# Development of Galois-Teichmüller Theory and Anabelian Geometry

 October 29 Friday, 16:00--16:50 H. Furusho (Nagoya University) Geometric interpretation of double shuffle relations of multiple polylogarithms at roots of unity I will give a geometric interpretation of the generalized (including the regularization relation) double shuffle relation for multiple $L$-values. I will explain that Enriquez' mixed pentagon equation implies the relations. As a corollary, an embedding from his cyclotomic analogue of Grothendieck-Teichmüller group into Racinet's cyclotomic double shuffle group is obtained, which extends my provious result.