[Seminar] Matrix Models and Topological Recursion (Dr. Kento Osuga, University of Sheffield, UK)

Title: Matrix Models and Topological Recursion

Abstract: Hermitian matrix models are simplest quantum gauge field theory, namely quantum gauge theory in zero dimensions, and their correlation functions can be computed by a mathematical framework, the so-called topological recursion. In this review talk, I first present properties of Hermitian matrix models such as the 1/N-expansion, Virasoro constraints, loop equations, and the associated spectral curve. I will then give a technical overview of how we can recursively solve the loop equations of Hermitian matrix models by utilising the geometry of the spectral curve. Collecting the key geometric features, I will define the topological recursion with great generalities which makes it possible to apply the topological recursion beyond Hermitian matrix models.