Amanda Hirschi, Sorbonne Université

Title: An open-closed Deligne-Mumford field theory associated to a Lagrangian submanifold

Abstract: In order to prove that homological mirror symmetry implies enumerative mirror symmetry, one has to extract the Gromov-Witten theory of a symplectic manifold from its Fukaya category. Costello outlined a strategy in 2007, which involves the notion of a topological conformal field theory. This is an algebraic structure based on moduli spaces of curves with boundary. I will define and describe the construction of a variant of a TCFT, called an open-closed DMFT, which relies on moduli spaces of stable maps with boundary on a Lagrangian submanifold. In particular, I will show how to deal with the required virtual techniques and how to incorporate curvature. This is joint work with Kai Hugtenburg.