Gaëtan Borot

An introduction to topological recursion

Asymptotic expansions in random matrix theory, enumeration of ribbon graphs, Weil-Petersson volumes of the moduli of hyperbolic surfaces, Masur-Veech volumes for the moduli of quadratic differentials on a surface... can be computed with a universal recursion (on the order of asymptotic expansion, random matrix theory, on the topology of the surfaces in enumerative geometry), called topological recursion. I give a brief introduction to the topic, with emphasis on examples, and explain geometric principles that (sometimes) explain why topological recursion appears.