Gandalf (Pure Maths Student Seminar): The Alexander polynomial as a Reshetikhin-Turaev invariant
22 October 2014 15:00 in CM221
The Alexander polynomial is a classical invariant of knots introduced in the 1920's with clear connections to the topology of knots and surfaces. The Reshetikhin-Turaev invariants are much more recent, and are in general much more poorly understood. These often arise from the representation theory of quantum groups. I will show how the Alexander polynomial can be interpreted as a Reshetikhin-Turaev invariant using representations of U_q(gl(1|1)), and show how this can be used to understand a category of representations of U_q(gl(1|1)). Finally, I will give some suggestions about how this should tie into categorifications of knot invariants, and particularly the connection between HOMFLY homology and Heegaard Floer knot homology.
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.