We use the relation between the volumes of the strata of meromorphic quadratic differentials with at most simple poles on ℂP1 and counting functions of the number of (bands of) simple closed geodesics in associated flat metrics with singularities to prove a very explicit formula for the volume of each such stratum conjectured by M. Kontsevich a decade ago. Applying ergodic techniques to the Teichmüller geodesic flow we obtain quadratic asymptotics for the number of (bands of) closed trajectories and for the number of generalized diagonals in almost all right-angled billiards.
|Number of pages||76|
|Journal||Annales Scientifiques de l'Ecole Normale Superieure|
|Publication status||Published - 1 Nov 2016|