Asymptotic coefficients of Weil-Petersson volumes in the large genus

Abstract

Mirzakhani-Zograf proved the large genus asymptotic expansions of Weil-Petersson volumes and showed that the asymptotic coefficients are polynomials in $\mathbb{Q}[{\pi }^{-2},{\pi }^2]$. They also conjectured that these are actually polynomials in $\mathbb{Q}[{\pi }^{-2}]$. In this paper, we prove Mirzakhani-Zograf's conjecture.