Infinity Inner Products and Open Gromov-Witten Invariants

In this 1-hour 8-minute Symplectic Geometry Seminar talk, explore Sebastian Haney's research on Infinity Inner Products and Open Gromov-Witten Invariants. Presented at the Institute for Advanced Study, this lecture by the Columbia University researcher delves into the open Gromov-Witten (OGW) potential, a function defined on the Maurer-Cartan space of closed Lagrangian submanifolds in symplectic manifolds with values in the Novikov ring. Learn how these potentials allow for the extraction of open Gromov-Witten invariants that count pseudoholomorphic disks with boundary on the Lagrangian. Discover Haney's novel construction of the OGW potential that yields invariants valued in any field of characteristic zero, extending beyond traditional real or complex number valuations. Understand the crucial algebraic foundation of this work: a homotopy cyclic inner product on the curved Fukaya A-infinity algebra, which generalizes cyclically symmetric inner products and is determined by proper Calabi-Yau structures on the Fukaya category.