Masur--Veech volumes of quadratic differentials and their asymptotics

Abstract: Based on the Chen--M\"oller--Sauvaget formula, we apply the theory of integrable systems to derive three equations for the generating series of the Masur--Veech volumes ${\rm Vol} \, \mathcal{Q}{g,n}$ associated with the principal strata of the moduli spaces of quadratic differentials, and propose refinements of the conjectural formulas given in [12,4] for the large genus asymptotics of ${\rm Vol} \, \mathcal{Q}{g,n}$ and of the associated area Siegel--Veech constants.