# Modular categories and Reshetikhin-Turaev TQFTs

## 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:

[1](PW: ^U.un3qd)  [2](PW: VT@DY3H8)  [3](PW: VvsDi72%)  [4](PW: &J1P.b&9)  [5](PW: @rH0F#*F)  [6](PW: d7\$g.np2)  [7](PW: eqea=5^M)  [8](PW: kbPEZ4?m)  [9](PW: p=U8FiPi)  [10](PW: K+e=8C90)  [11](PW: NNH7A@!9)  [12](PW: KE5G^\$@9)  [13](PW: #RJi!93!)  [14]  [15](PW: \$1MUwReD)  [16](PW: 1%+XFcaD)  [17]  [18](PW: wb9HyG!j)  [19]

Notes:

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