sl(n) link homology via Bott-Samelson spaces

Bott-Samelson spaces are spaces with an action of a torus, such that their equivariant cohomology recovers Soergel bimodules and their Hochschild homology. These spaces, originally appearing as resolutions of Schubert varieties, have been used in several ways to give geometric constructions of Khovanov-Rozansky HOMFLY-PT link homology. They are also the starting point for generalizations of Soergel bimodules to other cohomology theories such as K-theory. In this talk, I will explore some implications of this torus-equivariant perspective. In particular, I will show how to obtain (Dunfield-Gukov-Rasmussen) differentials for integral sl(n) link homology as topologically defined classes in equivariant cohomology of Bott-Samelson spaces, with close ties to the equivariant Schubert calculus of the flag manifold.