Interesting structures arise by considering the space of objects in a Fukaya category of Lagrangian submanifolds. These include knot invariants, cluster algebras, open Gromov-Witten invariants, BPS numbers, D-modules and noncommutative geometry. Despite the panoply of topics, I will try to make the talk accessible, telling a story through illustrative examples. Speaker(s): Eric Zaslow (Northwestern University)