Abstract. This not being a job talk, I can tell you about what I really care about even though it's not my work and I don't understand it. So I will start by quickly telling you about the Jones polynomial and its homologification by Khovanov, and why I care about it, and why I feel I understand it quite well (though not well enough). And then I will describe the Khovanov-Rozansky homologification of another knot invariant, the HOMFLY-PT polynomial. With the standards set by our understanding of the Jones case, we don't understand this homology theory at all. But that's just for the better - we have some good work to do and the results are guaranteed to be interesting - for the underlying ideas are novel and cool.
Handouts: LocalDifferentials.pdf, KRC2.pdf.