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Speaker:

Danylo Radchenko
Affiliation:

MPIM
Date:

Tue, 2019-01-08 14:00 - 15:00
Location:

MPIM Lecture Hall
Parent event:

Seminar on Algebra, Geometry and Physics 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 "quadruple ratio" and as a by-product we get an explicit formula

for the Borel regulator of K_7 in terms of the tetralogarithm function

(joint work with S. Charlton and H. Gangl).

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