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math.CO2025
Tridendriform and dendriform Zeta Values from Schroeder trees
Pierre Catoire, Pierre Clavier, Douglas Modesto da Fraga Candido
To build new generalisations of Multiple Zeta Values, we define new spaces of formal series and formal integrals. We show that they are tridendriform and dendriform algebras. This…
math-ph2025
TRAPs, Generalisations of MZVs, Locality and Resurgence for Quantum Field Theories
Pierre J. Clavier
This thesis presents some mathematical results related to quantum field theory. The first chapter is dedicated to TRAPs and how they could be used to rigorously define Feynman rule…
math.CO2025
Coalgebras, bialgebras and Rota-Baxter algebras from shuffles of rooted forests
Pierre J. Clavier, Douglas Modesto
We construct and study new generalisations to rooted trees and forests of some properties of shuffles of words. First, we build a coproduct on rooted trees which, together with the…