Speaker: Sebastian Haney (Columbia University)

Title: Infinity inner products and open Gromov--Witten invariants

Abstract: The open Gromov-Witten (OGW) potential is a function defined on the Maurer-Cartan space of a closed Lagrangian submanifold in a symplectic manifold with values in the Novikov ring. From the values of the OGW potential, one can extract open Gromov-Witten invariants, which count pseudoholomorphic disks with boundary on the Lagrangian. Existing definitions of the OGW potential only allow for the construction of OGW invariants with values in the real or complex numbers. In this talk, we will present a construction of the OGW potential which gives invariants valued in any field of characteristic zero. The main algebraic input for our construction is an infinity inner product, which comes from a proper Calabi-Yau structure on the Fukaya category. If time permits, we will also discuss a partial extension of our results that give OGW invariants valued in fields of positive characteristic, and connections to homological mirror symmetry.