11 citations · 19 across the 14 of their papers we have counts for
15 papers
On the surjectivity conjectures of Dupont and Monod
Alexander Kupers, Daniil Rudenko, Ismael Sierra
In this paper we apply our work on polylogarithmic cocycles representing the Borel classes to establish that the comparison map from bounded continuous cohomology to continuous coh…
Mixed Tate motives over number fields
Alexander Kupers, Daniil Rudenko, Ismael Sierra
This paper relates algebraic K-theory of fields to polylogarithms via general linear groups. We focus on the case of number fields and prove that the motivic realisation map from t…
The Goncharov Lie coalgebra of a field
Alexander Kupers, Daniil Rudenko, Ismael Sierra
This paper relates algebraic -theory of fields to polylogarithms via general linear groups. We introduce the Goncharov Lie coalgebra, defined in terms of the -homology…
Multiple polylogarithms and the Steinberg module
Steven Charlton, Danylo Radchenko, Daniil Rudenko
We establish a connection between multiple polylogarithms on a torus and the Steinberg module of , and show that multiple polylogarithms of depth and weight can…
The Hopf algebra of formal multiple polylogarithms
Steven Charlton, Andrei Matveiakin, Danylo Radchenko +1
We define a Hopf algebra of polylogarithms of an arbitrary field, which is a candidate for a conjectural Hopf algebra of framed mixed Tate motives. Our definition is elementary and…
Joseph Wolstenholme and the Trigonometry of Tetrahedra
Daniil Rudenko
We describe the results in the trigonometry of tetrahedra obtained by Joseph Wolstenholme in the last few years of his life. 'The late Professor Wolstenholme, M.A., Sc.D., shortly…
On the Goncharov Depth Conjecture and polylogarithms of depth two
Steven Charlton, Herbert Gangl, Danylo Radchenko +1
We prove the surjectivity part of Goncharov's depth conjecture. We also show that the depth conjecture implies that multiple polylogarithms of depth and weight can be expre…
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…
Motivic correlators, cluster varieties and Zagier's conjecture on zeta(F,4)
Alexander B. Goncharov, Daniil Rudenko
We prove Zagier's conjecture on the value at s=4 of the Dedekind zeta-function of a number field F. For any field F, we define a map from the appropriate pieces of algebraic K-theo…
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…
The Strong Suslin Reciprocity Law
Daniil Rudenko
We prove the strong Suslin reciprocity law conjectured by A. Goncharov. The Suslin reciprocity law is a generalization of the Weil reciprocity law to higher Milnor theory. The…
A property of trivalent graphs related to equidissections
Daniil Rudenko
Monsky proved that a square cannot be dissected into an odd number of triangles of equal area. Stein conjectured that the same holds for any polygon whose edges can be paired into…
On equidissection of balanced polygons
Daniil Rudenko
In this paper we show that a lattice balanced polygon of odd area cannot be cut into an odd number of triangles of equal areas. First result of this type was obtained by Paul Monsk…