UIUC Topology Seminar

University of Illinois at Urbana-Champaign

**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.

Slide: T95.html.