On cubic Hodge integrals and random matrices

TL;DR

This paper explores a conjectural link between the GUE partition function with even couplings and specific cubic Hodge integrals on moduli spaces of stable algebraic curves, aiming to deepen understanding of their mathematical relationship.

Contribution

It proposes a conjectural relationship connecting random matrix theory and algebraic geometry through cubic Hodge integrals and GUE partition functions.

Findings

Formulation of the conjectural relationship.

Insights into the structure of cubic Hodge integrals.

Potential implications for random matrix theory and algebraic geometry.

Abstract

A conjectural relationship between the GUE partition function with even couplings and certain special cubic Hodge integrals over the moduli spaces of stable algebraic curves is under consideration.