מכון איינשטיין למתמטיקה
Einstein Institute of Mathematics
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Prof. Peter Ozsváth Princeton
The lectures were held at the Edmond Safra Campus Givat Ram, Jerusalem
Thursday, Jan. 7th, Colloquium, 14:30-15:30
Einstein Institute of Mathematics, Lecture Hall 2|
Title: Knot Floer homology
A gathering in memory of Prof. Alexander Zabrodsky will be held at 15:30 in the faculty lounge.
Abstract: Knot Floer homology is an invariant for knots, defined using methods from symplectic geometry. This invariant contains topological information about the knot, such as its Seifert genus; it can be used to give bounds on the unknotting number; and it can be used to shed light on the structure of the knot concordance group. I will outline the construction and basic properties of knot Floer. Knot Floer homology was originally defined in collaboration with Zoltan Szabo, and independently by Jacob Rasmussen.
Sunday, Jan. 10th, 16:00-17:00, Ross 70A|
Title: Computational aspects of knot Floer homology
Abstract: The original construction uses the theory of pseudo-holomorphic curves. In this lecture, I will describe an explicit combinatorial algorithm for computing knot Floer homology in terms of grid diagrams. In this lecture, I will describe joint work with Ciprian Manolescu, Sucharit Sarkar, Zoltan Szabo, and Dylan Thurston.
Monday, Jan. 11th, 12:00-13:00 Ross 70A|
Title: Bordered Floer homology
Abstract: Bordered Floer homology is an invariant for three-manifolds with boundary, defined in collaboration with Robert Lipshitz and Dylan Thurston. The invariant associates a DG algebra to a parameterized surface, and a module over that algebra to a three-manifold with boundary. I will explain how methods from bordered Floer homology can be used to give a tidy description of knot Floer homology. This is joint work with Zoltan Szabo.
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