This mini-workshop will allow for exchanges between experts with different backgrounds, ranging from combinatorics and theory of operads to mathematical physics and dynamical systems, on the theme of graded Hopf algebras. The aim is to compare different viewpoints on the underlying algebraic structures: combinatorial Hopf algebras, trees, pre-Lie algebras, dendriform algebras, quasi-symmetric functions, Ecalle's moulds. We plan to have a few talks prepared in advance but also to provide ample space for discussions through informal sessions.