Topological recursion for Masur–Veech volumes

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