Gandalf (Pure Maths Student Seminar): Quantum Invariants of Knots
20 February 2014 16:00 in CG85
After the Jones polynomial was discovered in the 80's, Jones's methods were generalised repeatedly until Reshetikhin and Turaev described a very general method for constructing polynomial invariants of knots. For any representation of any simple Lie algebra, their method describes a procedure for constructing a knot invariant from it. This procedure involves the so-called 'quantum groups' described by physicists, which (for the purposes of this talk) are 1-parameter deformations of universal enveloping algebras. Even in the simplest cases, these knot invariants are quite poorly understood and are still very actively researched. In this talk I will try and describe (without too many messy details) quantum groups and how knot polynomials are obtained from them, with the construction of the Jones polynomial as an example.
Gandalf is the pure maths student seminar. Gandalf stands for the Geometry AND ALgebra Forum. It is run by and for pure postgraduates, but welcomes anyone who is interested in coming along.
Content from previous talks is available at the gandalf seminar home page.