On the large genus asymptotics of Weil-Petersson volumes

TL;DR

This paper introduces a fast algorithm for computing Weil-Petersson volumes of moduli spaces, proposes conjectural large genus asymptotics based on numerical data, and suggests highly accurate asymptotic formulas for intersection numbers involving psi-classes.

Contribution

It presents a new efficient algorithm for Weil-Petersson volume computation and conjectures precise large genus asymptotics and intersection number formulas.

Findings

Proposed a fast algorithm for Weil-Petersson volumes

Conjectured large genus asymptotics based on numerical data

Suggested highly accurate asymptotic formulas for intersection numbers

Abstract

A relatively fast algorithm for evaluating Weil-Petersson volumes of moduli spaces of complex algebraic curves is proposed. On the basis of numerical data, a conjectural large genus asymptotics of the Weil-Petersson volumes is computed. Asymptotic formulas for the intersection numbers involving $\psi$-classes are conjectured as well. The accuracy of the formulas is high enough to believe that they are exact.