23rd Annual Cantrell Lecture Series
Monday, February 20, 2017
3:30pm, Miller Learning Center, Room 101
An introduction to Heegaard Floer homology
"Knot theory" is the study of closed, embedded curves in three-dimensional space. Classically, knots can be studied via a various computable polynomial invariants, such as the Alexander polynomial. In this first talk, I will recall the basics of knot theory and the Alexander polynomial, and then move on to a more modern knot invariant, "knot Floer homology", a knot invariant with more algebraic structure associated to a knot. I will describe applications of knot Floer homology to traditional questions in knot theory, and sketch its definition. This knot invariant was originally defined in 2003 in joint work with Zoltan Szabo, and independently by Jake Rasmussen. A combinatorial formulation was given in joint work with Ciprian Manolescu and Sucharit Sarkar in 2006.
Tuesday, February 21, 2017
3:30pm, Room 328 Boyd Graduate Studies Bldg.
Bordered techniques in Heegaard Floer homology.
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. In joint work with Robert Lipshitz and Dylan Thurston from 2008, the theory was extended to an invariant for three-manifolds with boundary, "bordered Floer homology". I will describe Heegaard Floer homology, motivate its construction, list some of its key properties and applications, and then sketch the algebraic input for the bordered version.
Wednesday, February 22, 2017
3:30pm, Room 328, Boyd Graduate Studies Bldg.
Bordered knot invariants
I will describe a bordered construction of knot Floer homology, defined as a computable, combinatorial knot invariant. Generators correspond to Kauffman states, and the differentials have an algebraic interpretation in terms of a certain derived tensor product. I will also explain how methods from bordered Floer homology prove that this invariant indeed computes the holomorphically defined knot Floer homology. This is joint work with Zoltan Szabo.
Refreshments will be served preceeding each lecture.
A banquet honoring Dr.Peter Ozsváth will be held on the evening of Monday, Feb. 20, 2017 at The National. Please download and print the baquet registration form here. Space is limited so please return your registration to Gail Suggs no later than Friday, Feb. 17, 2017.