Proceedings of International congress of mathematicians

829 Pages·1999·5.11 MB·English

by  S.D. Chatterji

Preface
WhenwestartedplanningtheeditionoftheProceedingsoftheInternationalCongress
ofMathematicians2006(ICM2006),weconsideredthepossibilityofpublishingonly
an electronic version. However, it is pretty difficult to break traditions, particularly
foranactivityliketheICMwithanexistenceofmorethanahundredyears. Thus,we
finallydecidedtomimicthemodelthatstartedinBerlin98: topublishboth,aprinted
andanelectronicversionoftheProceedings. However,youmaynoticetheinfluence
oflivingtheInternetEra,wherelengthoffilesisnotreallyabigissue,bythenumber
ofpages,altogetheralmost4400,probablyarecordforthehistoryofICMs.
TheseProceedingsconsistofthreevolumes. VolumeIisdividedintofourparts.
Thefirstonegathersthespeechesattheopeningceremonyincludingthepresentation
oftheFieldsMedals,theRolfNevanlinnaPrizeandthenewlyawardedGaussPrize
forApplicationsofMathematicsaswellasthespeechesattheclosingceremony. It
also contains information about the organization of the Congress, the committees,
sponsorsandothercollaborators. Thesecondpartcontainsthetraditionallaudationes
fortheprizes,thatis,anextensivepresentationoftheworkoftheawardees. Thethird
partisthemainbodyofthevolumeandconsistsofthearticleswrittenbytheplenary
lecturers of the Congress. One of the characteristics of this ICM has been the large
numberofdiverseactivitiesaccompanyingdaybydaytheprogramfixedbytheIMU
ScientificProgramCommittee. Inthefourthpartofthevolume,youcanfindarticles
correspondingtosomeofthem.
VolumesIIandIIIwereprintedbeforetheCongressanddistributedtothepartici-
pantsinMadrid. Theygatherthearticleswrittenbytheinvitedspeakersinthedifferent
scientificsectionsoftheCongress.
The on-line version of these volumes is accessible at the address http://www.
icm2006.org/proceedings
We take this opportunity to express our thanks to the authors of the articles for
theireffortinthepreparationofexcellentcontributions. Wealsowouldliketoexpress
ourgratitudetotheEMSPublishingHouseforthesuperbjobintheeditionofthese
ProceedingsandalltheprintedmaterialoftheICM2006.
March2007 MartaSanz-Solé
JavierSoria
JuanLuisVarona
JoanVerdera

Contents
Preface ................................................................. v
Pastcongresses ......................................................... 1
PastFieldsMedalistsandRolfNevanlinnaPrizeWinners ................... 2
OrganizationoftheCongress ............................................. 3
ThecommitteesoftheCongress .......................................... 13
OthercollaboratorsoftheICM2006 ....................................... 22
Listofsponsors ......................................................... 23
Openingceremony ...................................................... 25
Closingceremony ....................................................... 45
TheworkoftheFieldsMedalists,theRolfNevanlinnaPrizeWinner
andtheGaussPrizeWinner ............................................ 53
GiovanniFelder
TheworkofAndreiOkounkov ........................................ 55
JohnLott
TheworkofGrigoryPerelman ........................................ 66
CharlesFefferman
TheworkofTerenceTao .............................................. 78
CharlesM.Newman
TheworkofWendelinWerner ......................................... 88
JohnHopcroft
TheworkofJonKleinberg ............................................ 97
HansFöllmer
OnKiyosiItô’sworkanditsimpact .................................... 109
PlenaryLectures
PercyDeift
Universalityformathematicalandphysicalsystems ..................... 125
Jean-PierreDemailly
Kählermanifoldsandtranscendentaltechniquesinalgebraicgeometry .... 153
RonaldA.DeVore
Optimalcomputation ................................................. 187
YakovEliashberg
Symplecticfieldtheoryanditsapplications ............................. 217
viii Contents
ÉtienneGhys
Knotsanddynamics .................................................. 247
HenrykIwaniec
PrimenumbersandL-functions ....................................... 279
IainM.Johnstone
Highdimensionalstatisticalinferenceandrandommatrices .............. 307
KazuyaKato
Iwasawatheoryandgeneralizations .................................... 335
RobertV.Kohn
Energy-drivenpatternformation ....................................... 359
IbMadsen
Modulispacesfromatopologicalviewpoint ............................ 385
ArkadiNemirovski
Advancesinconvexoptimization: conicprogramming ................... 413
SorinPopa
DeformationandrigidityforgroupactionsandvonNeumannalgebras .... 445
AlfioQuarteroni
Cardiovascularmathematics ........................................... 479
OdedSchramm
Conformallyinvariantscalinglimits: anoverviewandacollection
ofproblems ......................................................... 513
RichardP.Stanley
Increasinganddecreasingsubsequencesandtheirvariants ............... 545
TerenceTao
Thedichotomybetweenstructureandrandomness,
arithmeticprogressions,andtheprimes ................................. 581
JuanLuisVázquez
Perspectivesinnonlineardiffusion: betweenanalysis,physics
andgeometry ........................................................ 609
MichèleVergne
Applicationsofequivariantcohomology ................................ 635
AviWigderson
P,NP andmathematics–acomputationalcomplexityperspective ....... 665
Specialactivities
JohnW.Morgan
ThePoincaréConjecture .............................................. 713
PaneldiscussionorganisedbytheEuropeanMathematicalSociety
Shouldmathematicianscareaboutcommunicatingtobroadaudiences? .... 737
Contents ix
ICM2006Closingroundtable
Arepureandappliedmathematicsdriftingapart? ........................ 757
Culturalactivities
JoséM.Sánchez-Ron
TheroadfromZurich(1897)toMadrid(2006) .......................... 777
Listofparticipants ...................................................... 795
Participantsbycountry .................................................. 830
Authorindex ............................................................ 831

