# Clément Dupont: The Hopf algebra of dissection polylogarithms

**Abstract**:

Combinatorial Hopf algebras have become popular in quantum field theory since the work of Connes and Kreimer on renormalization. The aim of this talk is to present a Hopf algebra that appears in the motivic world and has the same combinatorial taste as the Connes-Kreimer Hopf algebra.

We introduce a class of multivalued functions called "dissection polylogarithms" which generalize the iterated integrals on the punctured complex plane. They are indexed by combinatorial objects called dissection diagrams. We compute the coproduct of the motivic versions of the dissection polylogarithms and relate it to a combinatorial Hopf algebra based on the dissection diagrams.