Séminaire Gaston Darboux :

Le 05 février 2016 à 11:15 - salle 430

Présentée par Erlandsson Viveka - University of Bristol

Counting curves on hyperbolic surfaces.

In this talk I will discuss the growth of the number of closed geodesic of bounded length, and the length grows. More precisely, let c be a closed curve on a hyperbolic surface $S=S(g,n)$ and let $N_c(L)$ denote the number of curves in the mapping class orbit of c with length bounded by L. Due to Mirzikhani it is know that in the case that c is simple this number is asymptotic to $L^{(6g-6+2n)}$. Here we consider the case when c is an arbitrary closed curve, i.e. not necessarily simple. This is joint work with Juan Souto.