QFT learning seminar 2017 (Quantum invariants of knots and links)

The seminar will meet Thursdays 3:00--4:30pm in 67-442. The topic is quantum invariants of knots and links.

Syllabus

1. Reidemeister and Markov moves. Some classical knot invariants.
1a. Jones polynomial via skein diagrams and via R-matrices.
2. String calculus for tensor categories
3. U_q(sl_2) with a view towards #2.
4. U_q(g) with a view towards #2.
5. Jones polynomial and its appearance via #3.
6. HOMFLY polynomial.

more detail

Here are some references which may be relevant for this year's seminar:

[K] Kassel, Quantum Groups
[KRT] Kassel, Rosso and Turaev, Quantum Groups and Knot Invariants
[O] Ohtsuki, Quantum Invariants (A study of knots, 3-manifolds, and their sets)
[Ti] Tingley, A minus sign that used to annoy me but now I know why it is there
[Tu] Turaev, Quantum Invariants of Knots and 3-manifolds

Schedule

This schedule is subject to change.

Semester 1
1 Mar 9 Peter McNamara Introduction
2 Mar 16 Ainsley Pullen Topology
3 Mar 23 Sam Weatherhog The Jones polynomial
4 Mar 30 CANCELLED
5 Apr 6 Aiden Suter Ribbon categories
6 Apr 13 Aiden Suter Ribbon categories (continued)
Easter Break
6 May 4 Alex Clarke Ribbon Hopf algebras
6 May 11 Marielle Ong Uq(g)
7 May 18 Sinead Wilson Synthesis
8 May 25 Chul-hee Lee HOMFLY polynomial
9 June 1 Ben Burton Further topics