16:00 - 17:00, March 13, 2025 (Thursday) R440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Goncharov's Programme and Depth Reductions of Multiple Polylogarithms Steven Charlton (Max Planck Institute)
Abstract
Multiple polylogarithms are a class of multi-variable special functions appearing in connection with K-theory, hyperbolic geometry, values of zeta functions /L-functions/ Mahler measures, mixed Tate motives, and in high-energy physics.
One of the main challenges in the study of multiple polylogarithms revolves around understanding how on many variables a multiple polylogarithm function (or 'interesting' combinations thereof) actually depend (''the depth''), as for example can already be expressed via . Goncharov gave a conjectural criterion (''the Depth Conjecture'') for determining this, using the motivic coproduct, as part of his programme to investigate Zagier's Polylogarithm Conjecture on values of the Dedekind zeta function .
I will give an overview of multiple polylogarithms, Goncharov's Depth Conjecture, and its implications. I will try to discuss what is currently known, including recent results in weight 6, and what we are still trying to investigate.
