Friday, August 5, 13.30, 7.527

Louis-Hadrien Robert (Hamburg)

Recent developements around the *sl*_{N}-homology.

Abstract:

(partly joint with Matt Hogancamp and Emmanuel Wagner)

The *sl*_{N}-invariant is a polynomial knot invariant built up
using the representations of the Hopf algebra *U_q*(*sl*_{N}).
The *sl*_{N}-homology is a categorification of the
*sl*_{N}-invariant: with every knot it associates a complex of
graded vector spaces whose graded Euler Characteristic is given by the
*sl*_{N}invariant.

After an introduction about the *sl*_{N}-invariant, I'll
describe the knot homology machinery, then I will explain how some easy
but somewhat new constructions in the category of
*sl*_{N}representations permits to extend the categorification
to the so-called fully colored *sl*_{N}invariant.