Daniil Rudenko

I am an assistant professor at the University of Chicago and a von Neumann Fellow at the Institute for Advanced Study in Fall 2026. I work on polylogarithms, algebraic K-theory of fields, and scissors congruence. I am also fond of the trigonometry of a tetrahedron. My CV is here.

For 18,783 mathematical problems published in the British periodical Educational Times, visit the database woollymathematics created in collaboration with S. Despeaux and S. Vorobiev. This project was inspired by the story of Joseph Wolstenholme.

Preprints

• Mixed Tate motives over number fields, with A. Kupers and I. Sierra
• The Goncharov Lie coalgebra of a field, with A. Kupers and I. Sierra
• Multiple polylogarithms and the Steinberg module, with S. Charlton and D. Radchenko
• Cluster polylogarithms, with A. Matveiakin

Selected Publications

• Motivic correlators, cluster varieties and Zagier's conjecture on ζ_F(4), with A. Goncharov, to appear in Annals of Mathematics
• The Hopf algebra of formal multiple polylogarithms , with S. Charlton, A. Matveiakin, and D. Radchenko, IMRN (2026)
• On the Goncharov depth conjecture and polylogarithms of depth two, with S. Charlton, H. Gangl, and D. Radchenko, Selecta Mathematica (2024)
• On the Goncharov depth conjecture and a formula for volumes of orthoschemes, JAMS (2023)
• Rational elliptic surfaces and the trigonometry of tetrahedra, Inventiones mathematicae (2022)
• The strong Suslin reciprocity law, Compositio Mathematica (2021)

Selected Talks

• Multiple polylogarithms, algebraic K-Theory, and the Steinberg module, IAS, May 2025
• Volumes of hyperbolic polytopes, cluster polylogarithms, and the Goncharov depth conjecture, Conference "On the Crossroads of Algebra, Geometry and Physics," Yale, May 2022
• Rational elliptic surfaces and trigonometry of non-Euclidean tetrahedra, Stanford, May 2022