Modular categories and Reshetikhin-Turaev TQFTs
This course gives an introduction to modular categories with an emphasize on the 3-dimensional Reshetikhin-Turaev (RT) TQFTs. We will start by introducing the notion of modular categories and a graphical calculus on them. We will see how this hybrid of algebra and topology enables us to define invariants of framed links and 3-manifolds. We will then give an axiomatic definition of TQFTs and discuss some general properties of them. Finally, we will focus on the 3-dimensional RT-TQFT associated to modular categories with examples involving groups and quantum groups. Time permitted, we will discuss the mapping class group representations of an RT-TQFT in depth.
讲师
日期
2021年09月14日 至 12月09日
修课要求
Linear algebra, basic category theory
参考资料
Turaev, Vladimir G., Quantum Invariants of Knots and 3-Manifolds, Berlin, Boston: De Gruyter, 2016.
视频公开
公开
笔记公开
公开
讲师介绍
王亦龙于2018年从俄亥俄州立大学数学专业博士毕业,之后在路易斯安那州立大学任博士后,并于2021年加入BIMSA任助理研究员。主要研究方向为量子代数与量子拓扑,具体课题包括模张量范畴及其对应的拓扑量子场论的代数与数论性质。