Euler sums and the cyclotomic Grothendieck-Teichmüller group

Hybrid. Contact: Pieter Moree (moree @ mpim-bonn.mpg.de)

Euler sums are real numbers defined by iterated integrals on the projective line minus $0,\infty,1,-1$.  In this talk, we introduce a family of linear relations among Euler sums which exhausts all motivic linear relations. This gives an explicit description of the level two motivic Galois group. We also show that the level two motivic Galois group coincides with the cyclotomic Grothendieck-Teichmüller group introduce by Benjamin Enriquez. Some part of this talk is based on a joint work with Nobuo Sato.