  These are the notes of the lectures delivered by the author at CIME in June
2018. The main purpose of the notes is to provide an overview of the techniques
used in the construction of the triply graded link homology. The homology is
space of global sections of a particular sheaf on the Hilbert scheme of points
on the plane. Our construction relies on existence on the natural push-forward
functor for the equivariant matrix factorizations, we explain the subtleties on
the construction in these notes. We also outline a proof of the Markov moves
for our homology as well as some explicit localization formulas for knot
homology of a large class of links.
