@article{Clavier2020,
  author    = {Clavier, Pierre J.},
  title     = {Double shuffle relations for arborified zeta values},
  series = {Journal of algebra},
  volume    = {543},
  journal   = {Journal of algebra},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0021-8693},
  doi       = {10.1016/j.jalgebra.2019.10.015},
  pages     = {111 -- 155},
  year      = {2020},
  abstract  = {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 relate them to multiple zeta values. Generalisations to rooted trees of the stuffle and shuffle products are defined and studied. It is further shown that arborified zeta values are algebra morphisms for these new products on trees.},
  language  = {en}
}
@article{Clavier2021,
  author    = {Clavier, Pierre J.},
  title     = {Borel-{\´E}calle resummation of a two-point function},
  series = {Annales Henri Poincar{\´e} : a journal of theoretical and mathematical physics / ed. jointly by the Institut Henri Poincar{\´e} and by the Swiss Physical Society},
  volume    = {22},
  journal   = {Annales Henri Poincar{\´e} : a journal of theoretical and mathematical physics / ed. jointly by the Institut Henri Poincar{\´e} and by the Swiss Physical Society},
  number    = {6},
  publisher = {Springer},
  address   = {Cham},
  issn      = {1424-0637},
  doi       = {10.1007/s00023-021-01057-w},
  pages     = {2103 -- 2136},
  year      = {2021},
  abstract  = {We provide an overview of the tools and techniques of resurgence theory used in the Borel-ecalle resummation method, which we then apply to the massless Wess-Zumino model. Starting from already known results on the anomalous dimension of the Wess-Zumino model, we solve its renormalisation group equation for the two-point function in a space of formal series. We show that this solution is 1-Gevrey and that its Borel transform is resurgent. The Schwinger-Dyson equation of the model is then used to prove an asymptotic exponential bound for the Borel transformed two-point function on a star-shaped domain of a suitable ramified complex plane. This proves that the two-point function of the Wess-Zumino model is Borel-ecalle summable.},
  language  = {en}
}
@article{ClavierGuoPaychaetal.2019,
  author    = {Clavier, Pierre J. and Guo, Li and Paycha, Sylvie and Zhang, Bin},
  title     = {An algebraic formulation of the locality principle in renormalisation},
  series = {European Journal of Mathematics},
  volume    = {5},
  journal   = {European Journal of Mathematics},
  number    = {2},
  publisher = {Springer},
  address   = {Cham},
  issn      = {2199-675X},
  doi       = {10.1007/s40879-018-0255-8},
  pages     = {356 -- 394},
  year      = {2019},
  abstract  = {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 locality during the renormalisation procedure. Viewing renormalisation in the framework of Connes and Kreimer as the algebraic Birkhoff factorisation of characters on a Hopf algebra with values in a Rota-Baxter algebra, we build locality variants of these algebraic structures, leading to a locality variant of the algebraic Birkhoff factorisation. This provides an algebraic formulation of the conservation of locality while renormalising. As an application in the context of the Euler-Maclaurin formula on lattice cones, we renormalise the exponential generating function which sums over the lattice points in a lattice cone. As a consequence, for a suitable multivariate regularisation, renormalisation from the algebraic Birkhoff factorisation amounts to composition by a projection onto holomorphic multivariate germs.},
  language  = {en}
}
@incollection{ClavierGuoPaychaetal.2020,
  author    = {Clavier, Pierre J. and Guo, Li and Paycha, Sylvie and Zhang, Bin},
  title     = {Renormalisation and locality},
  series = {Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA) Volume 2},
  booktitle = {Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA) Volume 2},
  publisher = {European Mathematical Society Publishing House},
  address   = {Z{\"u}rich},
  isbn      = {978-3-03719-205-4 print},
  doi       = {10.4171/205},
  pages     = {85 -- 132},
  year      = {2020},
  language  = {en}
}