Paul Wedrich (U Cambridge): Categorified colored HOMFLY invariants of rational tangles (Simons Lecture on Mathematical Physics)

Paul Wedrich (U Cambridge)

Abstract: The colored Jones and HOMFLY polynomials are invariants of knots in S^3 that are defined via the representation theory of quantum sl(N). I will start by explaining how these invariants generalize to the case of tangles, i.e. knot fragments in B^3. For the case of rational tangles, I will introduce a picture-way of computing  a categorified version of colored HOMFLY polynomials, thereby proving a tangle-analogue of a conjecture of Gukov and Stosic.  Based on joint work with Mihajlo Cekic and Jake Rasmussen.


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June 30, 2014