© 2020

Geometric Aspects of Functional Analysis

Israel Seminar (GAFA) 2017-2019 Volume I

  • Bo'az Klartag
  • Emanuel Milman

Part of the Lecture Notes in Mathematics book series (LNM, volume 2256)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. David Alonso-Gutiérrez, Julio Bernués, Bernardo González Merino
    Pages 29-48
  3. Franck Barthe, Paata Ivanisvili
    Pages 49-61
  4. Jean Bourgain, Ciprian Demeter
    Pages 99-111
  5. Jean Bourgain, Ciprian Demeter, Dominique Kemp
    Pages 113-125
  6. Patrick Cattiaux, Arnaud Guillin
    Pages 171-217
  7. Dario Cordero-Erausquin, Liran Rotem
    Pages 247-262
  8. Back Matter
    Pages 341-342

About this book


Continuing the theme of the previous volume, these seminar notes reflect general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. 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 order in high dimensions. Central to the text is 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 concept and properties of Entropy form an important subject, with Bourgain's slicing problem and its variants drawing much attention. Constructions related to Convexity Theory are proposed and revisited, as well as inequalities that go beyond the Brunn–Minkowski theory. One of the major current research directions addressed is the identification of lower-dimensional structures with remarkable properties in rather arbitrary high-dimensional objects. In addition to functional analytic results, connections to Computer Science and to Differential Geometry are also discussed.


Asymptotic Geometric Analysis Convex Geometry Functional Analysis Functional Inequalities Geometric Probability

Editors and affiliations

  • Bo'az Klartag
    • 1
  • Emanuel Milman
    • 2
  1. 1.School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel, Department of MathematicsWeizmann Institute of ScienceRehovotIsrael
  2. 2.Department of MathematicsTechnion – Israel Institute of TechnologyHaifaIsrael

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