Topological recursion an Gromov Witten theory

Topological recursion is a recursive definition, that to a spectral curve (an analytic plane curve with some extra structure) associates an infinite sequence of meromorphic n-forms on the curve, denoted W{g,n}. - If one takes as spectral curve, the mirror of a toric Calabi-Yau 3-fold, then W{g,n} happens to coincide with the generating series of open Gromov-Witten invariants of genus g with n boundaries (this was the BKMP conjecture, now proved). - more generally, there is a formula, giving the W{g,n} of an arbitrary curve, in terms of integrals of Chiodo tautological classes in the moduli space of curves of genus g with n marked points. This formula makes the link with Givental formalism. - Also, if one takes as spectral curve the A-polynomial of a knot, the W{g,n} seem to recover the asymptotic expansion of the Jones polynomial (W_{0,1} is the differential of the hyperbolic volume). This is only a conjecture, waiting for a proof.