Integrable Systems and Algebraic Geometry: A Celebration of Emma Previato’s 65th Birthday

536 Pages·2020·2.943 MB·English

by  Ron Donagi, Tony Shaska

Cambridge University Press
978-1-108-71577-5 — Integrable Systems and Algebraic Geometry
Edited by Ron Donagi , Tony Shaska
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LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES
ManagingEditor:ProfessorEndreSu¨li,MathematicalInstitute,UniversityofOxford,
WoodstockRoad,OxfordOX26GG,UnitedKingdom
Thetitlesbelowareavailablefrombooksellers,orfromCambridgeUniversityPressat
www.cambridge.org/mathematics
352 Numbertheoryandpolynomials,J.MCKEE&C.SMYTH(eds)
353 Trendsinstochasticanalysis,J.BLATH,P.MO¨RTERS&M.SCHEUTZOW(eds)
354 Groupsandanalysis,K.TENT(ed)
355 Non-equilibriumstatisticalmechanicsandturbulence,J.CARDY,G.FALKOVICH&K.GAWEDZKI
356 EllipticcurvesandbigGaloisrepresentations,D.DELBOURGO
357 Algebraictheoryofdifferentialequations,M.A.H.MACCALLUM&A.V.MIKHAILOV(eds)
358 Geometricandcohomologicalmethodsingrouptheory,M.R.BRIDSON,P.H.KROPHOLLER&
I.J.LEARY(eds)
359 Modulispacesandvectorbundles,L.BRAMBILA-PAZ,S.B.BRADLOW,O.GARC´IA-PRADA&
S.RAMANAN(eds)
360 Zariskigeometries,B.ZILBER
361 Words:Notesonverbalwidthingroups,D.SEGAL
362 Differentialtensoralgebrasandtheirmodulecategories,R.BAUTISTA,L.SALMERO´N&R.ZUAZUA
363 Foundationsofcomputationalmathematics,HongKong2008,F.CUCKER,A.PINKUS&M.J.TODD(eds)
364 Partialdifferentialequationsandfluidmechanics,J.C.ROBINSON&J.L.RODRIGO(eds)
365 Surveysincombinatorics2009,S.HUCZYNSKA,J.D.MITCHELL&C.M.RONEY-DOUGAL(eds)
366 Highlyoscillatoryproblems,B.ENGQUIST,A.FOKAS,E.HAIRER&A.ISERLES(eds)
367 Randommatrices:Highdimensionalphenomena,G.BLOWER
368 GeometryofRiemannsurfaces,F.P.GARDINER,G.GONZA´LEZ-DIEZ&C.KOUROUNIOTIS(eds)
369 Epidemicsandrumoursincomplexnetworks,M.DRAIEF&L.MASSOULIE´
370 Theoryofp-adicdistributions,S.ALBEVERIO,A.YU.KHRENNIKOV&V.M.SHELKOVICH
371 Conformalfractals,F.PRZYTYCKI&M.URBAN´SKI
372 Moonshine:Thefirstquartercenturyandbeyond,J.LEPOWSKY,J.MCKAY&M.P.TUITE(eds)
373 Smoothness,regularityandcompleteintersection,J.MAJADAS&A.G.RODICIO
374 Geometricanalysisofhyperbolicdifferentialequations:Anintroduction,S.ALINHAC
375 Triangulatedcategories,T.HOLM,P.JØRGENSEN&R.ROUQUIER(eds)
376 Permutationpatterns,S.LINTON,N.RUSˇKUC&V.VATTER(eds)
377 AnintroductiontoGaloiscohomologyanditsapplications,G.BERHUY
378 Probabilityandmathematicalgenetics,N.H.BINGHAM&C.M.GOLDIE(eds)
379 Finiteandalgorithmicmodeltheory,J.ESPARZA,C.MICHAUX&C.STEINHORN(eds)
380 Realandcomplexsingularities,M.MANOEL,M.C.ROMEROFUSTER&C.T.CWALL(eds)
381 Symmetriesandintegrabilityofdifferenceequations,D.LEVI,P.OLVER,Z.THOMOVA&
P.WINTERNITZ(eds)
382 Forcingwithrandomvariablesandproofcomplexity,J.KRAJ´ICˇEK
383 Motivicintegrationanditsinteractionswithmodeltheoryandnon-ArchimedeangeometryI,R.CLUCKERS,
J.NICAISE&J.SEBAG(eds)
384 Motivicintegrationanditsinteractionswithmodeltheoryandnon-ArchimedeangeometryII,R.CLUCKERS,
J.NICAISE&J.SEBAG(eds)
385 EntropyofhiddenMarkovprocessesandconnectionstodynamicalsystems,B.MARCUS,K.PETERSEN&
T.WEISSMAN(eds)
386 Independence-friendlylogic,A.L.MANN,G.SANDU&M.SEVENSTER
387 GroupsStAndrews2009inBathI,C.M.CAMPBELLetal(eds)
388 GroupsStAndrews2009inBathII,C.M.CAMPBELLetal(eds)
389 Randomfieldsonthesphere,D.MARINUCCI&G.PECCATI
390 Localizationinperiodicpotentials,D.E.PELINOVSKY
391 Fusionsystemsinalgebraandtopology,M.ASCHBACHER,R.KESSAR&B.OLIVER
392 Surveysincombinatorics2011,R.CHAPMAN(ed)
393 Non-abelianfundamentalgroupsandIwasawatheory,J.COATESetal(eds)
394 Variationalproblemsindifferentialgeometry,R.BIELAWSKI,K.HOUSTON&M.SPEIGHT(eds)
395 Howgroupsgrow,A.MANN
396 Arithmeticdifferentialoperatorsoverthep-adicintegers,C.C.RALPH&S.R.SIMANCA
397 Hyperbolicgeometryandapplicationsinquantumchaosandcosmology,J.BOLTE&F.STEINER(eds)
398 Mathematicalmodelsincontactmechanics,M.SOFONEA&A.MATEI
399 Circuitdoublecoverofgraphs,C.-Q.ZHANG
400 Densespherepackings:ablueprintforformalproofs,T.HALES
401 AdoubleHallalgebraapproachtoaffinequantumSchur–Weyltheory,B.DENG,J.DU&Q.FU
402 Mathematicalaspectsoffluidmechanics,J.C.ROBINSON,J.L.RODRIGO&W.SADOWSKI(eds)
403 Foundationsofcomputationalmathematics,Budapest2011,F.CUCKER,T.KRICK,A.PINKUS&
A.SZANTO(eds)
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404 Operatormethodsforboundaryvalueproblems,S.HASSI,H.S.V.DESNOO&F.H.SZAFRANIEC(eds)
405 Torsors,e´talehomotopyandapplicationstorationalpoints,A.N.SKOROBOGATOV(ed)
406 Appalachiansettheory,J.CUMMINGS&E.SCHIMMERLING(eds)
407 Themaximalsubgroupsofthelow-dimensionalfiniteclassicalgroups,J.N.BRAY,D.F.HOLT&
C.M.RONEY-DOUGAL
408 Complexityscience:theWarwickmaster’scourse,R.BALL,V.KOLOKOLTSOV&R.S.MACKAY(eds)
409 Surveysincombinatorics2013,S.R.BLACKBURN,S.GERKE&M.WILDON(eds)
410 Representationtheoryandharmonicanalysisofwreathproductsoffinitegroups,
T.CECCHERINI-SILBERSTEIN,F.SCARABOTTI&F.TOLLI
411 Modulispaces,L.BRAMBILA-PAZ,O.GARC´IA-PRADA,P.NEWSTEAD&R.P.THOMAS(eds)
412 Automorphismsandequivalencerelationsintopologicaldynamics,D.B.ELLIS&R.ELLIS
413 Optimaltransportation,Y.OLLIVIER,H.PAJOT&C.VILLANI(eds)
414 AutomorphicformsandGaloisrepresentationsI,F.DIAMOND,P.L.KASSAEI&M.KIM(eds)
415 AutomorphicformsandGaloisrepresentationsII,F.DIAMOND,P.L.KASSAEI&M.KIM(eds)
416 Reversibilityindynamicsandgrouptheory,A.G.O’FARRELL&I.SHORT
417 Recentadvancesinalgebraicgeometry,C.D.HACON,M.MUSTAT¸A˘&M.POPA(eds)
418 TheBloch–KatoconjecturefortheRiemannzetafunction,J.COATES,A.RAGHURAM,A.SAIKIA&
R.SUJATHA(eds)
419 TheCauchyproblemfornon-Lipschitzsemi-linearparabolicpartialdifferentialequations,J.C.MEYER&
D.J.NEEDHAM
420 Arithmeticandgeometry,L.DIEULEFAITetal(eds)
421 O-minimalityandDiophantinegeometry,G.O.JONES&A.J.WILKIE(eds)
422 GroupsStAndrews2013,C.M.CAMPBELLetal(eds)
423 Inequalitiesforgrapheigenvalues,Z.STANIC´
424 Surveysincombinatorics2015,A.CZUMAJetal(eds)
425 Geometry,topologyanddynamicsinnegativecurvature,C.S.ARAVINDA,F.T.FARRELL&
J.-F.LAFONT(eds)
426 Lecturesonthetheoryofwaterwaves,T.BRIDGES,M.GROVES&D.NICHOLLS(eds)
427 RecentadvancesinHodgetheory,M.KERR&G.PEARLSTEIN(eds)
428 GeometryinaFre´chetcontext,C.T.J.DODSON,G.GALANIS&E.VASSILIOU
429 Sheavesandfunctionsmodulop,L.TAELMAN
430 RecentprogressinthetheoryoftheEulerandNavier–Stokesequations,J.C.ROBINSON,J.L.RODRIGO,
W.SADOWSKI&A.VIDAL-LO´PEZ(eds)
431 Harmonicandsubharmonicfunctiontheoryontherealhyperbolicball,M.STOLL
432 Topicsingraphautomorphismsandreconstruction(2ndEdition),J.LAURI&R.SCAPELLATO
433 RegularandirregularholonomicD-modules,M.KASHIWARA&P.SCHAPIRA
434 Analyticsemigroupsandsemilinearinitialboundaryvalueproblems(2ndEdition),K.TAIRA
435 GradedringsandgradedGrothendieckgroups,R.HAZRAT
436 Groups,graphsandrandomwalks,T.CECCHERINI-SILBERSTEIN,M.SALVATORI&
E.SAVA-HUSS(eds)
437 Dynamicsandanalyticnumbertheory,D.BADZIAHIN,A.GORODNIK&N.PEYERIMHOFF(eds)
438 Randomwalksandheatkernelsongraphs,M.T.BARLOW
439 Evolutionequations,K.AMMARI&S.GERBI(eds)
440 Surveysincombinatorics2017,A.CLAESSONetal(eds)
441 Polynomialsandthemod2SteenrodalgebraI,G.WALKER&R.M.W.WOOD
442 Polynomialsandthemod2SteenrodalgebraII,G.WALKER&R.M.W.WOOD
443 Asymptoticanalysisingeneralrelativity,T.DAUDE´,D.HA¨FNER&J.-P.NICOLAS(eds)
444 Geometricandcohomologicalgrouptheory,P.H.KROPHOLLER,I.J.LEARY,C.MART´INEZ-PE´REZ&
B.E.A.NUCINKIS(eds)
445 Introductiontohiddensemi-Markovmodels,J.VANDERHOEK&R.J.ELLIOTT
446 Advancesintwo-dimensionalhomotopyandcombinatorialgrouptheory,W.METZLER&
S.ROSEBROCK(eds)
447 Newdirectionsinlocallycompactgroups,P.-E.CAPRACE&N.MONOD(eds)
448 Syntheticdifferentialtopology,M.C.BUNGE,F.GAGO&A.M.SANLUIS
449 Permutationgroupsandcartesiandecompositions,C.E.PRAEGER&C.SCHNEIDER
450 Partialdifferentialequationsarisingfromphysicsandgeometry,M.BENAYEDetal(eds)
451 Topologicalmethodsingrouptheory,N.BROADDUS,M.DAVIS,J.-F.LAFONT&I.ORTIZ(eds)
452 Partialdifferentialequationsinfluidmechanics,C.L.FEFFERMAN,J.C.ROBINSON&
J.L.RODRIGO(eds)
453 Stochasticstabilityofdifferentialequationsinabstractspaces,K.LIU
454 Beyondhyperbolicity,M.HAGEN,R.WEBB&H.WILTON(eds)
455 GroupsStAndrews2017inBirmingham,C.M.CAMPBELLetal(eds)
456 Surveysincombinatorics2019,A.LO,R.MYCROFT,G.PERARNAU&A.TREGLOWN(eds)
457 Shimuravarieties,T.HAINES&M.HARRIS(eds)
458 IntegrablesystemsandalgebraicgeometryI,R.DONAGI&T.SHASKA(eds)
459 IntegrablesystemsandalgebraicgeometryII,R.DONAGI&T.SHASKA(eds)
460 Wigner-typetheoremsforHilbertGrassmannians,M.PANKOV
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Cambridge University Press
978-1-108-71577-5 — Integrable Systems and Algebraic Geometry
Edited by Ron Donagi , Tony Shaska
Frontmatter
More Information
LondonMathematicalSocietyLectureNoteSeries:459
Integrable Systems and
Algebraic Geometry
A Celebration of Emma Previato’s 65th Birthday
Volume 2
Editedby
RON DONAGI
UniversityofPennsylvania
TONY SHASKA
OaklandUniversity,Michigan
© in this web service Cambridge University Press www.cambridge.org
Cambridge University Press
978-1-108-71577-5 — Integrable Systems and Algebraic Geometry
Edited by Ron Donagi , Tony Shaska
Frontmatter
More Information
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978-1-108-71577-5 — Integrable Systems and Algebraic Geometry
Edited by Ron Donagi , Tony Shaska
Frontmatter
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Contents of Volume 2
ContentsofVolume1 pagevii
AlgebraicGeometry:ACelebrationofEmmaPreviato’s
65thBirthday 1
RonDonagiandTonyShaska
1 ArithmeticAnaloguesofHamiltonianSystems 13
AlexandruBuium
2 AlgebraicSpectralCurvesoverQandtheirTau-Functions 41
BorisDubrovin
3 FrobeniusSplitAnticanonicalDivisors 92
Sa´ndorJ.Kova´cs
4 HalvesofPointsofanOddDegreeHyperellipticCurve
initsJacobian 102
YuriG.Zarhin
5 NormalFormsforKummerSurfaces 119
AdrianClingherandAndreasMalmendier
6 σ-Functions:OldandNewResults 175
V.M.Buchstaber,V.Z.EnolskiandD.V.Leykin
