Classical and Quantum Teichmüller Theory
In the first part of the course, we will review the theory of Teichmüller spaces of surfaces from the perspective of hyperbolic geometry. The second part will explore the quantization of these concepts and their connections to representation theory. If time permits, we will also discuss how quantum invariants of 3-manifolds arise in this framework.
Lecturer
Date
24th September ~ 24th December, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday | 14:20 - 17:50 | A14-202 | ZOOM 02 | 518 868 7656 | BIMSA |
Prerequisite
Mathematical Analysis, Linear Algebra, Abstract Algebra
Reference
1. B. Martelli. "An Introduction to Geometric Topology." (Part II)
2. Fock, Vladimir V., and Leonid O. Chekhov. "A quantum Teichmüller space." Theoretical and Mathematical Physics 120.3 (1999): 1245-1259.
3. Kashaev, Rinat M. "Quantization of Teichmüller spaces and the quantum dilogarithm." Letters in Mathematical Physics 43.2 (1998): 105-115.
4. Frenkel, Igor B., and Hyun Kyu Kim. "Quantum Teichmüller space from the quantum plane." Duke Math. J. 161(2): 305-366 (2012): 305-366.
5. Andersen, Jørgen Ellegaard, and Rinat Kashaev. "A TQFT from quantum Teichmüller theory." arXiv preprint arXiv:1109.6295 (2011).
6. Collier, Scott, Lorenz Eberhardt, and Mengyang Zhang. "Solving 3d gravity with Virasoro TQFT." SciPost Physics 15.4 (2023): 151.
2. Fock, Vladimir V., and Leonid O. Chekhov. "A quantum Teichmüller space." Theoretical and Mathematical Physics 120.3 (1999): 1245-1259.
3. Kashaev, Rinat M. "Quantization of Teichmüller spaces and the quantum dilogarithm." Letters in Mathematical Physics 43.2 (1998): 105-115.
4. Frenkel, Igor B., and Hyun Kyu Kim. "Quantum Teichmüller space from the quantum plane." Duke Math. J. 161(2): 305-366 (2012): 305-366.
5. Andersen, Jørgen Ellegaard, and Rinat Kashaev. "A TQFT from quantum Teichmüller theory." arXiv preprint arXiv:1109.6295 (2011).
6. Collier, Scott, Lorenz Eberhardt, and Mengyang Zhang. "Solving 3d gravity with Virasoro TQFT." SciPost Physics 15.4 (2023): 151.
Audience
Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
Yes
Notes Public
Yes
Language
Chinese
, English