Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA) - Volume 1

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Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA) IRMA Lectures in Mathematics and Theoretical Physics Vol. 31 Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA) Volume 1 Editors: Frédéric Chapoton (Université de Strasbourg, France) Frédéric Fauvet (Université de Strasbourg, France) Claudia Malvenuto (Università di Roma La Sapienza, Italy) Jean-Yves Thibon (Université Paris-Est Marne-la-Vallée, France) ISBN print 978-3-03719-204-7, ISBN online 978-3-03719-704-2 DOI 10.4171/204 February 2020, 354 pages, softcover, 17 x 24 cm. 58.00 Euro This is volume 1 of a 2-volume work comprising a total of 14 refereed research articles which stem from the CARMA Conference (Algebraic Combinatorics, Resurgence, Moulds and Applications), held at the Centre International de Rencontres Mathématiques in Luminy, France, from June 26 to 30, 2017. The conference did notably emphasise the role of Hopf algebraic techniques and related concepts (e.g. Rota–Baxter algebras, operads, Ecalle’s mould calculus) which have lately proved pervasive in combinatorics, but also in many other fields, from multiple zeta values to the algebraic study of control systems and the theory of rough paths. The volumes should be useful to researchers or graduate students in mathematics working in these domains and to theoretical physicists involved with resurgent functions and alien calculus. Keywords: Operad, Hopf algebra, algebraic combinatorics, moulds, renormalization, periods, multiple zeta values, resurgent functions, alien calculus, vector fields, diffeomorphisms Shuffle quadri-algebras and concatenation Mohamed Belhaj Mohamed, Dominique Manchon Structure theorems for dendriform and tridendriform algebras Emily Burgunder, Bérénice Delcroix-Oger A group-theoretical approach to conditionally free cumulants Kurusch Ebrahimi-Fard, Frédéric Patras The Natural Growth Scale Jean Ecalle Realizations of Hopf algebras of graphs by alphabets Loïc Foissy Duplicial algebras, parking functions, and Lagrange inversion Jean-Christophe Novelli, Jean-Yves Thibon The triduplicial operad is Koszul Anthony Mansuy The Hopf algebra of integer binary relations Vincent Pilaud and Viviane Pons List of contributors