Functors, Fukaya Categories, and Heegaard Floer Homology
Abstract: Heegaard Floer homology is a powerful invariant of 3 and 4-manifolds which fits (roughly) into the framework of a TQFT: it defines a functor from the category of closed oriented 3-manifolds and cobordisms between them to the category of abelian groups. An important problem, initiated by the work of Lipshitz-Ozsvath-Thurston, is to understand this theory as an extended TQFT which incorporates invariants for surfaces and 3-manifolds with boundary. The invariant for a 3-manifold with boundary, for example, should be an object in a category associated to the boundary surface; in the case at hand, Auroux identified this category as a Fukaya category of a symmetric product of the boundary. I'll discuss explicit ways of thinking about some of these categories and what they tell us about functoriality.
Dr. Rasmussen received his PhD from Harvard University in 2003 and is currently a Professor at the University of Cambridge.
Join via Zoom: https://illinois.zoom.us/j/87873784137?pwd=QmZPaXl3VGl5dGhXcmdNM0JPb3BPUT09&from=addon
