Masur and Veech constructed a natural measure with finite mass on the moduli space of meromorphic quadratic differentials of area one with n simple poles on a smooth complex curve of genus g. I will explain that they can be computed by two different topological recursions (i.e. recursions on 2g - 2 + n). The first one exploits the relation of Masur-Veech volumes with asymptotic statistics of simple geodesics on hyperbolic surfaces and the theory of the geometric recursion that I developed with Andersen and Orantin (joint work with Andersen, Charbonnier, Delecroix, Giacchetto, Lewanski, Wheeler). The second one relies on the recent work of Chen, Moeller and Sauvaget who expressed Masur-Veech volumes as the top intersection of a modification of Chiodo's class, and follows from general properties of the topological recursion (joint work with Giacchetto and Lewanski).

 

海报