UCLA Mathnet Login

Peter Ozsvath

Princeton University
Wednesday, June 6, 2018 to Friday, June 8, 2018

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.

Click HERE to view recording. 

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.

Click HERE to view recording. 

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.

Click HERE to view recording.