Goncharov depth conjecture and volumes of orthoschemes

by Daniil Rudenko (University of Chicago)

Thursday 28 Jan 2021, 12:30 → 14:30 Europe/Moscow

818-1526-4739 (Zoom)

Goncharov conjectured that any multiple polylogarithm can be expressed via polylogarithms of depth at most half of the weight. In the first part of the talk I will explain how this conjecture fits into the general scheme of conjectures about mixed Tate motives. In the second part of the talk I will explain an idea behind the proof of the Goncharov conjecture. The proof is based on an explicit formula, involving a summation over trees that correspond to decompositions of a polygon into quadrangles. Surprisingly, almost the same formula gives a volume of a hyperbolic orthoscheme generalising the formula of Lobachevsky in dimension 3 to an arbitrary dimension. 

The talk is based on the preprint https://arxiv.org/abs/2012.05599v1

Notes from the talk Video