Joint GT-UGA Seminar at UGA - A spectral sequence from Khovanov homology to knot Floer homology

Series
Geometry Topology Seminar
Time
Monday, March 25, 2019 - 2:30pm for 1 hour (actually 50 minutes)
Location
Boyd
Speaker
Nathan Dowlin – Dartmouth
Organizer
Caitlin Leverson
Khovanov homology and knot Floer homology are two knot invariants which are defined using very different techniques, with Khovanov homology having its roots in representation theory and knot Floer homology in symplectic geometry. However, they seem to contain a lot of the same topological data about knots. Rasmussen conjectured that this similarity stems from a spectral sequence from Khovanov homology to knot Floer homology. In this talk I will give a construction of this spectral sequence. The construction utilizes a recently defined knot homology theory HFK_2 which provides a framework in which the two theories can be related.