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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Gandalf (Pure Maths Student Seminar): The Alexander polynomial as a Reshetikhin-Turaev invariant

Presented by Jonathan Grant, Durham

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.

Contact j.w.lawson@durham.ac.uk or steven.charlton@durham.ac.uk for more information

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.