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

358 Pages·2020·5.831 MB·English

by  Frédéric Chapoton, Frédéric Fauvet, Claudia Malvenuto, Jean-Yves Thibon

IRMA Lectures in Mathematics
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ISBN 978-3-03719-204-7
www.ems-ph.org
Chapoton et al. | IRMA 31 | FONT: Rotis Sans | Farben: Pantone 287, Pantone 116 | 170 x 240 mm | RB: 23? mm
IRMA Lectures in Mathematics and Theoretical Physics 31
Edited by Christian Kassel and Vladimir G. Turaev
Institut de Recherche Mathématique Avancée
CNRS et Université de Strasbourg
7 rue René Descartes
67084 Strasbourg Cedex
France
IRMA Lectures in Mathematics and Theoretical Physics
Edited by Christian Kassel and Vladimir G. Turaev
This series is devoted to the publication of research monographs, lecture notes, and other material
arising from programs of the Institut de Recherche Mathématique Avancée (Strasbourg, France).
The goal is to promote recent advances in mathematics and theoretical physics and to make them
accessible to wide circles of mathematicians, physicists, and students of these disciplines.
For a complete listing see our homepage at www.ems-ph.org.
10 Physics and Number Theory, Louise Nyssen (Ed.)
11 Handbook of Teichmüller Theory, Volume I, Athanase Papadopoulos (Ed.)
12 Quantum Groups, Benjamin Enriquez (Ed.)
13 Handbook of Teichmüller Theory, Volume II, Athanase Papadopoulos (Ed.)
14 Michel Weber, Dynamical Systems and Processes
15 Renormalization and Galois Theory, Alain Connes, Frédéric Fauvet and Jean-Pierre Ramis (Eds.)
16 Handbook of Pseudo-Riemannian Geometry and Supersymmetry, Vicente Cortés (Ed.)
17 Handbook of Teichmüller Theory, Volume III, Athanase Papadopoulos (Ed.)
18 Strasbourg Master Class on Geometry, Athanase Papadopoulos (Ed.)
19 Handbook of Teichmüller Theory, Volume IV, Athanase Papadopoulos (Ed.)
20 Singularities in Geometry and Topology. Strasbourg 2009, Vincent Blanlœil and Toru Ohmoto
(Eds.)
21 Faà di Bruno Hopf Algebras, Dyson–Schwinger Equations, and Lie–Butcher Series,
Kurusch Ebrahimi-Fard and Frédéric Fauvet (Eds.)
22 Handbook of Hilbert Geometry, Athanase Papadopoulos and Marc Troyanov (Eds.)
23 Sophus Lie and Felix Klein: The Erlangen Program and Its Impact in Mathematics and Physics,
Lizhen Ji and Athanase Papadopoulos (Eds.)
24 Free Loop Spaces in Geometry and Topology, Janko Latschev and Alexandru Oancea (Eds.)
25 Takashi Shioya, Metric Measure Geometry. Gromov‘s Theory of Convergence and Concentration
of Metrics and Measures
26 Handbook of Teichmüller Theory, Volume V, Athanase Papadopoulos (Ed.)
27 Handbook of Teichmüller Theory, Volume VI, Athanase Papadopoulos (Ed.)
28 Yann Bugeaud, Linear Forms in Logarithms and Applications
29 Eighteen Essays in Non-Euclidean Geometry, Vincent Alberge and Athanase Papadopoulos (Eds.)
30 Handbook of Teichmüller Theory, Volume VII, Athanase Papadopoulos (Ed.)
Algebraic Combinatorics,
Resurgence, Moulds and
Applications (CARMA)
Volume 1
Frédéric Chapoton
Frédéric Fauvet
Claudia Malvenuto
Jean-Yves Thibon
Editors
Editors:
Frédéric Chapoton Frédéric Fauvet
IRMA, UFR Mathématiques et Informatique IRMA, UFR Mathématiques et Informatique
Université de Strasbourg Université de Strasbourg
7, rue René Descartes 7, rue René Descartes
67084 Strasbourg CEDEX, France 67084 Strasbourg CEDEX, France
e-mail: [email protected] e-mail: [email protected]
Claudia Malvenuto Jean-Yves Thibon
Dipartimento di Matematica “Guido Castelnuovo” Laboratoire d’Informatique Gaspard Monge
Università di Roma La Sapienza Université Paris-Est Marne-la-Vallée
Piazzale A. Moro 5 5, boulevard Descartes, Champs sur Marne
00185 Roma, Italy 77454 Marne-la-Vallée CEDEX 2, France
e-mail: [email protected] e-mail: [email protected]
2010 Mathematics Subject Classification: 05E, 81T15, 81T18, 81Q30, 34C20, 37C10, 18D50, 34M40, 34M60,
11M32, 30D60
Key words: Operad, Hopf algebra, algebraic combinatorics, moulds, renormalization, periods, multiple zeta
values, resurgent functions, alien calculus, vector fields, diffeomorphisms
ISBN 978-3-03719-204-7
The Swiss National Library lists this publication in The Swiss Book, the Swiss national bibliography, and the
detailed bibliographic data are available on the Internet at http://www.helveticat.ch.
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Contents of Volume 1
Shufflequadri-algebrasandconcatenation
byMohamedBelhajMohamed,DominiqueManchon : : : : : : : : : : : : : : : : 1
Structuretheoremsfordendriformandtridendriformalgebras
byEmilyBurgunder,BéréniceDelcroix-Oger: : : : : : : : : : : : : : : : : : : : : : 29
Agroup-theoreticalapproachtoconditionallyfreecumulants
byKuruschEbrahimi-Fard,FrédéricPatras : : : : : : : : : : : : : : : : : : : : : : 67
TheNaturalGrowthScale
byJeanEcalle : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 95
RealizationsofHopfalgebrasofgraphsbyalphabets
byLoïcFoissy : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 225
Duplicialalgebras,parkingfunctions,andLagrangeinversion
byJean-ChristopheNovelli,Jean-YvesThibon : : : : : : : : : : : : : : : : : : : : : 263
ThetriduplicialoperadisKoszul
byAnthonyMansuy : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 291
TheHopfalgebraofintegerbinaryrelations
byVincentPilaudandVivianePons : : : : : : : : : : : : : : : : : : : : : : : : : : : : 299
Listofcontributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
Combinatoire Algébrique, Résurgence, Moules et Applications
(Algebraic Combinatorics, Resurgence, Moulds and Applications)
Conférence de clôture du 26 au 30 juin 2017
Ines Aniceto (Krakow)
David Broadhurst (Open U.)
Francis Brown (Oxford)
Emily Burgunder (Toulouse)
Gerald Dunne (U. Connecticut)
Kurusch Ebrahimi-Fard (Trondheim)
Jean Écalle (Orsay)
Michael Hoffman (Annapolis)
Carlos Mafra (Southampton)
Dominique Manchon (Clermont-Ferrand)
Marcos Marino (Genève)
Frédéric Menous (Orsay)
Jean-Christophe Novelli (Marne-la-Vallée)
Erik Panzer (Oxford)
Frédéric Patras (Nice)
Viviane Pons (Orsay)
David Sauzin (Pisa)
Karen Yeats (Vancouver)
Scientific & Organizing Committee
Frédéric Chapoton (CNRS/Strasbourg) Frédéric Fauvet (Strasbourg)
Claudia Malvenuto (Roma) Jean-Yves Thibon (Marne-la-Vallée)
Contents of Volume 2
Specialvaluesoffinitemultipleharmonicq-seriesatrootsofunity
byHenrikBachmann,YoshihiroTakeyamaandKojiTasaka : : : : : : : : : : : : 1
Mouldcalculus: fromprimarytosecondarymouldsymmetries
byOlivierBouillot : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 19
Renormalisationandlocality: branchedzetavalues
byPierreClavier,LiGuo,SylviePaychaandBinZhang : : : : : : : : : : : : : : 85
Thescramblingoperatorsappliedtomultizetaalgebra
andsingularperturbationanalysis
byJeanEcalle : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 135
Quasi-shufflealgebrasandapplications
byMichaelE.Hoffman : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 327
Planarbinarytreesinscatteringamplitudes
byCarlosR.Mafra: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 349
Astudyonprefixesofc invariants
2
byKarenYeats: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 367
Listofcontributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

