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 …

We identify the Givental formula for the ancestor formal Gromov–Witten potential with a
version of the topological recursion procedure for a collection of isolated local germs of the …

To any spectral curve S, we associate a topological class {\Lambda}(S) in a moduli space
M^ b_ {g, n} of" b-colored" stable Riemann surfaces of given topology (genus g, n …

A bstract We introduce a new formulation of the so-called topological recursion, that is
defined globally on a compact Riemann surface. We prove that it is equivalent to the …

We formulate a notion of abstract loop equations, and show that their solution is provided by
a topological recursion under some assumptions, in particular the result takes a universal …

We study the set of solutions (ωg, n) g⩾ 0, n⩾ 1 of abstract loop equations. We prove that
ωg, n is determined by its purely holomorphic part: this results in a decomposition that we …

We define a collection Θ g, n∈ H 4 g− 4+ 2 n (ℳg, n, ℚ) for 2 g− 2+ n> 0 of cohomology
classes that restrict naturally to boundary divisors. We prove that the intersection …

The Eynard-Orantin recursion formula provides an effective tool for certain enumeration
problems in geometry. The formula requires a spectral curve and the recursion kernel. We …

We generalize the topological recursion of Eynard–Orantin (JHEP 0612: 053, 2006;
Commun Number Theory Phys 1: 347–452, 2007) to the family of spectral curves of Hitchin …

Abstract The Eynard–Orantin topological recursion relies on the geometry of a Riemann
surface S and two meromorphic functions x and y on S. To formulate the recursion, one must …