Abstract Analogues of Flux as Symplectic Invariants

This talk is part of a circle of ideas that one could call ``categorical dynamics''. We look at how objects of the Fukaya category move under deformations prescribed by fixing an odd degree quantum cohomology class. This is an analogue of moving Lagrangian submanifolds under non-Hamiltonian deformations. It leads to a new invariant of closed symplectic manifolds, which can distinguish deformation equivalent symplectic structures.