Introduction
Thisisthefirstoftwovolumesthatconstituteafollow-uptotheCARMAConference
(AlgebraicCombinatorics,Resurgence,MouldsandApplications),heldattheCentre
Internationalde RencontresMathématiquesin Luminy, France, from June26 to 30,
2017.
The CARMA projectof the FrenchNationalResearchAgencydevotedto Alge-
braicCombinatorics,Resurgence,MouldsandApplicationswasstartedin2012.
The conference CARMA 2017 aimed at taking stock of the numerous recent
achievementsandpublicationsonthesetopics,fromexpertsbothoutsideandinside
thisresearchgroup.
TheconferencedidnotablyemphasisetheroleofHopfalgebraictechniquesand
related objects such as Rota Baxter algebras, operads and Ecalle s mould calculus.
They have lately provedpervasivein combinatoricsas well as in many other fields,
from multiple zeta values to the algebraic study of control systems and the theory
of rough paths. Moreover, recent years have seen a burst of articles in various ar-
eas of theoretical physics that enhance the role of resurgent functions beyond their
originalapplicationsindynamicalsystems,whichwerealsoamongthetopicsofthe
conference.
Some of the papers in these volumes correspond to talks given during the con-
ference, others are original articles from participants. The contributions to the first
volume essentially center about mould calculus and combinatorial Hopf algebras.
Thesecondvolumemainlydealswithmultizetasandphysicalapplications,although
thereisnoclearcutseparationbetweenboth.