Speaker:  William Ballinger (Harvard University)

Title: The SO(8) invariant of trivalent graphs and its categorification

Abstract: The SO(2n) Reshetikhin-Turaev invariant of a link in the vector representation admits a conjectural categorification due to Khovanov and Rozansky - they prove that their construction is invariant under the first two Reidemeister moves, but not the third. I will present a proof that this is in fact a link invariant in the SO(8) case, based on extending the construction to give an invariant for knotted trivalent graphs, colored by the vector and two spinor representations. Essential simplifications are provided by the triality automorphisms, which allow the three colors to be treated symmetrically. I will also discuss some skein theory for the decategorified invariant.