Invariants of Knots and 3-manifolds, Representation Theory and Quantum Field Theory.
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 Kauffman 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.