ONLINE: Zagier's polylogarithm conjecture and an explicit 4-ratio

Zoom Online Meeting ID: 919 6497 4060
For password see the email or contact Pieter Moree (moree@mpim...).

In his celebrated proof of Zagier's polylogarithm conjecture
for weight 3 Goncharov introduced a "triple ratio", a projective
invariant akin to the classical cross-ratio. He has also conjectured the
existence of "higher ratios" that should play an important role for
Zagier's conjecture in higher weights. Recently, Goncharov and Rudenko
proved the weight 4 case of Zagier's conjecture with a somewhat indirect
method where they avoided the need to define a corresponding "quadruple
ratio". We propose an explicit candidate for such a "quadruple ratio"
and as a by-product we get an explicit formula for the Borel regulator
of K7 in terms of the tetralogarithm function (joint work with H. Gangl
and D. Radchenko).