  We 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.
