Knots: advanced topics
                       Fizmatclub, Spring 2006

14 lectures.

1. Operator invariants of links.
2. Temperley--Lieb algebra and skein invariants.
3. Knots and 3-manifolds, Dehn surgery on framed links.
4. Quantum groups and quantum invariants.
5. Hyperbolic knots. Volume conjecture.
6. Categorification, Khovanov homology.

Literature

R.Lickorish. An introduction to knot theory.
D.Rolfsen. Knots and Links.
N.Saveliev. Lectures on the topology of 3-manifolds.
T.Ohtsuki. Quantum invariants.
P.Etingof, O.Schiffmann. Lectures on quantum groups.
C.Kassel. Quantum groups.
W.Thurston. Geometry and Topology of 3-manifolds.
  Online at http://www.msri.org/publications/books/gt3m/.
W.Thurston. Three-dimensional geometry and topology, vol. 1.
  (published in Russian by MCCME).
Y.Yokota. From the Jones polynomial ot the A-polynomial of hyperbolic knots.
  Preprint. http://www.comp.metro-u.ac.jp/~jojo/papers.html
H.Murakami. Kashaev's invariant and the volume of a hyperbolic knot after
  Y.Yokota. arXiv:math.GT/0008027.
M.Khovanov. A categorification of the Jones polynomial. arXiv:math.QA/9908171.
D.Bar-Natan. On Khovanov's categorification of the Jones polynomial.
  arXiv:math.QA/0201043.
D.Bar-Natan. Khovanov's homology for tangles and cobordisms.
  arXiv:math.GT/0410495.
J.Rasmussen. Khovanov homology and the slice genus. arXiv:math.GT/0402131.
Problems on invariants of knots and 3-manifolds. Ed. by T.Ohtsuki.
  arXiv:math.GT/0406190.