Quantum Invariants and Quantum Representations

主讲人 Speaker:杨田
时间 Time: 每周二、周四13:30-15:05,2019-7-23 ~ 8-21
地点 Venue:清华大学近春园西楼第一会议室

课程描述 Description

This is an introduction to quantum Topology.
In the first half of this series of lectures, I will introduce the colored Jones polynomials of knots and links, the Reshetikin-Tureav invariants of 3-manifolds and the Volume Conjecture that relate those invariants with hyperbolic geometry.
The second half of the series will focus on the Reshetikhin-Turaev representations of the mapping class group of surfaces. The AMU Conjecture claiming that those representations respect the Nielsen-Thurston classification will be introduced.
I will use the skein theoretical approach to the theory which requires the minimum prerequisites.

预备知识 Prerequisites

Basic abstract algebra, basic knowledge of smooth manifolds, fundamental group and homology.

参考资料 References

[1] W.B.R. Lickorish,  The skein method for three-manifold invariants, J. Knot Theory Ramifications 2 (1993), no. 2, 171–194.
[2] Chen, Q. and Yang, T., Volume conjectures for the Reshetikhin-Turaev and the Turaev-Viro invariants, Quantum Topoolgy, 9 (2018), no. 3, 419–460.
[3] Marche J. Introduction to quantum representations of mapping class groups .