Séminaires : Séminaire de Systèmes Dynamiques

Equipe(s) : gd,
Responsables :H. Eliasson, B. Fayad, R. Krikorian, P. Le Calvez
Email des responsables :
Salle : 15-25-502
Adresse :Campus Pierre et Marie Curie

Archive avant 2015

Hébergé par le projet Géométrie et Dynamique de l’IMJ

Orateur(s) Elise Goujard - Bordeaux,
Titre Number of components of a random multicurve
Horaire14:00 à 15:45
RésumeWe 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.
AdresseCampus Pierre et Marie Curie