Arbeitstagung Bonn 2013: In Memory of Friedrich Hirzebruch PDF
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Progress in Mathematics 319 Werner Ballmann Christian Blohmann Gerd Faltings Peter Teichner Don Zagier Editors Arbeitstagung Bonn 2013 In Memory of Friedrich Hirzebruch Progress inMathematics Volume319 SeriesEditors AntoineChambert-Loir Jiang-HuaLu YuriTschinkel Moreinformationaboutthisseriesathttp://www.springer.com/series/4848 Werner Ballmann • Christian Blohmann Gerd Faltings (cid:129) Peter Teichner (cid:129) Don Zagier Editors Arbeitstagung Bonn 2013 In Memory of Friedrich Hirzebruch Editors WernerBallmann ChristianBlohmann MaxPlanckInstituteforMathematics MaxPlanckInstituteforMathematics Bonn,Germany Bonn,Germany GerdFaltings PeterTeichner MaxPlanckInstituteforMathematics MaxPlanckInstituteforMathematics Bonn,Germany Bonn,Germany DonZagier MaxPlanckInstituteforMathematics Bonn,Germany ISSN0743-1643 ISSN2296-505X (electronic) ProgressinMathematics ISBN978-3-319-43646-3 ISBN978-3-319-43648-7 (eBook) DOI10.1007/978-3-319-43648-7 LibraryofCongressControlNumber:2016957869 MathematicsSubjectClassification(2010):00B20,00B30 ©SpringerInternationalPublishingSwitzerland2016 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. Printedonacid-freepaper ThisbookispublishedunderthetradenameBirkhäuser,www.birkhauser-science.com TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface The first Arbeitstagung was organized by Friedrich Hirzebruch in 1957. The six participantswereMichaelAtiyah,HansGrauert,AlexanderGrothendieck,Friedrich Hirzebruch, Nicolaas Kuiper, and Jacques Tits. Already at the first Arbeitstagung theprinciplewasestablishedwhichwastobecomeitsmostdistinctivefeature:The programwasnotdeterminedbeforehandbytheorganizers,butduringthemeeting byallparticipantsinanopendiscussion,albeitskillfullyguidedbyHirzebruch.The curiosityaboutwhowouldbespeakingandonwhattopicwaspartoftheexcitement ofthisconferenceseries,whichquicklygrewinpopularity,reachingwellover250 participants in later years. More importantly, the spontaneous proposal of talks made it possible to always cover the latest developments in mathematics. Many importantresults,suchastheAtiyah-Singerindextheorem,werefirstintroducedto thelargermathematicscommunityattheArbeitstagung.Moreover,itmeantthatthe conferenceswerenotconfinedtoaspecifictopic,representingovertheyearsalmost allfieldsofmathematics. TheArbeitstagung2013wasdedicatedtothememoryofFriedrichHirzebruch, who passed away on May 27, 2012. This volume contains contributions from speakers and participants, covering a variety of topics from algebraic geometry, topology,differentialgeometry,operatortheory,andrepresentationtheory.Wehope that it still captures some of the unique character and spirit of Fritz Hirzebruch’s originalArbeitstagung. Bonn,Germany WernerBallmann June2016 ChristianBlohmann GerdFaltings PeterTeichner DonZagier v Contents TheHirzebruchSignatureTheoremforConicalMetrics ................... 1 MichaelAtiyah DepthandtheLocalLanglandsCorrespondence ............................ 17 Anne-Marie Aubert, Paul Baum, Roger Plymen, andMaartenSolleveld GuidetoEllipticBoundaryValueProblemsforDirac-TypeOperators... 43 ChristianBärandWernerBallmann SymplecticandHyperkählerImplosion....................................... 81 AndrewDancer,BrentDoran,FrancesKirwan,andAndrewSwann Kazhdan–LusztigConjecturesandShadowsofHodgeTheory............. 105 BenEliasandGeordieWilliamson UniformSup-Norm Bounds onAverage for Cusp Forms ofHigherWeights................................................................ 