Speaker: Mohammed Abouzaid (Stanford University)

Title: Some questions in bordism arising from Floer theory

Abstract: Many constructions in Floer theory can be formulated in terms of variants of the notion of a Flow category introduced by Cohen, Jones, and Segal. There are notions of left and right modules over such categories, which lift to the setting of spectra (or more generally modules over an appropriate ring spectrum) the notions of Floer homology and cohomology that are familiar for the ordinary case. In the presence of a group action, this results in a pairing, over manifold bordism, which in the simplest case is a pairing between equivariant free and derived (or homotopical) bordism. Knowing some properties of this pairing may be helpful for applications.