Speaker: Ian Zemke (University of Oregon)

Title: Bordered Floer homology and knot Floer homology

Abstract: Lipshitz, Ozsvath and Thurston assign an algebra to the torus, and to a 3-manifold with torus boundary, they assign an A_infty module over this algebra. Knot Floer homology is an invariant due to Ozsvath and Szabo for knots in 3-manifolds. An enhancement of knot Floer homology can be used to compute the Heegaard Floer homology of Dehn surgeries on a knot. This can also be packaged in terms of an A_infty module over an algebra called the surgery algebra. In this talk we discuss how certain natural categories of modules over the torus algebra and the surgery algebra are equivalent as A_infty categories. We describe applications towards immersed curve invariants from Heegaard Floer homology. This is joint work with Hanselman and Levine.