Lecture notes on topological recursion and geometry

Abstract

These are lecture notes for a 4h mini-course held in Toulouse, May 9-12th, at the thematic school on "Quantum topology and geometry". The goal of these lectures is to (a) explain some incarnations, in the last ten years, of the idea of topological recursion: in two dimensional quantum field theories, in cohomological field theories, in the computation of Weil-Petersson volumes of the moduli space of curves; (b) relate them more specifically to Eynard-Orantin topological recursion (revisited from Kontsevich-Soibelman point of view based on quantum Airy structures).

48 pages, 16 figures

References in corpus (1)

• The ABCD of topological recursion

Cited by in corpus (7)

• The ABCD of topological recursion
• A universe field theory for JT gravity
• Topological recursion for Masur-Veech volumes
• Whittaker vectors for $\mathcal{W}$-algebras from topological recursion
• Log topological recursion through the prism of $x-y$ swap
• On the Kontsevich geometry of the combinatorial Teichmüller space
• Airy structures for semisimple Lie algebras