Invariants of knots and Quantum Groups, Fall 2021

These are the records of the course that I taught at Tsinghua University in Yau Center for Mathematical Sciences in the Fall 2021.

Reading material.

Here is a list a list of books. This list is incomplete, but cover the subject sufficiently.

Here is the link to notes from the class “Quantum groups and knot theory” which was taught by E. Opdam and J. Stokman at the University of Amsterdam.

Here is the link to the book “Tensor Categories” by P. Etingof, S. Gelaki, D. Nikshych and V. Ostrik.

Here is the link to lecture notes by P. Safronov on quantum groups.

Here is my old paper on solutions to the Yang-Baxter equation and invariants of knots where it is shown that Jones twist exists for any strongly non-degenerate R-matrix.

Here is an old paper on quantum sl(2) and invariants of knots. This is where quantum 6j-symbols in the context of representations of quantum sl(2) and colored Jones polynomials were introduced.

Recordings of Lectures

Recordings can be found here.

Lecture Notes

These are the notes that I prepared in advance.

Notes during lectures

Here are the notes that I made during zoom lectures.

Exam

Here is the take home exam.