127 JoshuaS.Friedman,JayJorgenson,andJürgKramer Fivebranesand4-Manifolds .................................................... 155 AbhijitGadde,SergeiGukov,andPavelPutrov HiggsBundlesandCharacteristicClasses .................................... 247 NigelHitchin Hirzebruch–MilnorClassesandSteenbrinkSpectraofCertain ProjectiveHypersurfaces........................................................ 265 LaurentiuMaxim,MorihikoSaito,andJörgSchürmann OnLusztig’sq-AnaloguesofAllWeightMultiplicities ofaRepresentation .............................................................. 289 DmitriI.Panyushev vii viii Contents TheTriangulationofManifolds:Topology,GaugeTheory,andHistory .. 307 FrankQuinn EllipticCalabi–YauThreefoldsoveradelPezzoSurface.................... 337 SimonRoseandNorikoYui RemarksonCohomologicalHallAlgebrasandTheirRepresentations ... 355 YanSoibelman AStratificationontheModuliofK3SurfacesinPositive Characteristic..................................................................... 387 GerardvanderGeer TheRightAdjointoftheParabolicInduction................................ 405 Marie-FranceVignéras Contributors MichaelAtiyah SchoolofMathematics,JCMB,Edinburgh,UK Anne-Marie Aubert Institut de Mathématiques de Jussieu – Paris Rive Gauche, U.M.R.7586duC.N.R.S.,U.P.M.C.,Paris,France WernerBallmann MaxPlanckInstituteforMathematics,Bonn,Germany ChristianBär InstitutfürMathematik,UniversitätPotsdam,Potsdam,Germany Paul Baum Mathematics Department, Pennsylvania State University, University Park,PA,USA AndrewDancer JesusCollege,Oxford,UK BrentDoran DepartmentofMathematics,ETHZürich,Zürich,Switzerland BenElias DepartmentofMathematics,UniversityofOregon,Eugene,OR,USA Joshua S. Friedman Department of Mathematics and Science, United States MerchantMarineAcademy,KingsPoint,NY,USA AbhijitGadde CaliforniaInstituteofTechnology,Pasadena,CA,USA SergeiGukov CaliforniaInstituteofTechnology,Pasadena,CA,USA NigelHitchin MathematicalInstitute,RadcliffeObservatoryQuarter,Oxford,UK Jay Jorgenson Department of Mathematics, The City College of New York, NewYork,NY,USA FrancesKirwan BalliolCollege,Oxford,UK Jürg Kramer Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin, Germany Laurentiu Maxim Department of Mathematics, University of Wisconsin- Madison,Madison,WI,USA ix x Contributors Dmitri I. Panyushev Institute for Information Transmission Problems of the R.A.S.,Moscow,Russia IndependentUniversityofMoscow,Moscow,Russia Roger Plymen School of Mathematics, Southampton University, Southampton, UK SchoolofMathematics,ManchesterUniversity,Manchester,UK PavelPutrov CaliforniaInstituteofTechnology,Pasadena,CA,USA FrankQuinn DepartmentofMathematics,VirginiaPolytechnicInstituteandState University,Blacksburg,VA,USA Simon Rose Department of Mathematical Sciences, University of Copenhagen, Copenhagen,Denmark MorihikoSaito RIMSKyotoUniversity,Kyoto,Japan Jörg Schürmann Mathematisches Institut, Universität Münster, Münster, Germany YanSoibelman DepartmentofMathematics,KSU,Manhattan,KS,USA MaartenSolleveld RadboudUniversiteitNijmegen,Nijmegen,TheNetherlands Andrew Swann Department of Mathematics, Aarhus University, Aarhus, Denmark CP3-Origins, Centre of Excellence for Cosmology and Particle Physics Phenomenology,UniversityofSouthernDenmark,Odense,Denmark Gerardvander Geer Korteweg-deVries Instituut, UniversiteitvanAmsterdam, Amsterdam,TheNetherlands Marie-France Vignéras Institut de Mathematiques de Jussieu, Université de Paris7,Paris,France GeordieWilliamson Max-Planck-InstitutfürMathematik,Bonn,Germany Noriko Yui Department of Mathematics and Statistics, Queen’s University, Kingston,ON,Canada
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