Computation and Combinatorics in Dynamics, Stochastics and Control: The Abel Symposium, Rosendal, Norway, August 2016 PDF
Preview Computation and Combinatorics in Dynamics, Stochastics and Control: The Abel Symposium, Rosendal, Norway, August 2016
Abel Symposia 13 Elena Celledoni Giulia Di Nunno Kurusch Ebrahimi-Fard Hans Zanna Munthe-Kaas Editors Computation and Combinatorics in Dynamics, Stochastics and Control The Abel Symposium, Rosendal, Norway, August 2016 ABEL SYMPOSIA Edited by the Norwegian Mathematical Society Moreinformationaboutthisseriesathttp://www.springer.com/series/7462 s) a a K e- h nt u M H. o: ot h P ( m. u si o p m y S el b A 6 1 0 2 n i s nt a p ci arti P Elena Celledoni • Giulia Di Nunno (cid:129) Kurusch Ebrahimi-Fard (cid:129) Hans Zanna Munthe-Kaas Editors Computation and Combinatorics in Dynamics, Stochastics and Control The Abel Symposium, Rosendal, Norway, August 2016 123 Editors ElenaCelledoni GiuliaDiNunno DepartmentofMathematicalSciences DepartmentofMathematics NorwegianUniversityofScience UniversityofOslo andTechnology Oslo,Norway Trondheim,Norway KuruschEbrahimi-Fard HansZannaMunthe-Kaas DepartmentofMathematicalSciences DepartmentofMathematics NorwegianUniversityofScience UniversityofBergen andTechnology Bergen,Norway Trondheim,Norway ISSN2193-2808 ISSN2197-8549 (electronic) AbelSymposia ISBN978-3-030-01592-3 ISBN978-3-030-01593-0 (eBook) https://doi.org/10.1007/978-3-030-01593-0 LibraryofCongressControlNumber:2018966592 Mathematics Subject Classification (2010): 15A52, 16W30, 17D25, 35R60, 37E20, 60H15, 76M35, 93C10 ©SpringerNatureSwitzerlandAG2018 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Foreword TheNorwegiangovernmentestablishedtheAbelPrizeinmathematicsin2002,and the first prize was awarded in 2003. In addition to honoring the great Norwegian mathematicianNielsHenrikAbelbyawardinganinternationalprizeforoutstanding scientificworkinthefieldofmathematics,theprizeshallcontributetowardraising the status of mathematics in society and stimulate the interest for science among schoolchildrenandstudents.Inkeepingwiththisobjective,theNielsHenrikAbel Board has decided to finance annual Abel Symposia. The topic of the symposia maybeselectedbroadlyintheareaofpureandappliedmathematics.Thesymposia should be at the highest international level and serve to build bridges between thenationalandinternationalresearchcommunities.TheNorwegianMathematical Societyisresponsiblefortheevents.Ithasalsobeendecidedthatthecontributions fromthese symposia shouldbe presentedin a series of proceedings,and Springer Verlag has enthusiastically agreed to publish the series. The Niels Henrik Abel Boardisconfidentthattheserieswillbeavaluablecontributiontothemathematical literature. ChairoftheNielsHenrikAbelBoard KristianRanestad v Preface In recent years we have witnessed a remarkable convergence between individual mathematical disciplines that approach deterministic and stochastic dynamical systems from mathematical analysis, computational mathematics, and control theoretical perspectives. One of the prime examples is the theory of rough paths, pioneered by Terry Lyons (Oxford). Massimiliano Gubinelli (Paris/Bonn) subse- quently developed the notions of controlled and branched rough paths. This line of work culminated in the 2014 Fields Medal being awarded to Martin Hairer (Warwick/London)forhisfar-reachingworkonregularitystructures,whichledhim tobreakthroughdiscoveriesinthetheoryofstochasticpartialdifferentialequations. Rough paths theory has strong connections to the analysis of geometric inte- grationalgorithmsfordeterministicflows, wherethe needto understandstructure preservation has led to the developmentof new analytical tools based on modern algebraandcombinatorics.Recentdevelopmentsinthesefieldsprovideacommon mathematicalframeworkforattackingmanydifferentproblemsrelatedtodifferen- tialgeometry,analysisandalgorithmsforstochasticanddeterministicdynamics. In the AbelSymposium2016(August16–19),leadingresearchersin the fields of deterministic and stochastic