Polygonal combinatorics for algebraic cycles

Herbert Gangl  (University of Durham, United Kingdom)
Monday, February 05, 2007
Starting from comparably explicit objects (algebraic cycles), Bloch and Kriz have given a tentative definition of a small yet rich category of motives (mixed Tate motives), at least over a field. They also exhibited a distinguished class of cycles corresponding to polylogarithms. One can also find multiple polylogarithms as algebraic cycles, and it turns out that their differential structure can be conveniently described with the help of combinatorics of polygons. This leads to a coproduct on polygons which is a variant of the Connes-Kreimer coproduct on rooted trees.

Grothendieck's Motives

Norbert Schappacher  (University of Strasbourg, France)
Monday, February 05, 2007
In this talk we will describe Grothendieck's first idea and his basic formalism of motives. At the same time we will cite later results which shed light on certain aspects of Grothendieck's programme. The talk is intended as a basis for the very recent material presented by the other speakers.