Soergel bimodules, matrix factorizations and Hilbert schemes

My talk is based on joint work with L. Rozansky. In our work we study a category MF_n of matrix factorizations that categorifies the finite Hecke algebra. I will explain a construction of a fully faithful functor from SBim_n to MF_n. We compose this functor with the Chern functor CH: MF_n → Coh^per(Hilb_n(C²)) to obtain a two-periodic complex of sheaves S_b for a braid b ∈ Br_n such that H^*(S_b) is equal to the triply graded homology of b. Some explicit examples of S_b will be shown.