2017 MATRIX Annals PDF
Preview 2017 MATRIX Annals
MATRIX Book Series 2 David R. Wood Editor-in-chief Jan de Gier · Cheryl E. Praeger Terence Tao Editors 2017 MATRIX Annals MATRIX Book Series 2 Editors DavidR.Wood(Editor-in-Chief) JandeGier CherylE.Praeger TerenceTao MATRIXisAustralia’sinternationalandresidentialmathematicalresearchinstitute. It facilitates new collaborations and mathematical advances through intensive residentialresearchprograms,eachlasting1–4weeks. Moreinformationaboutthisseriesathttp://www.springer.com/series/15890 David R. Wood Editor-in-Chief Jan de Gier(cid:129)Cheryl E. Praeger(cid:129)Terence Tao Editors 2017 MATRIX Annals 123 Editors DavidR.Wood(Editor-in-Chief) JandeGier MonashUniversity TheUniversityofMelbourne Melbourne,Australia Melbourne,Australia CherylE.Praeger TerenceTao UniversityofWesternAustralia UCLA Perth,Australia LosAngeles,CA,USA ISSN2523-3041 ISSN2523-305X (electronic) MATRIXBookSeries ISBN978-3-030-04160-1 ISBN978-3-030-04161-8 (eBook) https://doi.org/10.1007/978-3-030-04161-8 Mathematics Subject Classification (2010): 05-XX, 11-XX, 14-XX, 35-XX, 35R30, 81-XX, 82-XX, 91Gxx ©SpringerNatureSwitzerlandAG2019 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 Preface MATRIXisAustralia’sinternationalandresidentialmathematicalresearchinstitute. It was established in 2015 and launched in 2016 as a joint partnership between MonashUniversityandThe Universityof Melbourne,with seed fundingfromthe ARCCentreofExcellenceforMathematicalandStatisticalFrontiers.Thepurpose ofMATRIXistofacilitatenewcollaborationsandmathematicaladvancesthrough intensive residential research programs, which are currently held in Creswick, a smalltownnestledinthebeautifulforestsoftheMacedonRanges,130kmwestof Melbourne. ThisbookisascientificrecordoftheeightprogramsheldatMATRIXin2017: (cid:129) HypergeometricMotivesandCalabi–YauDifferentialEquations (cid:129) ComputationalInverseProblems (cid:129) IntegrabilityinLow-DimensionalQuantumSystems (cid:129) EllipticPartialDifferentialEquationsofSecondOrder:Celebrating40Yearsof GilbargandTrudinger’sBook (cid:129) Combinatorics,StatisticalMechanics,andConformalFieldTheory (cid:129) MathematicsofRisk (cid:129) TutteCentenaryRetreat (cid:129) GeometricR-Matrices:fromGeometrytoProbability TheMATRIXScientificCommitteeselectedtheseprogramsbasedonscientific excellenceandtheparticipationrateofhigh-profileinternationalparticipants.This committee consists of: Jan de Gier (Melbourne University, Chair), Ben Andrews (AustralianNationalUniversity),DarrenCrowdy(ImperialCollegeLondon),Hans De Sterck (Monash University), Alison Etheridge (University of Oxford), Gary Froyland(UniversityofNewSouthWales),LizaLevina(UniversityofMichigan), Kerrie Mengersen(QueenslandUniversityof Technology),Arun Ram (University of Melbourne), Joshua Ross (University of Adelaide), Terence Tao (University of California,LosAngeles),OleWarnaar(UniversityofQueensland),andDavidWood (MonashUniversity). These programs involved organisers from a variety of Australian universities, includingAustralian NationalUniversity,MonashUniversity,QueenslandUniver- v vi Preface sity of Technology,University of Newcastle, University of Melbourne,University of Queensland,Universityof Sydney,Universityof TechnologySydney,andUni- versityofWesternAustralia,alongwithinternationalorganisersandparticipants. Each program lasted 1–4 weeks, and included ample unstructured time to encouragecollaborativeresearch. Some of the longer programshad an embedded conferenceorlectureseries.Allparticipantswereencouragedtosubmitarticlesto theMATRIXAnnals. The articles were grouped into refereed contributions and other contributions. Refereed articles contain original results or reviews on a topic related to the MATRIX program. The other contributions are typically lecture notes or short articlesbasedontalksoractivitiesatMATRIX.Aguesteditororganisedappropriate refereeingandensuredthescientificqualityofsubmittedarticlesarisingfromeach program. The Editors (Jan de Gier, Cheryl E. Praeger, Terence Tao and myself) finallyevaluatedandapprovedthepapers. Manythankstotheauthorsandtotheguesteditorsfortheirwonderfulwork. MATRIX is hosting eight programs in 2018, with more to come in 2019; see