A short overview of the "Topological recursion"

B Eynard (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

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.

Keywords: random matrices; moduli spaces; topological recursion

Domains: Mathematical Physics [math-ph]; High Energy Physics - Theory [hep-th]

B Eynard. A short overview of the "Topological recursion": (extended version of the Seoul ICM 2014 proceedings). 2014. ⟨cea-01093070v2⟩