Open-closed Deligne-Mumford field theories associated to Lagrangian submanifoldsMPIM

by Amanda Hirschi (MPIM)

Monday Nov 16, 2026, 2:00 PM → 3:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

MPI Topology Seminar

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. 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 explain how to deal with common difficulties, such as curve and lack of transversality. This is joint work with Kai Hugtenburg and no prior knowledge of symplectic geometry is assumed.