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.
Lecturer
Date
24th March ~ 7th July, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday | 09:50 - 12:15 | A14-201 | ZOOM 07 | 559 700 6085 | BIMSA |
Prerequisite
Undergraduate Algebra, Undergraduate Topology.
Syllabus
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)
Reference
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)
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
, Postdoc
Video Public
Yes
Notes Public
Yes
Language
Chinese