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:

[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:

[1]  [2]  [3]  [4]  [5]  [6]  [7]  [8]  [9]  [10]  [11]  [12]  [13]  [14]  [15]  [16]  [17]  [18]  [19]  

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