Modular categories and Reshetikhin-Turaev TQFTs

Speaker: Yilong Wang

Date：Every Tuesday & Thursday 2021-09-13~12-03, 17:05-18:40

Venue：BIMSA Rm 1120

Zoom ID：638 227 8222，Password：BIMSA

Absrtract：

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.

Prerequisite：

Linear algebra, basic category theory
Reference：

Turaev, Vladimir G., Quantum Invariants of Knots and 3-Manifolds, Berlin, Boston: De Gruyter, 2016.

Videos:

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Notes:

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If there is any change of the time and place of the course, please refer to the latest information published on the website