Operadic and simplicial background of some classical Hopf algebras

The Hopf algebras of the title are the cobar contruction on a reduced simplicial set, with
its Hopf algebra structure discovered by Baues, the algebra of rooted forests of Connes
and Kreimer, and the algebra of multi zeta values of Goncharov. In this talk we present
an operadic (and essentially simplicial) construction that encompasses and unies all of
these examples, giving deeper insight into each of them. Indeed, any cooperad which
has a suitably compatible multiplication may be given a canonical (innitesimal) bialgebra
structure, which is a Hopf algebra under connectivity assumptions. Further, we can show
that any reasonable Feynman category gives rise to a Hopf algebra. [Report on joint work
with I Galvez-Carrillo and R Kaufmann]