Colloquium De Giorgi 2009 PDF
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3 COLLOQUIA MichaelG.Cowling SchoolofMathematicsandStatistics UniversityofNewSouthWales SydneyNSW2052,Australia JosephA.Wolf DepartmentofMathematics UniversityofCalifornia Berkeley California94720–3840,U.S.A. GisbertWu¨stholz DepartementMathematik ETHZu¨rich Ra¨mistrasse101 CH-8092Zu¨rich,Switzerland DavidMumford DivisionofAppliedMathematics BrownUniversity 182GeorgeStreet Providence RI02912,USA ColloquiumDeGiorgi2009 Colloquium De Giorgi 2009 edited by Umberto Zannier (cid:2)c 2012ScuolaNormaleSuperiorePisa ISBN 978-88-7642-388-8 ISBN 978-88-7642-387-1(eBook) Contents Preface vii MichaelG.Cowling IsomorphismsoftheFiga`-Talamanca–Herzalgebras A (G) p forconnectedLiegroupsG 1 JosephA.Wolf ClassicalanalysisandnilpotentLiegroups 19 GisbertWu¨stholz Leibniz’conjecture,periods&motives 33 DavidMumford Thegeometryandcurvatureofshapespaces 43 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 De Giorgi” in 2009 and also in the past years, and a table of contents of thefirsttwovolumestoo. 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 Hyperbolicityforproductsof2×2matrices GiovanniJona-Lasinio Probabilita` emeccanicastatistica JohnH.Hubbard Thurston’stheoremoncombinatoricsofrationalfunctionsanditsgener- alizationtoexponentials MarceloViana Equilibriumstates BorisRozovsky StochasticNavier-Stokesequationsforturbulentflows MarcRossoBraidsandshuffles 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
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