Homological Mirror Symmetry Seminar

I will describe a system of differential equations for the genus 0 open Gromov-Witten potential of a Lagrangian submanifold fixed by an anti-symplectic involution. These equations involve both the open Gromov-Witten potential and the closed Gromov-Witten potential. They are so restrictive, that in important examples they completely determine both the open and closed Gromov-Witten potentials up to a finite number of constants. The proof relies on an open-closed generalization of the topological conformal field theory behind the WDVV equation.