The notions of a post-group and a pre-group are introduced as a unification and enrichment
of several group structures appearing in diverse areas from numerical integration to the …

In this paper, we explore the version of Hairer's regularity structures based on a greedier
index set than trees, as introduced in (Otto et al. in A priori bounds for quasi-linear SPDEs in …

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 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 …

Given a commutative algebra $ A $, we exhibit a canonical structure of post-Lie algebra on
the space $ A\otimes Der (A) $ where $ Der (A) $ is the space of derivations on $ A $, in …

In this paper, first, we introduce the notion of post-Hopf algebra, which gives rise to a post-
Lie algebra on the space of primitive elements and the fact that there is naturally a post-Hopf …

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 …

Malliavin calculus provides a characterization of the centered model in regularity structures
that is stable under removing the small-scale cut-off. In conjunction with a spectral gap …

In this work, we introduce Regularity Structures B-series which are used for describing
solutions of singular stochastic partial differential equations (SPDEs). We define composition …