Knot homology and sheaves on the Hilbert scheme of points on the plane.
For each braid β∈Brn we construct a 2-periodic complex Sβ of quasi-coherent C∗×C∗-equivariant sheaves on the non-commutative nested Hilbert scheme Hilbfree1,n. We show that the triply graded vector space of the hypecohomology H(Sβ⊗∧∙(B)) with B being tautological vector bundle, is an isotopy invariant of the knot obtained by the closure of β. We also show that the support of cohomology of the complex Sβ is supported on the ordinary nested Hilbert scheme Hilb1,n⊂Hilbfree1,n, that allows us to relate the triply graded knot homology to the sheaves on Hilb1,n. Talk is based on joint work with Lev Rozansky.