Multiple polylogarithms and the Steinberg module

 Multiple polylogarithms appear to be central for many seemingly unrelated areas of mathematics: volumes of hyperbolic polytopes, scissors congruence, algebraic K-theory, special values of zeta functions, etc. Despite the existence of this wide network of connections, the most fundamental properties of these functions, predicted by the Goncharov program, remain conjectural. I will talk about the recent progress in the Goncharov program, which is based on the connection between multiple polylogarithms and the Steinberg module of Q. The talk is based on the joint work with Steven Charlton and Danylo Radchenko.