# From minimal gravity to open intersection theory

## TL;DR

This paper explores the connection between minimal gravity with boundaries and open intersection theory, deriving explicit generating functions using Laplace transforms to relate their boundary parameters.

## Contribution

It introduces a conjecture linking the two theories via Laplace transform and derives explicit formulas for their generating functions on disk and cylinder geometries.

## Key findings

- Derived compact expressions for open intersection theory generating functions.
- Established a conjectural relation between minimal gravity and open intersection theory.
- Provided a mathematical framework connecting boundary parameters through Laplace transforms.

## Abstract

We investigated the relation between the two-dimensional minimal gravity (Lee-Yang series) with boundaries and open intersection theory. It is noted that the minimal gravity with boundaries is defined in terms of boundary cosmological constant $\mu_B$ and the open intersection theory in terms of boundary marked point generating parameter $s$. Based on the conjecture that the two different descriptions of the generating functions are related by the Laplace transform, we derive the compact expressions for the generating function of the intersection theory from that of the minimal gravity on a disk and on a cylinder.