Lecture 1: Knot Floer homology
Knot Floer homology is an invariant for knots in three-space, defined using
the theory of pseudo-holomorphic disks. It has the form of a bigraded
vector space, encoding topological information about the knot. The
invariant was originally defined in collaboration with Zoltan Szabo, and
indepedently by Jacob Rasmussen. I will describe the structure of this
invariant and discuss some of its topological applications.
Lecture 2: An algebraic construction of knot Floer homology
Bordered Floer homology is an invariant for three-manifolds with
boundary. I will discuss an algebraic approach to computing knot
Floer homology, based on decomposing knot diagrams. This is joint
work with Zoltan Szabo, influenced by earlier joint work with Ciprian
Manolescu and Sucharit Sarkar; and Robert Lipshitz and Dylan Thurston.