Reshetikhin-Turaev method for calculating invariants of knots and links

A big breakthrough in knot theory occurred when N. Reshetikhin and V. Turaev developed a method for calculating invariants of knots and links using $R$- matrix — a solution to the Yang-Baxter equation. This method opened up access to a large set of analytical knot invariants associated with finite- dimensional irreducible representations of quantum algebras. Our focus will be on the HOMFLY-PT polynomials, which are connected with quantum algebra $sl(N)$. They coincide with Wilson loop averages in the quantum topological Chern-Simons theory with $SU(N)$ gauge group. At the seminar we will get acquainted with the basics of the theory of knots and their invariants, and also consider the Reshetikhin-Turaev method and its modification for calculating knot invariants at roots of unity.