Chern-Simons theory

Wednesdays 1:30–3pm, 740 Evans, CCN 24270
(Simultaneously, 4:30-6 EST at Harvard)

Topic

We will start with an introduction to Chern-Simons theory for compact groups and proceed to discussing the (much less developed) case of complex Lie groups.
References will be updated.

Discord server

Discord server

Tentative schedule:
Date Topic Speaker References
1/24 Introduction and Organization Freed and Teleman 1,3,7,8
1/31 Review of Chern-Simons for compact groups, I Teleman 1
2/7 Chern-Simons for compact groups II Freed 1
2/14 Chern-Simons for torus groups

8

2/21

 Quantum groups and 3-manifold invariants Reshetikhin
2/28 Analytic Continuation of Chern-Simons theory Charlie Reid 4; 3,5?
3/6 On the Volume conjecture Rinat Kashaev

9

3/13

 CS and WZW. Harvard Spring Break – no Zoom Constantin Teleman

8
3/20 Perturbative Chern-Simons Theory Erik Herrera

10, 11
3/27 Berkeley Spring Break – No meeting

4/3 Quantum Riemann surfaces I Sunghyuk Park 7
4/10 TBD


4/17



6, 7
4/25



6,7


References (with links)

  1. E. Witten, Quantum Field Theory and the Jones Polynomial
  2. E. Witten, D. Bar-Natan, Perturbative expansion of Chern-Simons theory with non-compact gauge group
  3. E. Witten, Quantization of Chern-Simons theory with complex gauge group
  4. E. Witten, Analytic continuation of Chern-Simons theory
  5. E. Witten, A new look at the Path Integral of Quantum Mechanics.
  6. S. Gukov, Three-dimensional quantum gravity, Chern-Simons Theory and the A-polynomial
  7. T. Dimofte: Perturbative and Nonperturbative aspects of complex Chern-Simons Theory (survey)
  8. G. Moore: Introduction to Chern-Simons Theory (survey)
  9. R. Kashaev: The hyperbolic volume of knots and quantum dilogarithm
  10. D. Bar-natan: Perturbative Chern-Simons theory
  11. S. Axelrod, I.M. Singer:Chern-Simons Perturbation Theory

Lecture Notes