11 citations · 19 across the 14 of their papers we have counts for
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Cluster Polylogarithms I: Quadrangular Polylogarithms
Andrei Matveiakin, Daniil Rudenko
We suggest a definition of cluster polylogarithms on an arbitrary cluster variety and classify them in type . We find functional equations for multiple polylogarithms which gene…
On the Goncharov depth conjecture and a formula for volumes of orthoschemes
Daniil Rudenko
We prove a conjecture of Goncharov, which says that any multiple polylogarithm can be expressed via polylogarithms of depth at most half of the weight. We give an explicit formula…
Rational Elliptic Surfaces and the Trigonometry of Tetrahedra
Daniil Rudenko
We study the trigonometry of non-Euclidean tetrahedra using tools from algebraic geometry. We establish a bijection between non-Euclidean tetrahedra and certain rational elliptic s…
On the functional equations for polylogarithms in one variable
Daniil Rudenko
We develop a new approach to the study of the functional equations satisfied by classical polylogarithms, inspired by Goncharov's conjectures. We prove a sharpened version of Zagie…