Table Of ContentProgress 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
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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