7 BergmanTau-Function:FromEinsteinEquationsand
Dubrovin-FrobeniusManifoldstoGeometryofModuliSpaces 215
DmitryKorotkin
8 TheRigidBodyDynamicsinanIdealFluid:ClebschTopand
KummerSurfaces 288
Jean-PierreFranc¸oiseandDaisukeTarama
v
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978-1-108-71577-5 — Integrable Systems and Algebraic Geometry
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vi ContentsofVolume2
9 AnExtensionofDelsarte,GoethalsandMacWilliams
TheoremonMinimalWeightCodewordstoaClassof
Reed-MullerTypeCodes 313
C´ıceroCarvalhoandVictorG.L.Neumann
10 APrimeronLaxPairs 346
L.M.BatesandR.C.Churchill
11 Lattice-TheoreticCharacterizationsof
ClassesofGroups 367
RolandSchmidt
12 JacobiInversionFormulaeforaCurveinWeierstrass
NormalForm 383
JiyroKomedaandShigekiMatsutani
13 Spectral Construction of Non-Holomorphic Eisenstein-Type
SeriesandtheirKroneckerLimitFormula 405
JamesCogdell,JayJorgensonandLejlaSmajlovic´
14 SomeTopologicalApplicationsofThetaFunctions 440
MauroSpera
15 MultipleDedekindZetaValuesarePeriodsofMixed
TateMotives 485
IvanHorozov
16 NoncommutativeCross-RatioandSchwarzDerivative 499
VladimirRetakh,VladimirRubtsovandGeorgySharygin
© in this web service Cambridge University Press www.cambridge.org
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978-1-108-71577-5 — Integrable Systems and Algebraic Geometry
Edited by Ron Donagi , Tony Shaska
Frontmatter
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Contents of Volume 1
ContentsofVolume2 pagevii
IntegrableSystems:ACelebrationofEmmaPreviato’s
65thBirthday 1
RonDonagiandTonyShaska
1 TraceIdealPropertiesofaClassofIntegralOperators 13
FritzGesztesyandRogerNichols
2 ExplicitSymmetriesoftheKeplerHamiltonian 38
HorstKno¨rrer
3 ANoteontheCommutatorofHamiltonianVectorFields 57
HenrykZ˙oła¸dek
4 NodalCurvesandaClassofSolutionsoftheLaxEquationfor
ShockClusteringandBurgersTurbulence 63
Luen-ChauLi
5 Solvable Dynamical Systems in the Plane with Polynomial
Interactions 93
FrancescoCalogeroandFarrinPayandeh
6 TheProjectionMethodinClassicalMechanics 109
A.M.Perelomov
7 Pencils of Quadrics, Billiard Double-Reflection and Confocal
IncircularNets 133
VladimirDragovic´,MilenaRadnovic´andRogerFide`leRanomenjanahary
8 Bi-FlatF-Manifolds:ASurvey 167
AlessandroArsieandPaoloLorenzoni
vii
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978-1-108-71577-5 — Integrable Systems and Algebraic Geometry
Edited by Ron Donagi , Tony Shaska
Frontmatter
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viii ContentsofVolume1
9 ThePeriodic6-ParticleKac-vanMoerbekeSystem 192
PolVanhaecke
10 IntegrableMappingsfromaUnifiedPerspective 217
TovaBrownandNicholasM.Ercolani
11 Onan Arnold-Liouville Type Theorem for the Focusing NLS
andtheFocusingmKdVEquations 265
T.KappelerandP.Topalov
12 CommutingHamiltonianFlowsofCurvesinReal
SpaceForms 291
AlbertChern,FelixKno¨ppel,FranzPeditandUlrichPinkall
13 TheKowalewskiTopRevisited 329
F.Magri
14 TheCalogero-Franc¸oiseIntegrableSystem:Algebraic
Geometry,HiggsFields,andtheInverseProblem 356
StevenRayan,ThomasStanleyandJacekSzmigielski
15 TropicalMarkovDynamicsandCayleyCubic 383
K.SpaldingandA.P.Veselov
16 PositiveOne–PointCommutingDifferenceOperators 395
GulnaraS.MauleshovaandAndreyE.Mironov
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