**Series title: Holomorphic disks, algebra, and knot invariants**

**Lecture 1 (6/6): An introduction to knot Floer homology**

Knot Floer homology is an invariant for knots in three-dimensional

space, defined using methods from symplectic geometry (the theory of

pseudo-holomorphic curves). After giving some geometric motivation

for its construction, I will sketch the construction of this

invariant, and describe some of its key properties and

applications. Knot Floer homology was originally defined in joint work

with Zoltan Szabo, and independently by Jacob Rasmussen; but this

lecture will touch on work of many others. This first lecture is

intended for a general audience.

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**Lecture 2 (6/7): Bordered Floer homology**

Bordered Floer homology is an invariant for three-manifolds with

parameterized boundary. It associates a differential graded algebra to

a surface, and certain modules to three-manifolds with specified

boundary. I will describe properties of this invariant, with a

special emphasis on its algebraic structure. Bordered Floer homology

was defined in joint work with Dylan Thurston and Robert Lipshitz.

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**Lecture 3 (6/8): A bordered approach to knot Floer homology**

I will describe current work with Zoltan Szabo, in which we compute a

suitable specialization of knot Floer homology, using bordered

techniques. The result is a purely algebraic formulation of knot Floer

homology, which can be explicitly computed even for fairly large knots.

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