Geometric Aspects of Functional Analysis: Israel Seminar (GAFA) 2017-2019 Volume I PDF
Preview Geometric Aspects of Functional Analysis: Israel Seminar (GAFA) 2017-2019 Volume I
Lecture Notes in Mathematics 2256 Bo’az Klartag Emanuel Milman Editors Geometric Aspects of Functional Analysis Israel Seminar (GAFA) 2017-2019 Volume I Lecture Notes in Mathematics Volume 2256 Editors-in-Chief Jean-MichelMorel,CMLA,ENS,Cachan,France BernardTeissier,IMJ-PRG,Paris,France SeriesEditors KarinBaur,UniversityofLeeds,Leeds,UK MichelBrion,UGA,Grenoble,France CamilloDeLellis,IAS,Princeton,NJ,USA AlessioFigalli,ETHZurich,Zurich,Switzerland AnnetteHuber,AlbertLudwigUniversity,Freiburg,Germany DavarKhoshnevisan,TheUniversityofUtah,SaltLakeCity,UT,USA IoannisKontoyiannis,UniversityofCambridge,Cambridge,UK AngelaKunoth,UniversityofCologne,Cologne,Germany ArianeMézard,IMJ-PRG,Paris,France MarkPodolskij,AarhusUniversity,Aarhus,Denmark SylviaSerfaty,NYUCourant,NewYork,NY,USA GabrieleVezzosi,UniFI,Florence,Italy AnnaWienhard,RuprechtKarlUniversity,Heidelberg,Germany This series reports on new developments in all areas of mathematics and their applications-quickly,informallyandatahighlevel.Mathematicaltextsanalysing newdevelopmentsinmodellingandnumericalsimulationarewelcome.Thetypeof materialconsideredforpublicationincludes: 1. Research monographs 2. Lectures on a new field or presentations of a new angle in a classical field 3. Summer schools and intensive courses on topics of currentresearch. Textswhichareoutofprintbutstillindemandmayalsobeconsiderediftheyfall withinthesecategories.Thetimelinessofamanuscriptissometimesmoreimportant thanitsform,whichmaybepreliminaryortentative. Moreinformationaboutthisseriesathttp://www.springer.com/series/304 Bo’az Klartag (cid:129) Emanuel Milman Editors Geometric Aspects of Functional Analysis Israel Seminar (GAFA) 2017-2019 Volume I Editors Bo’azKlartag EmanuelMilman SchoolofMathematicalSciences DepartmentofMathematics TelAvivUniversity Technion–IsraelInstituteofTechnology TelAviv,Israel Haifa,Israel DepartmentofMathematics WeizmannInstituteofScience Rehovot,Israel ISSN0075-8434 ISSN1617-9692 (electronic) LectureNotesinMathematics ISBN978-3-030-36019-1 ISBN978-3-030-36020-7 (eBook) https://doi.org/10.1007/978-3-030-36020-7 MathematicsSubjectClassification(2010):Primary:46-XX;Secondary:52-XX ©SpringerNatureSwitzerlandAG2020 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG. Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Since the mid-1980s, the following volumes containing collections of papers reflecting the activity of the Israel Seminar in Geometric Aspects of Functional Analysishaveappeared: 1983–1984 PublishedprivatelybyTelAvivUniversity 1985–1986 SpringerLectureNotesinMathematics,vol.1267 1986–1987 SpringerLectureNotesinMathematics,vol.1317 1987–1988 SpringerLectureNotesinMathematics,vol.1376 1989–1990 SpringerLectureNotesinMathematics,vol.1469 1992–1994 OperatorTheory:AdvancesandApplications,vol.77,Birkhäuser 1994–1996 MSRIPublications,vol.34,CambridgeUniversityPress 1996–2000 SpringerLectureNotesinMathematics,vol.1745 2001–2002 SpringerLectureNotesinMathematics,vol.1807 2002–2003 SpringerLectureNotesinMathematics,vol.1850 2004–2005 SpringerLectureNotesinMathematics,vol.1910 2006–2010 SpringerLectureNotesinMathematics,vol.2050 2011–2013 SpringerLectureNotesinMathematics,vol.2116 2014–2016 SpringerLectureNotesinMathematics,vol.2169 ThefirstsixwereeditedbyLindenstraussandMilman,theseventhbyBalland Milman, the subsequentfour by Milman and Schechtman, the subsequent one by Klartag,Mendelson,andMilman,andthelasttwobythepresenteditors. Thisisthefirstoftwovolumesfromtheyears2017–2019,thesecondvolumeis publishedinSpringerLectureNotesinMathematics,vol.2266.Asintheprevious SeminarNotes,thesetwovolumesreflectgeneraltrendsinthestudyofGeometric Aspectsof FunctionalAnalysis,understoodin a broadsense. Two classical topics represented are the Concentration of Measure Phenomenon in the Local Theory of Banach Spaces, which has recently had triumphs in Random Matrix Theory, and the Central Limit Theorem, one of the earliest examples of regularity