2 citations · 3 across the 2 of their papers we have counts for
4 papers
ProPs of graphs and generalised traces
Pierre J. Clavier, Loic Foissy, Sylvie Paycha
We assign generalised convolutions (resp. traces) to graphs whose edges are decorated by smooth kernels (resp. smoothing operators) on a closed manifold. To do so, we introduce the…
Double shuffle relations for arborified zeta values
Pierre J. Clavier
Arborified zeta values are defined as iterated series and integrals using the universal properties of rooted trees. This approach allows to study their convergence domain and to re…
Locality and renormalisation: universal properties and integrals on trees
Pierre Clavier, Li Guo, Sylvie Paycha +1
The purpose of this paper is to build an algebraic framework suited to regularise branched structures emanating from rooted forests and which encodes the locality principle. This i…
An algebraic formulation of the locality principle in renormalisation
Pierre Clavier, Li Guo, Sylvie Paycha +1
We study the mathematical structure underlying the concept of locality which lies at the heart of classical and quantum field theory, and develop a machinery used to preserve local…