Contributor info: Dr Alessandro Giacchetto

Alessandro Giacchetto, Danilo Lewański

SciPost Phys. Lect. Notes 111 (2026) · published 22 January 2026 | Toggle abstract · pdf

In these lecture notes, we provide an introduction to the moduli space of Riemann surfaces, a fundamental concept in the theories of 2D quantum gravity, topological string theory, and matrix models. We begin by reviewing some basic results concerning the recursive boundary structure of the moduli space and the associated cohomology theory. We then present Witten's celebrated conjecture and its generalisation, framing it as a recursive computation of cohomological field theory correlators via topological recursion. We conclude with a discussion of JT gravity in relation to hyperbolic geometry and topological strings.