New results of intersection numbers on moduli spaces of curves

TL;DR

This paper introduces new formulas, recursion relations, and proofs related to intersection numbers on moduli spaces of curves, advancing understanding of tautological classes and their generating functions.

Contribution

It provides novel formulas and recursion methods for intersection numbers, including proofs of conjectures and properties of generating functions.

Findings

Simple formula for n-point functions of Witten's τ classes

Effective recursion for Weil-Petersson volumes

Proof of Itzykson-Zuber conjecture on denominators

Abstract

We present a series of new results we obtained recently about the intersection numbers of tautological classes on moduli spaces of curves, including a simple formula of the n-point functions for Witten's $\tau$ classes, an effective recursion formula to compute higher Weil-Petersson volumes, several new recursion formulae of intersection numbers and our proof of a conjecture of Itzykson and Zuber concerning denominators of intersection numbers. We also present Virasoro and KdV properties of generating functions of general mixed $\kappa$ and $\psi$ intersections.