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The Alexander polynomial as a Reshetikhin-Turaev invariant

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  • UserJonathan Grant (Durham)
  • ClockFriday 06 March 2015, 15:00-16:00
  • HouseMR13.

If you have a question about this talk, please contact Joe Waldron.

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 explain how this relates to the theory of highest weight modules of U_q(gl(m)), and can be categorified using projective modules over cyclotomic KLR algebras, and how the theory of foams for sl_n knot homology fit into this picture.

This talk is part of the Junior Geometry Seminar series.

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