Seminar

I begin by reviewing the original construction of Khovanov-Rozansky knot invariant based on tensor products of matrix factorizations. I will then explain how techniques from homotopical algebra apply to show that it can also be described in terms of stable Hochschild homology of Soergel bimodules; the latter are prominent in representation theory and also occur in the construction of other knot invariants. The description and techniques also allow for an alternative proof of the fact that one gets a knot invariant.