清华主页 EN
导航菜单

【2022春】Quantum Teichmüller theory

来源: 06-01

时间:2022/4/2 周六

地点:Zoom Meeting

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.


Here's the wechat QR code for the course:


返回顶部
相关文章
  • 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...

  • 【2022秋】Topics in p-adic Hodge theory

    Description:The first half of this course gives a general introduction to p-adic Hodge theory. The second part discusses recent topics, including the Fargues-Fontaine curve and p-adic period domains.Prerequisite:Algebraic number theory and algebraic geometryReference:Laurent Fargues and Jean-Marc Fontaine. Courbes et fibrés vectoriels en théorie de Hodge p-adique. Astérisque (406).Jean-Franç...