Table Of ContentLecture Notes in Mathematics 2266
Bo’az Klartag
Emanuel Milman Editors
Geometric
Aspects
of Functional
Analysis
Israel Seminar (GAFA) 2017-2019
Volume II
Lecture Notes in Mathematics
Volume 2266
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
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Bo’az Klartag (cid:129) Emanuel Milman
Editors
Geometric Aspects
of Functional Analysis
Israel Seminar (GAFA) 2017-2019
Volume II
Editors
Bo’azKlartag EmanuelMilman
SchoolofMathematicalSciences DepartmentofMathematics
TelAvivUniversity Technion–IsraelInstituteofTechnology
TelAviv,Israel Haifa,Israel
DepartmentofMathematics
WeizmannInstituteofScience
Rehovot,Israel
ISSN0075-8434 ISSN1617-9692 (electronic)
LectureNotesinMathematics
ISBN978-3-030-46761-6 ISBN978-3-030-46762-3 (eBook)
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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.
Thisisthesecondoftwovolumesfromtheyears2017–2019,thefirstvolumeis
publishedinSpringerLectureNotesinMathematics,vol.2256.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
someofhislastpapersarepublishedintheseGAFASeminarNotes(VolumeI).
Mayherestinpeace.
TelAviv/Rehovot,Israel Bo’azKlartag(Editor)
Haifa,Israel EmanuelMilman(Editor)
TelAviv,Israel VitaliMilman(FoundingEditor)
Contents Overview for Volume I
1 Gromov’sWaistofNon-radialGaussianMeasuresandRadial
Non-GaussianMeasures
ArseniyAkopyanandRomanKarasev
2 Zhang’sInequalityforLog-ConcaveFunctions
DavidAlonso-Gutiérrez,JulioBernués,
andBernardoGonzálezMerino
3 Bobkov’sInequalityviaOptimalControlTheory
FranckBartheandPaataIvanisvili
4 ArithmeticProgressionsintheTraceofBrownianMotion
inSpace
ItaiBenjaminiandGadyKozma
5 Edgeworth Corrections in Randomized Central Limit
Theorems
SergeyG.Bobkov
6 ThreeApplicationsoftheSiegelMassFormula
JeanBourgainandCiprianDemeter
7 DecouplingsforRealAnalyticSurfacesofRevolution
JeanBourgain,CiprianDemeter,andDominiqueKemp
8 On Discrete Hardy–LittlewoodMaximal Functions over
theBallsinZd:Dimension-FreeEstimates
JeanBourgain,MariuszMirek,EliasM.Stein,andBłaz˙ejWróbel
9 OnthePoincaréConstantofLog-ConcaveMeasures
PatrickCattiauxandArnaudGuillin
10 OnPoincaréandLogarithmicSobolevInequalitiesforaClass
ofSingularGibbsMeasures
DjalilChafaïandJosephLehec
