Post-Lie algebras in Regularity Structures

In this talk, we will present a new construction of the deformed Butcher-Connes-Kreimer Hopf algebra coming from the theory of Regularity Structures as the universal envelope of a post-Lie algebra. It can be performed using either of the two combinatorial structures that have been proposed in the context of singular SPDEs: decorated trees and multi-indices. Our construction is inspired from multi-indices where the Hopf algebra was obtained as the universal envelope of a Lie algebra. We show that this Lie algebra comes from an underlying post-Lie structure.