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_Ninvariant.
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_Nrepresentations permits to extend the categorification to the so-called fully colored sl_Ninvariant.