differential equations, numerical analysis, control theory,algebra, and random processes met at the picturesqueBarony in Rosendal nearBergenforalivelyexchangeofresearchideasandpresentationofthecurrent state of the art in these fields. The currentAbelSymposia volume may serve as a pointofdepartureforexploringtheserelatedbutdiversefieldsofresearch,aswellas anindicatorofimportantcurrentandfuturedevelopmentsinmodernmathematics. Trondheim,Norway ElenaCelledoni Oslo,Norway GiuliaDiNunno Trondheim,Norway KuruschEbrahimi-Fard Bergen,Norway HansZannaMunthe-Kaas vii Contents FacilitatedExclusionProcess................................................... 1 JinhoBaik,GuillaumeBarraquand,IvanCorwin,andTouficSuidan Stochastic FunctionalDifferentialEquations and Sensitivity toTheirInitialPath.............................................................. 37 D.R.Baños,G.DiNunno,H.H.Haferkorn,andF.Proske Grassmannian Flows and Applications to Nonlinear Partial DifferentialEquations........................................................... 71 MargaretBeck,AnastasiaDoikou,SimonJ.A.Malham, andIoannisStylianidis GogandMagogTriangles....................................................... 99 PhilippeBiane TheClebschRepresentationinOptimalControlandLowRank IntegrableSystems............................................................... 129 AnthonyM.Bloch,FrançoisGay-Balmaz,andTudorS.Ratiu TheGeometryofCharactersofHopfAlgebras .............................. 159 GeirBogfjellmoandAlexanderSchmeding ShapeAnalysisonHomogeneousSpaces:A GeneralisedSRVT Framework........................................................................ 187 ElenaCelledoni,SølveEidnes,andAlexanderSchmeding UniversalityinNumericalComputationwithRandomData:Case Studies,AnalyticalResultsandSomeSpeculations.......................... 221 PercyDeiftandThomasTrogdon BSDEswithDefaultJump ...................................................... 233 RoxanaDumitrescu,MiryanaGrigorova,Marie-ClaireQuenez, andAgnèsSulem ix x Contents The Faà di Bruno Hopf Algebra for Multivariable Feedback RecursionsintheCenterProblemforHigherOrderAbelEquations ..... 265 KuruschEbrahimi-FardandW.StevenGray Continuous-Time Autoregressive Moving-AverageProcesses inHilbertSpace .................................................................. 297 FredEspenBenthandAndréSüss Pre-andPost-LieAlgebras:TheAlgebro-GeometricView................. 321 GunnarFløystadandHansMunthe-Kaas ExtensionoftheProductofaPost-LieAlgebraandApplication totheSISOFeedbackTransformationGroup................................ 369 LoïcFoissy InfiniteDimensionalRoughDynamics ........................................ 401 MassimilianoGubinelli HeavyTailedRandomMatrices:HowTheyDifferfromtheGOE, andOpenProblems.............................................................. 415 AliceGuionnet AnAnalyst’sTakeontheBPHZTheorem .................................... 429 MartinHairer ParabolicAndersonModelwithRoughDependenceinSpace.............. 477 YaozhongHu,JingyuHuang,KhoaLê,DavidNualart,andSamyTindel PerturbationofConservationLawsandAveragingonManifolds.......... 499 Xue-MeiLi Free Probability, Random Matrices, and Representations ofNon-commutativeRationalFunctions...................................... 551 TobiasMaiandRolandSpeicher AReviewonComodule-Bialgebras............................................ 579 DominiqueManchon Renormalization:AQuasi-shuffleApproach ................................. 599 FrédéricMenousandFrédéricPatras Hopf Algebra Techniques to Handle Dynamical Systems andNumericalIntegrators...................................................... 629 AnderMuruaandJesúsM.Sanz-Serna QuantitativeLimitTheoremsforLocalFunctionalsofArithmetic RandomWaves................................................................... 659 GiovanniPeccatiandMauriziaRossi Contents xi CombinatoricsonWordsandtheTheoryofMarkoff ....................... 691 ChristopheReutenauer AnAlgebraicApproachtoIntegrationofGeometricRoughPaths ........ 709 DanyuYang
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