Introduction to Quantum Topology I
This course is an introduction to quantum topology, a branch of low-dimensional topology informed by Chern-Simons theory and its generalizations. In the first part of the series, we will focus on combinatorial quantum invariants of links and 3-manifolds and their algebraic nature.
讲师
日期
2025年03月24日 至 07月07日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一 | 09:50 - 12:15 | A14-201 | ZOOM 07 | 559 700 6085 | BIMSA |
修课要求
Undergraduate Algebra, Undergraduate Topology.
课程大纲
In this course, we will cover the following topics:
1. Kauffman Bracket and Jones Polynomial, 2D topological quantum field theory.
2. Jones-Wenzl Projectors, Temperley Lieb Category, Ribbon Categories.
3. Reshetikhin-Turaev Functor.
4. Turaev-Viro invariant (TQFT) and Reshetikhin-Turaev invariant(TQFT).
5. Quantum Double, Tube Algebra(Category) and Alterfold construction.
6. Advanced Topics(Homotopy Quantum Field Theory, Modular Invariance and Conformal Field Theory)
1. Kauffman Bracket and Jones Polynomial, 2D topological quantum field theory.
2. Jones-Wenzl Projectors, Temperley Lieb Category, Ribbon Categories.
3. Reshetikhin-Turaev Functor.
4. Turaev-Viro invariant (TQFT) and Reshetikhin-Turaev invariant(TQFT).
5. Quantum Double, Tube Algebra(Category) and Alterfold construction.
6. Advanced Topics(Homotopy Quantum Field Theory, Modular Invariance and Conformal Field Theory)
参考资料
Turaev - Quantum Invariants of Knots and 3-Manifolds (1994)
Kirillov- Lectures on tensor categories and modular functor (2001)
Kirillov- Lectures on tensor categories and modular functor (2001)
听众
Undergraduate
, Advanced Undergraduate
, Graduate
, 博士后
视频公开
公开
笔记公开
公开
语言
中文