Abstract

Invariants counting holomorphic curves play a key role throughout symplectic topology. Such invariants are governed and constrained by their rich algebraic structures. The Fukaya category of a symplectic manifold collects the information of classical Lagrangian Floer cohomology; it relates to algebraic geometry via derived categories of sheaves, to representation theory via categories of constructible sheaves, and to low-dimensional topology via Atiyah-Floer type conjectures and relations to gauge theory. It has also become an important tool in symplectic topology in its own right. This conference will take stock of some recent developments in symplectic topology, with a focus on applications, computations and connections of (Fukaya-)categorical technology and related areas.