Topological recursion for Masur-Veech volumes

Understand

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 \cite{Delecroix} proved by combinatorial arguments.
• Our method is different: it relies on the geometric recursion and its application to statistics of hyperbolic lengths of multicurves developed in \cite{GRpaper}.