Uniform asymptotics and the Weil--Petersson constant
In their celebrated work on the large-genus asymptotic expansion of Weil--Petersson volumes, Mirzakhani and Zograf left open the question of whether the Weil--Petersson constant satisfies $C_{\mathrm{WP}}=\pi^{-1/2}$. We resolve the conjecture affirmatively. Our strategy is to consider a family of spectral curves inter...