String Theory Journal Club

In this talk I will present some of the main ideas behind the quantum invariants of knots: mainly Jones and HOMFLY-PT polynomials, and their categorifications/refinements in the form of Khovanov and HOMFLY-PT homologies, with the emphasis on the rich structure of differentials on these homologies. The existence of such differentials were originally conjectured by Dunfield, Gukov and Rasmussen in 2005, by using physics insights, and since then many of these things have been proved, expanded and generalized. The goal of the talk is to present some basic ideas of this theory, with various examples (and pictures), possibly together with the overview of the some of the more recent results.