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### 【2022春】Quantum Teichmüller theory    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 ReferencesTopics 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.

Here's the wechat QR code for the course: • ### 【2022春】Quantum Teichmüller theory

课程描述 DescriptionThe 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...

• ### Non-abelian Hodge theory and higher Teichmüller spaces

Abstract: Non-abelian Hodge theory relates representations of the fundamental group of a compact Riemann surface X into a Lie group G with holomorphic objects on X known as Higgs bundles, introduced by Hitchin more than 35 years ago. Starting with the case in which G is the circle, and the 19th century Abel-Jacobi's theory, we will move to the case of G=SL(2,R) and the relation to Teichmüller t...