Topological recursion for Masur Veech volumes.
We study the Masur Veech volumes $MV_{g,n} of the principal stratum of the moduli space of quadratic differentials of unit area on curves of genus $g$ with $n$ punctures. We show that the volumes $MV_{g,n} are the constant terms of a family of polynomials in $n$ variables governed by the topological recursion/Virasoro constraints. This is equivalent to a formula giving these polynomials as a sum over stable graphs, and retrieves a result of Delecroix, Goujard, Zograf and Zorich proved by combinatorial arguments. Our method is different: it relies on the geometric recursion and its application to statistics of hyperbolic lengths of simple multicurves developed by Andersen, Borot and Orantin. We also obtain an expression of the area Siegel Veech constants in terms of hyperbolic geometry. The topological recursion allows numerical computations of Masur Veech volumes, and thus of area Siegel Veech constants for low $g$ and $n$ which leads us to propose conjectural formulas for low $g$ but all $n$