Seminar by Nicolas Orantin (CAMGSD, Instituto Superior Téchnico, Lisboa)

Title: Graph combinatorics, Gromov-Witten invariants and topological recursion

2014.12.11 | Maja Malmdorf Andersen

Date Thu 18 Dec
Time 15:45 16:45
Location 1531-113 (Aud. D1)

Abstract: The computation of higher genus Gromov-Witten invariants of a manifold is a fundamental and complicated problem for solving topological string theories. Basically, it consists in the enumeration of surfaces embedded in a given target manifold. Following Givental, one can show that a procedure called topological recursion allows to compute higher genus Gromov-Witten invariants only in terms of simple genus 0 ones.

In this talk, I will present a simple case where one can extract this procedure from some simple enumeration of graphs.
Indeed, when the manifold exhibits some Toric symmetries, this problem drastically simplifies thanks to localization arguments. In particular, when one is interested in Toric Calabi-Yau 3-folds, Bouchard, Klemm, Mari\~no and Pasquetti conjectured that one can compute the generating functions of open Gromov-Witten invariants using a recursive procedure developed in the framework of random matrix theory. By using combinatorial arguments, I will explain how one can prove this conjecture and, on the way, present a combinatorial interpretation of mirror symmetry in this setup.