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 KontsevichWitten 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_{3g3} 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 squaretiled surface in genus g. Hence our work equivalently provides results on the geometry of random squaretiled surfaces. This is a joint work with V. Delecroix, P. Zograf and A. Zorich. 
Salle  1525502 
Adresse  Campus Pierre et Marie Curie 