2010 Chern Lectures

The 2010 Chern Lectures will be delivered by Peter S. Ozsvath on April 13, 15, 20 and 22, 2010.

Department of Mathematics, University of California, Berkeley, presents

The 2010 Chern Lectures
Peter S. Ozsvath
Columbia University

Heegaard Floer homology

Lecture 1: Introduction to Heegaard Floer homology
Tuesday, April 13, 2010
4:00 - 5:00 pm
Sibley Auditorium, Bechtel Hall

Heegaard Floer homology is an invariant for low-dimensional manifolds defined using methods from symplectic geometry (holomorphic disks, Lagrangian Floer homology). To a closed, oriented three-manifold, this invariant associates a module over the polynomial algebra in a formal variable U. I will outline the structure of this theory and discuss various of its topological applications. This construction (as an invariant for three- and four-manifolds) was originally discovered in collaboration with Zoltán Szabó. The generalization to knots was discovered independently by Jacob Rasmussen.

Lecture 2: Knot Floer homology
Thursday, April 15, 2010
4:00 - 5:00 pm
Sibley Auditorium, Bechtel Hall

Heegaard Floer homology can be used to define an invariant for knots in the three-sphere. This invariant, whose definition involves holomorphic curves, admits an elementary, combinatorial description in terms of grid diagrams. I will describe the construction, and sketch a combinatorial proof of its topological invariance. This lecture will cover joint work with Ciprian Manolescu, Sucharit Sarkar, Zoltán Szabó, and Dylan Thurston.

Lecture 3: Bordered Floer homology
Tuesday, April 20, 2010
4:00 -5:00 pm
Sibley Auditorium, Bechtel Hall

I will describe an extension of the U=0 specialization of Heegaard Floer homology, HF, to three-manifolds with parameterized boundary. The resulting theory, bordered Floer homology, associates a differential algebra to an oriented two-manifold, and a differential module module over that algebra to a three-manifold with boundary. These differential modules can also be used to reconstruct HF for closed three-manifolds. This is joint work with Robert Lipshitz and Dylan Thurston.

Lecture 4: Heegaard Floer homology and surgery formulas
Thursday, April 22, 2010
4:00 - 5:00 pm
Room 60, Evans Hall

After setting up some necessary background, I will turn attention to surgery formulas for reconstructing the Heegaard Floer homology groups of three-manifolds obtained as surgeries on knots and links. I will then explain how this can be used to, in principle, compute Heegaard Floer homology groups of closed (three- and four-) manifolds from data associated to grid diagrams.