A short overview of the "Topological recursion"

Abstract

This review is an extended version of the Seoul ICM 2014 proceedings.It is a short overview of the "topological recursion", a relation appearing in the asymptotic expansion of many integrable systems and in enumerative problems. We recall how computing large size asymptotics in random matrices, has allowed to discover some fascinating and ubiquitous geometric invariants. Specializations of this method recover many classical invariants, like Gromov--Witten invariants, or knot polynomials (Jones, HOMFLY,...). In this short review, we give some examples, give definitions, and review some properties and applications of the formalism.

2nd version: misprints corrected, and small modification of the abstract

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Cited by in corpus (6)

• JT gravity as a matrix integral
• Large genus behavior of topological recursion
• Topological Recursion, Airy structures in the space of cycles
• Topological recursion of Eynard-Orantin and the Harmonic Oscillator
• Volume of the moduli space of unmarked bounded positive convex ${\mathbb{RP}}^2$ structures
• Metropolis updates for Diagrammatic Monte-Carlo algorithms from Schwinger-Dyson equations