2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59142We discuss the following two problems: 1) The properties of the multiple zeta-values and their generalizations, multiple polylogarithms at N-th roots of unity; 2) The action of the absolute Galois group on the pro-l-completion of the fundamental group of the projective line without zero, infinity, and all N-th roots of unity; and a surprising connection of these problems with the geometry and topology of modular varieties for GL_m.24 pages, 8 pictures, talk at the European Congress of Math., 2000Algebraic GeometryNumber Theorytext