Colloquium De Giorgi 2010–2012 PDF
Preview Colloquium De Giorgi 2010–2012
4 COLLOQUIA YvesAndre´ De´partementdeMathe´matiquesetApplications E´coleNormaleSupe´rieure 45rued’Ulm 75230ParisCedex05,France NicholasM.Katz DepartmentofMathematics PrincetonUniversity 806FineHall Princeton,NJ08544-1000,USA EndreSzemere´di Alfre´dRe´nyiInstituteofMathematics HungarianAcademyofSciences Rea´ltanodan.13-15 H-1053Budapest,Hungarian DanAbramovich DepartmentofMathematics BrownUniversity Box1917 Providence,RI02912,USA EliasM.Stein DepartmentofMathematics PrincetonUniversity 802FineHall Princeton,NJ08544-1000,USA Shou-WuZhang DepartmentofMathematics PrincetonUniversity 505FineHall Princeton,NJ08544-1000,USA ColloquiumDeGiorgi2010-2012 Colloquium De Giorgi 2010-2012 edited by Umberto Zannier EDIZIONI DELLA NORMALE (cid:2)c 2013ScuolaNormaleSuperiorePisa ISBN978-88-7642-455-7 ISBN978-88-7642-457-1(eBook) Contents Preface vii YvesAndre´ Galoistheorybeyondalgebraicnumbersandalgebraicfunctions 1 NicholasM.Katz Simplethingswedon’tknow 9 EndreSzemere´di Islazinesspayingoff? (“Absorbing”method) 17 DanAbramovich Moduliofalgebraicandtropicalcurves 35 EliasM.Stein Threeprojectionoperatorsincomplexanalysis 49 Shou-WuZhang CongruentnumbersandHeegnerpoints 61 Preface Since2001theScuolaNormaleSuperiorediPisahasorganizedthe“Col- loquio De Giorgi”, a series of colloquium talks named after Ennio De Giorgi,theeminentanalystwhowasaProfessorattheScuolafrom1959 untilhisdeathin1996. The Colloquio takes place once a month. It is addressed to a general mathematicalaudience,andespeciallymeanttoattractgraduatestudents andadvancedundergraduatestudents. Thelecturesareintendedtobenot tootechnical,infieldsofwideinterest. Theyshouldprovideanoverview of the general topic, possibly in a historical perspective, together with a descriptionofmorerecentprogress. Theideaofcollectingthematerialsfromtheselecturesandpublishing theminannualvolumescameoutrecently,asarecognitionoftheirintrin- sicmathematicalinterest,andalsowiththeaimofpreservingmemoryof theseevents. Forthispurpose,theinvitedspeakersarenowaskedtocontributewith awrittenexpositionoftheirtalk,intheformofashortsurveyorextended abstract. Thisserieshasbeencontinuedinacollectionthatwehopeshall beincreasedinthefuture. Thisvolumecontainsacompletelistofthetalksheldinthe“Colloquio DeGiorgi”inrecentyearsbutalsointhepastandalsointhepastyears, andatableofcontentsofallthevolumestoo. Colloquiaheldin2001 PaulGauduchon Weaklyself-dualKa¨hlersurfaces TristanRivie`re Topologicalsingularitiesformapsbetweenmanifolds Fre´de´ricHe´lein Integrable systems in differential geometry and Hamiltonian stationary Lagrangiansurfaces viii Preface Jean-PierreDemailly NumericalcharacterizationoftheKa¨hlerconeofacompactKa¨hlerman- ifold EliasStein Discreteanaloguesinharmonicanalysis JohnN.Mather Differentiability of the stable norm in dimension less than or equal to threeandoftheminimalaverageactionindimensionlessthanorequal totwo GuyDavid AboutglobalMumford-Shahminimizers JacobPalis Aglobalviewofdynamics AlexanderNagel FundamentalsolutionsfortheKohn-Laplacian AlanHuckleberry Incidencegeometryandfunctiontheory Colloquiaheldin2002 MichaelCowling Generalizzazionidimappeconformi FelixOtto Thegeometryofdissipativeevolutionequations CurtisMcMullen Dynamicsoncomplexsurfaces NicolaiKrylov Some old and new relations between partial differential equations, stochasticpartialdifferentialequations,andfinepropertiesoftheWiener process TobiasH.Colding Disksthataredoublespiralstaircases Ce´dricVillani When statistical mechanics meets regularity theory: qualitative proper- tiesoftheBoltzmannequationwithlong-rangeinteractions ix Preface Colloquiaheldin2003 JohnToland Bernoullifreeboundaryproblems-progressandopenquestions Jean-MichelMorel Theaxiomaticmethodinperceptiontheoryandimageanalysis JacquesFaraut Randommatricesandinfinitedimensionalharmonicanalysis AlbertFathi C1 subsolutionsofHamilton-IacobiEquation HakanEliasson Quasi-periodicSchro¨dingeroperators-spectraltheoryanddynamics YakovPesin Ischaoticbehaviortypicalamongdynamicalsystems? DonB.Zagier Modularformsandtheirperiods DavidElworthy Functionsoffiniteenergyinfiniteandinfinitedimensions Colloquiaheldin2004 Jean-ChristopheYoccoz Hyperbolicityforproductsof 2×2matrices GiovanniJona-Lasinio Probabilita` emeccanicastatistica JohnH.Hubbard Thurston’stheoremoncombinatoricsofrationalfunctionsanditsgener- alizationtoexponentials MarceloViana Equilibriumstates BorisRozovsky StochasticNavier-Stokesequationsforturbulentflows MarcRosso Braidsandshuffles MichaelChrist The d-bar Neumann problem, magnetic Schro¨dinger operators, and the Aharonov-Bo¨hmphenomenon x Preface Colloquiaheldin2005 LouisNirenberg Onethingleadstoanother VivianeBaladi DynamicalzetafunctionsandanisotropicSobolevandHo¨lderspaces GiorgioVelo Scatteringnonlineare GerdFaltings Diophantineequations MartinNowak Evolutionofcooperation PeterSwinnerton-Dyer Countingrationalpoints: Manin’sconjecture Franc¸oisGolse TheNavier-StokeslimitoftheBoltzmannequation JosephJ.Kohn Existenceandhypoellipticitywithlossofderivatives DorianGoldfeld OnGauss’classnumberproblem Colloquiaheldin2006 YuriBilu Diophantineequationswithseparatedvariables CorradoDeConcini Algebrecontracceerappresentazionidigruppiquantici ZeevRudnick Eigenvaluestatisticsandlatticepoints LucienSzpiro AlgebraicDynamics SimonGindikin Harmonicanalysisoncomplexsemisimplegroupsandsymmetricspaces frompointofviewofcomplexanalysis DavidMasser From2topolarizationsonabelianvarieties
The list of books you might like
