Proceedings of International congress of mathematicians PDF
Preview Proceedings of International congress of mathematicians
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
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