Invariants of Knots and 3-manifolds

Teacher :Nicolai Reshetikhin
Schedule: Every Mon. 8:00-9:35 2021-9-13 ~ 12-31
Venue:Zoom Online + Rm 6A209 Sixth Teaching Bldg.


The goal of this course is an introduction to theory of invariants of knots and to closely related subjects such as representation theory of quantum groups and topological quantum field theory. We will start with a brief reminder of what are braids, knots, tangled graphs and 3-manifolds. Then invariants of knots will be constructed out of solutions to the Yang-Baxter equation. Examples of such construction are Jones, HOMFLY and Kauman polynomials. After this a functorial description of these invariants will be given following the work of Turaev and myself. For this we will make a detour into representation theory of Hopf algebras. After this we will discuss how these invariants of knots are related to quantum field theory.



Zoom Meeting ID:849 963 1368 

This course is organized by Qiuzhen College, Tsinghua University.