Gromov-Witten theory, Hurwitz numbers, and Matrix models, I

TL;DR

This paper introduces a novel approach linking Hurwitz numbers to Kontsevich's matrix model, providing insights into the intersection theory of moduli spaces of curves through combinatorial and geometric methods.

Contribution

It presents a new perspective connecting Hurwitz numbers with Gromov-Witten theory and matrix models, enriching the understanding of moduli space intersection theory.

Findings

Establishes a connection between Hurwitz numbers and matrix models.

Provides an exposition of the interplay between Gromov-Witten theory and combinatorics.

Lays groundwork for further exploration in subsequent work.

Abstract

The main goal of the paper is to present a new approach via Hurwitz numbers to Kontsevich's combinatorial/matrix model for the intersection theory of the moduli space of curves. A secondary goal is to present an exposition of the circle of ideas involved: Hurwitz numbers, Gromov-Witten theory of the projective line, matrix integrals, and the theory of random trees. Further topics will be treated in a sequel.