Two knot invariants and a spectral sequence

Khovanov homology is a powerful knot invariant with origins in representation theory and TQFTs. Knot Floer homology is another interesting invariant that comes from symplectic topology and the study of 3-manifolds. While these two knot homologies have quite different definitions, they also share a suspicious amount of similarities. I will talk about both constructions, the recently-discovered spectral sequence relating them, and our results on the "middle" pages of the sequence. This work is joint with Sam Tripp.