Abstracts of Blumenthal Lectures 2018

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.