# Moursund Lectures

# Moursund Lectures

### 17-19 May 2016

## Peter Ozsváth

### Princeton University

Professor Ozsváth will give three lectures on the general theme of

### Floer homology and 3-manifolds

- Lecture 1: Holomorphic disks and low-dimensional topology
**Abstract:**Heegaard Floer homology is a closed three-manifold invariant, defined in joint work with Zoltan Szabo, using methods from symplectic geometry (specifically, the theory of pseudo-holomorphic disks). The inspiration for this invariant comes from gauge theory. I will describe Heegaard Floer homology, motivate its construction, list some of its key properties, and give some of its topological applications.4pm, Tuesday, 17 May 2016, 145 Straub Hall

- Lecture 2: A knot invariant from grid diagrams
**Abstract:**Knot Floer homology is an invariant for knots in three-space, which arises naturally when one attempts to understand how Heegaard Floer homology transforms under certain three-dimensional operations. Knot Floer homology has the form of a bigraded vector space, encoding information about the complexity of the knot. The invariant was

originally defined in collaboration with Zoltan Szabo, and indepedently by Jacob Rasmussen. I will describe a combinatorial algorithm for computing this invariant, discovered in joint work with Ciprian Manolescu and Sucharit Sarkar, and further elaborated in joint work with Manolescu, Szabo, and Dylan Thurston. I will also sketch some of the applications of this invariant to knot theory, and some of its connection with other knot invariants.4pm, Wednesday, 18 May 2016, 110 Fenton Hall

- Lecture 3: Bordered Floer homology
**Abstract:**I will describe “bordered Floer homology”, an invariant for three-manifolds with boundary that generalizes Heegaard Floer homology. The bordered theory associates a differential graded algebra to a parameterized surface; it also assocates a graded module to a three-manifold with boundary. This construction leads to a better conceptual understanding of Heegaard Floer homology, and it also gives a method for computation. Bordered Floer homology was introduced in joint work with Robert Lipshitz and Dylan Thurston. Time permitting, I will also describe a bordered approach to knot invariants, which is joint work with Zoltan Szabo.4pm, Thursday, 19 May 2016, 145 Straub Hall