and orderin high dimensions.Centralto the textis the study of the Poincaré and log- Sobolev functional inequalities, their reverses, and other inequalities, in which a crucial role is often played by convexity assumptions such as log-concavity. The v vi Preface conceptandpropertiesofentropyformanimportantsubject,withBourgain’sslicing problemanditsvariantsdrawingmuchattention.Constructionsrelatedtoconvexity theory are proposed and revisited, as well as inequalities that go beyond the Brunn–Minkowskitheory. One of the major currentresearch directionsaddressed is the identification of lower-dimensionalstructures with remarkablepropertiesin ratherarbitraryhigh-dimensionalobjects.Inadditiontofunctionalanalyticresults, connectionstocomputerscienceandtodifferentialgeometryarealsodiscussed.All contributionsare originalresearchpapersandwere subjectto the usualrefereeing standards. We are grateful to Vitali Milman for his help and guidance in preparing and editingthesetwovolumes. TelAviv/Rehovot,Israel Bo’azKlartag Haifa,Israel EmanuelMilman Jean Bourgain: In Memoriam Our friend and mentor Jean Bourgainpassed away on December 22, 2018, at the ageof64. JeanBourgainbyJanRauchwerger.CourtesyofVitaliMilman Jean Bourgain was one of the most outstanding mathematicians of our time. Bourgain changed the face of analysis; he revolutionized our understanding of analysis. He has introduced, mastered, and perfected many different methods in every corner of analysis, including a dozen of neighboringfields, and has left his markineachofthesedirections.Hisachievements,vision,andinsightunitedmany distant and very diverse directions of mathematics into one enormously powerful and broad entity. When we say “Analysis” today we mean, besides classical directions,alsoergodictheory,PDE,severaldirectionsofanalyticalnumbertheory, geometry,andcombinatorics(includingcomplexity).Thisisundoubtedlytheresult of Bourgain’s activity, unprecedented in its strength and diversity. The torrent of his achievementsis difficult to grasp, the number of very long-standingproblems Bourgain has solved can be counted in tens, perhaps approaching a hundred, and thiswouldtakeawholebooktodescribe.Itisalmostimpossibletobelieve:∼550 hardanalysispaperswrittenoverlessthan40years. Jean’s passingis a terribleloss forhisfamilyandfriends,anda terribleloss to themathematicalworld.Weshudderatthethoughtofhowmanymoretheoremshe vii viii JeanBourgain:InMemoriam could have provedand open problemshe could have solved. He leaves behind an unbelievablelegacyofresultscarryinghisname,whosebreadthismatchedonlyby theirdepth. Inadditiontobeingamathematicalgiant,Jeanhaspersonallyinfluencedusall. HisinfluencewasalsowellfeltontheGAFAseminarnotes.Hehaspublishedatotal of50papers(3inthepresentvolume)ineveryvolumeoftheGAFAseminarnotes sinceitsinception(45inSpringerMath.Notesseries,2inBirkhauserseries,and3 inMathematicalSciencesResearchInstitute(MSRI),Berkeley).Weareproudthat someofhislastpapersarepublishedinthisvolume. Mayherestinpeace. TelAviv/Rehovot,Israel Bo’azKlartag(Editor) Haifa,Israel EmanuelMilman(Editor) TelAviv,Israel VitaliMilman(FoundingEditor) Contents Overview for Volume II 1 AGeneralizedCentralLimitConjectureforConvexBodies HaotianJiang,YinTatLee,andSantoshS.Vempala 2 The Lower Bound for Koldobsky’sSlicing Inequality via RandomRounding Bo’azKlartagandGalynaV.Livshyts 3 Two-SidedEstimatesforOrderStatisticsofLog-Concave RandomVectors RafałLatałaandMartaStrzelecka 4 FurtherInvestigationsofRényiEntropyPowerInequalities andanEntropicCharacterizationofs-ConcaveDensities JiangeLi,ArnaudMarsiglietti,andJamesMelbourne 5 SmallBallProbabilityfortheConditionNumberofRandom Matrices AlexanderE.Litvak,KonstantinTikhomirov, andNicoleTomczak-Jaegermann 6 ConcentrationoftheIntrinsicVolumesofaConvexBody MartinLotz,MichaelB.McCoy,IvanNourdin,GiovanniPeccati, andJoelA.Tropp 7 TwoRemarksonGeneralizedEntropyPowerInequalities MokshayMadiman,PiotrNayar,andTomaszTkocz 8 OntheGeometryofRandomPolytopes ShaharMendelson 9 ReciprocalsandFlowersinConvexity EmanuelMilman,VitaliMilman,andLiranRotem
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