February 29

Muriel Livernet ( MIT and Universite Paris 13 )

Posets, Groups and Hopf algebras associated to a set-operad

Abstract: In this talk we will review a result of Bruno Vallette linking the notion of Koszul duality of operads and Cohen-MacCauley posets. We'll present in this context a joint work with F. Chapoton, where we compare two groups, one built directly from operads, and another one associated to the incidence Hopf algebra of a family of posets. This leads us to a new link between the Hopf algebra of Connes and Kreimer in renormalisation theory and operads built on rooted trees.