Geometry of multiple zeta values

Abstract

Many relations are known between multiple zeta values ζ(_k_1,...,_k_n). A relation coming from the associator condition for the Drinfeld associator, the generating function of multiple zeta values, is a geometric relation. By the theory of mixed motives, we can control the dimension of the rational linear hull of multiple zeta values. The harmonic shuffle relation also comes from geometry, and more strongly, this is implied by the associator relation.