# Cyclic homology and $S^1$-equivariant symplectic cohomology

 Princeton/IAS Symplectic Geometry Seminar Topic: Cyclic homology and $S^1$-equivariant symplectic cohomology Speaker: Sheel Ganatra Affiliation: Stanford University Date: Friday, November 21 Time/Room: 1:30pm - 2:30pm/S-101 Video Link: http://video.ias.edu/pisgs/2014/1121-SheelGanatra

In this talk, we study two natural circle actions in Floer theory, one on symplectic cohomology and one on the Hochschild homology of the Fukaya category. We show that the geometric open-closed string map between these two complexes is $S^1$-equivariant, at a suitable chain level. In particular, there are induced maps between equivariant homology theories, natural with respect to Gysin sequences, which are isomorphisms whenever the non-equivariant map is.