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We explicitly compute the diverging factor in the large genus asymptotics ofthe Weil-Petersson volumes of the moduli spaces of $n$-pointed complexalgebraic curves. Modulo a universal multiplicative constant we prove theexistence of a complete asymptotic expansion of the Weil-Petersson volumes inthe inverse powers of the genus with coefficients that are polynomials in $n$.This is done by analyzing various recursions for the more general intersectionnumbers of tautological classes, whose large genus asymptotic behavior is alsoextensively studied.

Towards large genus asymtotics of intersection numbers on moduli spaces of curves