### The Hopf algebra of dissection polylogarithms

Dupont, C *(Institut de Mathématiques de Jussieu)*

Wednesday 10 April 2013, 10:30-11:30

Seminar Room 1, Newton Institute

#### 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.

#### Presentation

#### Video

**The video for this talk should appear here if JavaScript is enabled.**

If it doesn't, something may have gone wrong with our embedded player.

We'll get it fixed as soon as possible.

## Comments

Start the discussion!