Title: Quantum and symplectic invariants in low-dimensional topology.

Date: 01/15/2020

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

Khovanov homology and knot Floer homology are two powerful knot invariants developed around two decades ago. Knot Floer homology is defined using symplectic techniques, while Khovanov homology has its roots in the representation theory of quantum groups. Despite these differences, they seem to have many structural similarities. A well-known conjecture of Rasmussen from 2005 states that for any knot K, there is a spectral sequence from the Khovanov homology of K to the knot Floer homology of K. Using a new family of invariants defined using both quantum and symplectic techniques, I will give a proof of this conjecture and describe some topological applications.