Equivariant Floer Theory for Symplectic C*-manifolds

In this lecture from the IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar, Alexander Ritter from Oxford University presents his research on equivariant Floer theory for symplectic C*-manifolds. Explore recent progress from joint papers with Filip Živanović concerning a broad class of non-compact symplectic manifolds, including semiprojective toric manifolds, quiver varieties, and conical symplectic resolutions of singularities. Learn about these manifolds that admit a Hamiltonian circle action as part of a pseudo-holomorphic action of a complex torus. Discover how, despite the highly non-exact nature of the symplectic form on these spaces, Hamiltonian Floer cohomology can be applied to functions of the moment map of the circle action. Understand how Floer theory induces a filtration by ideals on quantum cohomology, and examine the recent developments in equivariant Floer cohomology that yield a filtration on equivariant quantum cohomology. The presentation may also cover a discussion of symplectic cohomology and quantum cohomology for semiprojective toric manifolds.