【2022春】Quantum Teichmüller theory-清华大学求真书院

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【2022春】Quantum Teichmüller theory

来源： 04-02

时间：4.2(周六)/4.6~6.24 (周一/周三) 9:50-11:25

地点：Zoom Meeting ID: 4552601552 Passcode: YMSC

组织者：Dylan Allegretti

主讲人：Dylan Allegretti

课程描述 Description

The Teichmüller space of a surface is a fundamental construction in low-dimensional geometry and topology. It is a space parametrizing hyperbolic structures on the surface up to isotopy. The goal of quantum Teichmüller is to construct a quantum deformation of the algebra of functions on the classical Teichmüller space. This course will give an introduction to these ideas and their applications in mathematical physics.

预备知识 Prerequisites

Basic differential geometry and algebraic topology

参考资料 References
Topics will be selected from influential papers in quantum Teichmüller theory, possibly including the following:

1. Andersen, J.E. and Kashaev, R. (2014). A TQFT from quantum Teichmüller theory.Communications in Mathematical Physics, 330, 887--934.

2. Bonahon, F. and Wong, H. (2011). Quantum traces for representations of surface groups in SL_2.Geometry & Topology, 15(3), 1569--1615.

3. Fock, V.V. and Chekhov, L.O. (1999). A quantum Teichmüller space.Theoretical and Mathematical Physics, 120(3), 1245--1259.

4. Fock, V.V. and Goncharov, A.B. (2009). The quantum dilogarithm and representations of quantum cluster varieties.Inventiones mathematicae, 175(2), 223--286.

5. Kashaev, R.M. (1998). Quantization of Teichmüller spaces and the quantum dilogarithm.Letters in Mathematical Physics, 43(2), 105--115.

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