# Tangle invariants for Khovanov homology and knot Floer homology

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Nathan Dowlin, Columbia University
Fine Hall 314

Khovanov homology and knot Floer homology are two powerful link invariants with many similarities despite their seemingly unrelated constructions. In 2005, Rasmussen conjectured that there is a spectral sequence from Khovanov homology to knot Floer homology, which would explain many of these similarities. I will discuss a proof of this conjecture, as well as a construction for tangles that relates a bordered theory for Khovanov homology to the recent bordered knot Floer invariant of Ozsvath and Szabo. This is joint work with Akram Alishahi.