Marko Stosic, Instituto de Sistemas e Robótica
Knots and HOMFLY I

In these two talks, I'll give a list of structural properties of colored HOMFLY homology that categorifies colored HOMFLY polynomial. The main ingredients are the colored differentials that relate homological invariants of knots colored by different representations. The differentials are predicted by the physics insights that include BPS states counting, Landau-Ginzburg theories. They give a very rigid structure on colored HOMFLY homology theories and also relate them to the super-A-polynomial that categorifies A-polynomial of a knot.