www.matrix-inst.org.au.Ourgoalistofacilitatecollaborationbetweenresearchers in universities and industry, and increase the international impact of Australian researchinthemathematicalsciences. DavidR.Wood MATRIXBookSeriesEditor-in-Chief Hypergeometric Motives and Calabi–Yau Differential Equations 8–27January2017 Organisers LingLong LouisianaStateUni MashaVlasenko InstituteofMathematicsofthe PolishAcademyofSciences WadimZudilin UniNewcastle The majorityof the articlespresentedbeloware extendedabstractsof the talks givenby programparticipantsatthe workshopthattookplace fromJanuary16to 20, 2017.Some of them presenta new perspectiveor results that appeareddue to collaborationfollowingtheactivityinCreswick. The two main topics of the program, Calabi–Yau differential equations and hypergeometric motives, provide an explicit approach and experimental ground to such important themes in contemporary arithmetic geometry as the Langlands program, motives and mirror symmetry. Hypergeometric motives are families of motives whose periods are given by generalised hypergeometric functions. Their L-functionsare expectedto covera wide rangeof knownL-functions.Due to the recent work of researchers (many of whom were present in Creswick) it is now possible to compute L-functions of hypergeometricmotives efficiently. Thus one cantestthestandardconjectures,e.g.onspecialvaluesandmodularity,formotives ofanydegreeandweight.Manyalgorithmsforcomputingwiththehypergeometric motivesarenowimplementedinthecomputeralgebrasystemMagma. LocalfactorsofhypergeometricL-functionscanbeinvestigatedbythemeansof finitehypergeometricfunctions,anothertopictowhichafewarticlesinthisvolume are devoted. The techniques developed by the authors allow to transport classical formulas to the finite field setting, count points on algebraic varieties over finite fields, study their congruence properties and Galois representations. Importantly, vii viii HypergeometricMotivesandCalabi–YauDifferentialEquations finite hypergeometric functions can be viewed as periods of motives over finite fields. Periodsoverfinitefieldsformanewangleofunderstandingtheintegralityphe- nomenonarisinginmirrorsymmetry.Originallydiscoveredbyphysicistsinthemid 1980s,mirrorsymmetryremainsoneofthecentralresearchthemesbindingstring theoryandalgebraicgeometry.Numerousexamplesshowthattheexpressionofthe mirrormapinso-calledcanonicalcoordinatespossessesricharithmeticproperties. ThisexpressioninvolvesparticularsolutionstoaPicard–Fuchsdifferentialequation of a family of Calabi–Yau manifolds near a singular point. Application of p-adic methods to the study of Calabi–Yau differential equationsgives a very promising prospective,asitisannouncedinthefinalarticlebyDucovanStraten. ThethreeweeksattheMATRIXinstitutewereintenseandfruitful.Toillustrate thesewords,therewasaspeciallecturebyFernandoRodriguezVillegasscheduled at the very last moment on Thursday afternoon of the workshop week, in which he presented, jointly with David Roberts and Mark Watkins, a new conjecture on motivicsupercongruencesthatwasinventedinCreswick.Thistalkinfluencedwhat happenedinthelastweekoftheworkshop.DavidBroadhurstgavehistwolectures ontheveryfirstandverylastdaysoftheprogram,reportinginthesecondtalkon thetremendousprogressachievedbyhimincollaborationwithDavidRobertsover thethreeweeks. We are confident that ideas and projects that emergedduring the programwill driveourfieldofresearchinthecomingyears. MashaVlasenko GuestEditor HypergeometricMotivesandCalabi–YauDifferentialEquations ix Participants James Wan (SUTD, Singapore), Fang-Ting Tu (Louisiana State), Yifan Yang (NationalChiao Tung University),Éric Delaygue (Institut Camille Jordan, Lyon), John Voight (Dartmouth), Adriana Salerno (Bates College), Alex Ghitza (Mel- bourne),MarkWatkins(Sydney),PiotrAchinger(IHES)withHelena,JandeGier (Melbourne), David Broadhurst (Open University), Ole Warnaar (Queensland), RaviRamakrishna(Cornell),FernandoRodriguezVillegas(ICTP,Trieste),Sharon Frechette(CollegeoftheHolyCross),RobertOsburn(UniversityCollegeDublin), Frits Beukers (Utrecht), Paul Norbury (Melbourne), David Roberts (Minnesota Morris), Duco van Straten (Johannes Gutenberg), Holly Swisher (Oregon State), AbdellahSebbar(Ottawa)
The list of books you might like
