/04/2021 |
| Horaire | 14:00 à 15:45 |
|
| Diffusion | |
| Résume | We study the number of components of a multicurve taken at random among all (simple closed geodesic) multicurves of length at most L on a hyperbolic surface S. We then let L tend to infinity and talk about a random multicurve on S. M. Mirzakhani proved that the number of components of a random multicurve on S only depends on the topology of S and not on the specific hyperbolic metric. It hence makes sense to talk about the number of components of a random multicurve of genus g. Furthermore M. Mirzakhani provided explicit formulas for this distribution involving the Kontsevich-Witten correlators. Thanks to the recent work of A. Aggarwal on the asymptotics of these correlators we describe its behavior as the genus g tend to infinity. We show that it asymptotically behaves as the number of cycles of a random permutation in Sym_{3g-3} taken with respect to a very explicit probability distribution. The number of components of a random multicurve of genus g coincide with the number of cylinders of a random square-tiled surface in genus g. Hence our work equivalently provides results on the geometry of random square-tiled surfaces. This is a joint work with V. Delecroix, P. Zograf and A. Zorich. |
| Salle | 15-25-502 |
| Adresse | Campus Pierre et Marie Curie |
