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The Hopf algebra of dissection polylogarithms

Presented by: 
C Dupont Institut de Mathématiques de Jussieu
Date: 
Wednesday 10th April 2013 - 10:30 to 11:30
Venue: 
INI Seminar Room 1
Abstract: 
Grothendieck's theory of motives has given birth to a conjectural Galois theory for periods. Replacing the periods with their motivic avatars, one gets an algebra of motivic periods that are acted upon by a motivic Galois group. Recently, the computation of this action for multiple zeta values has been studied and used by Deligne, Goncharov and Brown among others. In this talk we will introduce a family of periods indexed by some combinatorial objects called dissection diagrams, and compute the action of the motivic Galois group on their motivic avatars. This generalizes the case of (generic) iterated integrals on the punctured complex plane. We will show that the motivic action is given by a very simple combinatorial Hopf algebra.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons