Abstract. A new relation between homological mirror symmetry and representation theory solves the knot categorification problem.  The symplectic side geometry side of mirror symmetry is a theory which generalizes Heegaard-Floer theory from gl(1|1) to arbitrary simple Lie (super) algebras. The corresponding category of A-branes has many special features, which render it solvable explicitly. In this talk, I will describe how the theory is solved, and how homological link invariants arise from it.