Past congresses
1897 Zurich 1958 Edinburgh
1900 Paris 1962 Stockholm
1904 Heidelberg 1966 Moscow
1908 Rome 1970 Nice
1912 Cambridge,UK 1974 Vancouver
1920 Strasbourg 1978 Helsinki
1924 Toronto 1982 Warsaw(heldin1983)
1928 Bologna 1986 Berkeley
1932 Zurich 1990 Kyoto
1936 Oslo 1994 Zurich
1950 Cambridge,USA 1998 Berlin
1954 Amsterdam 2002 Beijing
Madrid2006
2
Past Fields Medalists and Rolf Nevanlinna Prize Winners
FieldsMedalists
1936 LarsV.Ahlfors 1978 PierreR.Deligne
JesseDouglas CharlesF.Fefferman
GrigoriiA.Margulis
1950 LaurentSchwartz DanielG.Quillen
AtleSelberg
1982 AlainConnes
1954 KunihikoKodaira WilliamP.Thurston
Jean-PierreSerre Shing-TungYau
1958 KlausF.Roth 1986 SimonK.Donaldson
ReneThom GerdFaltings
MichaelH.Freedman
1962 LarsHörmander
JohnW.Milnor 1990 VladimirG.Drinfeld
VaughanF.R.Jones
1966 MichaelF.Atiyah ShigefumiMori
PaulJ.Cohen EdwardWitten
AlexanderGrothendieck
SteveSmale 1994 JeanBourgain
Pierre-LouisLions
1970 AlanBaker Jean-ChristopheYoccoz
HeisukeHironaka
SergeiP.Novikov 1998 RichardE.Borcherds
JohnG.Thompson WilliamT.Gowers
MaximKontsevich
1974 EnricoBombieri CurtisT.McMullen
DavidB.Mumford
2002 LaurentLafforgue
VladimirVoevodsky
RolfNevanlinnaPrizeWinners
1982 RobertE.Tarjan 1994 AviWigderson
1986 LeslieG.Valiant 1998 PeterW.Shor
1990 AlexanderA.Razborov 2002 MadhuSudan
Organization of the Congress
ManueldeLeón,PresidentoftheICM2006
In1998,theRealSociedadMatemáticaEspañola,theSocietatCatalanadeMatemà-
tiques,theSociedadEspañoladeMatemáticaAplicadaandtheSociedaddeEstadís-
tica e Investigación Operativa got together to reorganize the Spanish Committee of
Mathematics (CEMAT) representing Spain at the IMU. This Committee, which in-
cludesthreeothersocieties(theFederaciónEspañoladeSociedadesdeProfesoresde
Matemáticas,theSociedadEspañoladeInvestigaciónenEducaciónMatemática,and
theSociedadEspañoladeHistoriadelasCienciasydelasTécnicas),putforwardthe
Spanishcandidacytohostthe25thInternationalCongressofMathematicsinMadrid
in2006,aswellastheIMUGeneralAssemblyinSantiagodeCompostela.
ThisbidwasinitiallybackedbytheCityofMadrid,theAutonomousCommunity
ofMadrid,theMinistryofEducation,CultureandSport,theMinistryofScienceand
Technology and the Ministry for ForeignAffairs. His Majesty King Juan Carlos I
alsogavehissupporttothecandidacywithaletterincludedinthedossier. Inaddi-
tion, backing was forthcoming from the universities in the region (the Universidad
ComplutensedeMadrid,theUniversidadAutónomadeMadrid,andtheUniversidad
Carlos III de Madrid) with letters from their respective rectors, as well as from the
presidentoftheConsejoSuperiordeInvestigacionesCientíficas(CSIC).Anassocia-
tionwascreatedtopromotethecandidacy,whichbroughttogetherthesupportofall
the above-mentioned bodies and institutions. The candidacy was advocated by the
SpanishdelegationheadedbyJoséLuisFernándezatthe24thGeneralAssemblyin
Shanghai,andwasunanimouslyapprovedbyvote. TheinvitationtocometoMadrid
wasformallymadeonbehalfofSpainbyCarlesCasacubertaattheICM2002closing
ceremonyinBeijing.
Theassociationformedtopresentthecandidacywasdissolvedonitsreturnfrom
China,andworkbeganontheorganizationoftheICM2006inMadridandtheGeneral
Assembly in Santiago. To this end, the ICM2006 Madrid Association was set up,
independently of the CEMAT and the societies but in complete co-ordination with
all of them. The first president of this association was CarlosAndradas, who was
replaced in 2003 by Manuel de León. At the same time, an Organizing Committee
responsiblefortheGeneralAssemblywassetupattheUniversidaddeSantiago. This
Committeeincludedthethreeuniversitiesintheregion(SantiagodeCompostela,La
CoruñaandVigo),andwasheadedbythedeanoftheFacultyofMathematics,Juan
Manuel Viaño. Both bodies have worked in full co-ordination with each other in
recentyears.
Afurtherimportantpointisthat,althoughtheICM2006wastobeheldinMadrid,
theorganizationofthecongresswasajointeffortacrossthewholecountry. Inaddition
totheGeneralAssemblyinSantiago,theCommitteewascomposedofmathematicians
from all over Spain, a reflection of the country’s historical and cultural wealth and
variety. Aconsultationofthewebpagewillrevealmessagesofwelcomenotonlyin