Georgia Institute of Technology College of Sciences

Heegaard Floer homology is a tool for studying three- and four-dimensional manifolds, using methods that are inspired by symplectic geometry. Bordered Floer homology is tool, currently under construction, for understanding how to reconstruct the Heegaard Floer homology in terms of invariants associated to its pieces. This approach has both conceptual and computational ramifications. In this talk, I will sketch the outlines of Heegaard Floer homology, with an emphasis on recent progress in bordered Floer homology. Heegaard Floer homology was developed in collaboration with Zoltan Szabo; bordered Floer homology is joint work with Robert Lipshitz and Dylan Thurston.