Chern-Simons Theory - Fall 2011
Mondays 11:30 - 1
Room: Evans 891
Outline
The goal is to learn Chern-Simons theory, starting from Witten's original paper and then working
our way up to
more advanced topics. The outline is pretty simple (at first): we'll spend
several
weeks working our way through
several papers on CS theory. From here we'll see the direction
people want to move - complex CS theory and
3-dim gravity, Gopakumar-Vafa
conjecture (relating
CS theory to Gromov-Witten theory via the large N-duality),
etc. We are assuming no prior background
in CS theory, only a (working) familarity with words like:
Lagrangian,
action, field, ...
Schedule
-
9/21 Addressing organizational issues
-
9/26 Classifying three dimensional Chern-Simons theories with compact G and possible WZW interactions of G (K. Wray) notes
-
10/10 Classical Chern-Simons theory (A. Husain) notes
-
10/17 Quantizing the Chern-Simons Lagrangian (K. Wray) notes
-
10/26 (Evans 740 11 - 12) Chern-Simons theory and knots (D. Halpern-Leistner) notes
-
10/27 (Evans 891 11:15 - 12:15) The Verlinde formula (D. Halpern-Leistner) notes
-
11/09 (Evans 891 11:30 - 12:30) Geometric Quantization of Chern-Simons theory (J. Aytac)
-
11/14 (Evans 891 11:30 - 12:30) Geometric Quantization of Chern-Simons theory (J. Aytac)
-
11/21 (Evans 891 11:30 - 12:30) Refined Chern-Simons theory, matrix models and Macdonald polynomials (S. Shakirov)
-
12/07 (Evans 891 11:30 - 12:30) Analytic Continuation of Chern-Simons Theory (A. Husain)
References
-
Dijkgraaf and Witten ''Topological Gauge Theories and Group Cohomology,'' Comm. Math. Phys. Volume 129, Number 2 (1990), 393-429.
-
Witten ''Quantum field theory and the Jones polynomial,'' Comm. Math. Phys. Volume 121, Number 3 (1989), 351-399.
-
Axelrod, Pietra and Witten ''Geometric Quantization of Chern-Simons Gauge Theory,'' J. Diff. Geom. Vol. 33 (1991), 787-902