Symplectic Geometry & Topology

Symplectic topology is at the crossroads of several mathematical disciplines such as low-dimensional topology, algebraic geometry, representation theory, Hamiltonian dynamics, integrable systems, mirror symmetry, and string theory.

 It comes with a surprising mixture of both rigid and flexible behavior. Current research areas of the symplectic topology group at Stanford include moduli spaces of holomorphic curves and their behavior under surgeries, Symplectic Field Theory and its relative versions, the theory of quasi-states and quasi-morphisms, as well as existence and flexibility results for Stein structures, Weinstein manifolds, and contact structures in higher dimensions.