Holomorphic Curves and Symplectic Topology
August 7 - August 11, 2017
For 30 years, the holomorphic curve invariants introduced by Gromov and Floer have played a central role in symplectic and contact topology. In the last few years, several new exciting directions have emerged, involving amongst others: new structures in holomorphic curve theory; applications of higher-dimensional moduli spaces of holomorphic curves; sheaf-theoretic or homological algebraic methods; explicit constructions, in part via h-principles and novel ideas of flexibility. These simultaneous developments have enabled significant new progress on the symplectic topology of Stein manifolds and Lagrangian embedding questions, connections to low-dimensional topology including Khovanov homology, connections to physics, including the link of knot contact homology with gauge theory and the topological string, proofs and applications of homological mirror symmetry, and new directions in dynamics.
This workshop will survey some of this recent progress, with a specific aim to identify open questions and promising avenues for applications of the new machinery in the subject.