Topological recursion and Gromov Witten theory

Vendredi 9 décembre 2016 14:00-15:00 - Bertrand Eynard - IPHT CEAEA Saclay, and CRM Montréal

Résumé : 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.

Lieu : Université de Nantes, salle Eole

Topological recursion and Gromov Witten theory  Version PDF