We provide an algebraic framework to describe renormalization in regularity structures
based on multi-indices for a large class of semi-linear stochastic PDEs. This framework is …

We replace trees by multi-indices as an index set of the abstract model space to tackle quasi-
linear singular stochastic partial differential equations. We show that this approach is …

In this work, we construct the deformed Butcher-Connes-Kreimer Hopf algebra coming from
the theory of Regularity Structures as the universal envelope of a post-Lie algebra. We show …

We use the diagram-free approach to regularity structures introduced by Otto et. al. to build
rough paths based on multi-indices. We identify the analogue of the insertion pre-Lie …

In this work, we introduce multi-Novikov algebras, a generalisation of Novikov algebras with
several binary operations indexed by a given set, and show that the multi-indices recently …

Typed decorated trees are used by Bruned, Hairer and Zambotti to give a description of a
renormalisation process on stochastic PDEs. We here study the algebraic structures on …

We introduce a unified framework of symmetric resonance based schemes which preserve
central symmetries of the underlying PDE. We extend the resonance decorated trees …

We introduce a general framework of low regularity integrators which allows us to
approximate the time dynamics of a large class of equations, including parabolic and …

We propose a novel way to study numerical methods for ordinary differential equations in
one dimension via the notion of multi‐indice. The main idea is to replace rooted trees in …

We prove the well-posed character of a regularity structure formulation of the quasilinear
generalized (KPZ) equation and give an explicit form for a renormalized equation in the full …