Algebra/Topology Seminar by Herbert Gangl

Abstract: In the early nineties, Goncharov proved the weight 3 case of Zagier's Conjecture

stating that the special value $\zeta_F(3)$ of a number field $F$ is essentially expressed

as a determinant of trilogarithm values taken in that field. He also envisioned a vast--partly conjectural--programme of how to approach the conjecture for higher weight. We can remove one important obstacle in weight~4 by solving one of Goncharov's conjectures. It further allows us to deduce a functional equation for $Li_4$ in four variables as one expects to enter in a more explicit definition of $K_7(F)$.