Seminar: "Knots, the Jones Polynomial, and Khovanov homology" by Prof. Andrew Lobb
Speaker: Dr. Lobb is a professor at Durham University and is currently visiting OIST (visit his page).
Abstract. I shall give constructions of the Jones polynomial and of Khovanov homology. These are both invariants of knots - the former is a polynomial, the latter is a vector space. They are interesting for many reasons and their construction is beautiful. There are deep connections with physics on which I'm not really qualified to comment (apologies), but those able may try looking at Kauffman's book "Knots and Physics", Witten's "Quantum Field Theory and the Jones Polynomial", or Gukov-Schwarz-Vafa's "Khovanov-Rozansky homology and topological strings". No knowledge of anything is assumed, and questions are encouraged.