Cluster polylogarithms, Grassmannian polylogarithms and Zagier's conjecture on zeta_F(n), n >= 5

• Applicant: Dr. Steven Charlton
• Subject Area: Mathematics
• Term: from 2020 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 442093436

• Final Report Year: 2023

Final Report Abstract

We established a number of important conceptual results on MPL’s and their special values, and investigated a new connection between number theory and differential geometry. Although one still does not have a proof of ζF (5), we have laid the groundwork for future attacks on Zagier’s conjecture with these new results. The project should therefore be viewed as very successful.

Publications

• Clean Single-Valued Polylogarithms. Symmetry, Integrability and Geometry: Methods and Applications.
  Charlton, Steven; Duhr, Claude & Gangl, Herbert
  
• Appendix A to L. Heller, S. Heller, and M. Traizet, Complete families of embedded high genus CMC surfaces in the 3-sphere”. Preprint. v3, Apr 2022, 55 pages
  Steven Charlton
  
• On two conjectures of Sun concerning Apéry-like series. Forum Mathematicum, 0(0).
  Charlton, Steven; Gangl, Herbert; Lai, Li; Xu, Ce & Zhao, Jianqiang
  
• Evaluation of and period polynomial relations. Forum of Mathematics, Sigma, 12.
  Charlton, Steven & Keilthy, Adam
  
• On the Goncharov depth conjecture and polylogarithms of depth two. Selecta Mathematica, 30(2).
  Charlton, Steven; Gangl, Herbert; Radchenko, Danylo & Rudenko, Daniil
  
• On motivic multiple t values, Saha’s basis conjecture, and generators of alternating MZV’s. Mathematische Annalen, 392(2), 1995-2079.
  Charlton, Steven
  
• Symmetry results for multiple t-values. Mathematische Zeitschrift, 309(4).
  Charlton, Steven & Hoffman, Michael E.
  
• Explicit formulas for Grassmannian polylogarithms in weights 4 and 5. Journal of Number Theory, 280, 537-582.
  Charlton, Steven; Gangl, Herbert & Radchenko, Danylo