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Geometric Aspects of Functional Analysis

Israel Seminar (GAFA) 2011-2013

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  • © 2014
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Overview

Editors:
  1. Bo'az Klartag

    1. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

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    You can also search for this editor in PubMed   Google Scholar

  2. Emanuel Milman

    1. Technion - Israel Institute of Technology, Haifa, Israel

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2116)

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Table of contents (31 chapters)

  1. Front Matter

    Pages i-ix
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  2. Dyson Processes Associated with Associative Algebras: The Clifford Case

    • Dominique Bakry, Marguerite Zani
    Pages 1-37
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  3. Gaussian Free Field on Hyperbolic Lattices

    • Itai Benjamini
    Pages 39-45
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  4. Point-to-Point Distance in First Passage Percolation on (Tree) ×Z

    • Itai Benjamini, Pascal Maillard
    Pages 47-51
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  5. A Lower Bound for the Bergman Kernel and the Bourgain-Milman Inequality

    • Zbigniew Błocki
    Pages 53-63
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  6. An Improved Estimate in the Restricted Isometry Problem

    • Jean Bourgain
    Pages 65-70
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  7. On Eigenvalue Spacings for the 1-D Anderson Model with Singular Site Distribution

    • Jean Bourgain
    Pages 71-83
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  8. On the Local Eigenvalue Spacings for Certain Anderson-Bernoulli Hamiltonians

    • Jean Bourgain
    Pages 85-96
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  9. On the Control Problem for Schrödinger Operators on Tori

    • Jean Bourgain
    Pages 97-105
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  10. Bounding the Norm of a Log-Concave Vector Via Thin-Shell Estimates

    • Ronen Eldan, Joseph Lehec
    Pages 107-122
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  11. On the Oscillation Rigidity of a Lipschitz Function on a High-Dimensional Flat Torus

    • Dmitry Faifman, Bo’az Klartag, Vitali Milman
    Pages 123-131
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  12. Identifying Set Inclusion by Projective Positions and Mixed Volumes

    • Dan Florentin, Vitali Milman, Alexander Segal
    Pages 133-145
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  13. Vitushkin-Type Theorems

    • Omer Friedland, Yosef Yomdin
    Pages 147-157
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  14. M-Estimates for Isotropic Convex Bodies and Their L q -Centroid Bodies

    • Apostolos Giannopoulos, Emanuel Milman
    Pages 159-182
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  15. Remarks on the Central Limit Theorem for Non-convex Bodies

    • Uri Grupel
    Pages 183-198
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  16. Reflectionless Measures and the Mattila-Melnikov-Verdera Uniform Rectifiability Theorem

    • Benjamin Jaye, Fedor Nazarov
    Pages 199-229
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  17. Logarithmically-Concave Moment Measures I

    • Bo’az Klartag
    Pages 231-260
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  18. Estimates for Measures of Sections of Convex Bodies

    • Alexander Koldobsky
    Pages 261-271
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  19. Remarks on the KLS Conjecture and Hardy-Type Inequalities

    • Alexander V. Kolesnikov, Emanuel Milman
    Pages 273-292
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  20. Modified Paouris Inequality

    • Rafał Latała
    Pages 293-307
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Keywords

About this book

As in the previous Seminar Notes, the current volume reflects general trends in the study of Geometric Aspects of Functional Analysis. Most of the papers deal with different aspects of Asymptotic Geometric Analysis, understood in a broad sense; many continue the study of geometric and volumetric properties of convex bodies and log-concave measures in high-dimensions and in particular the mean-norm, mean-width, metric entropy, spectral-gap, thin-shell and slicing parameters, with applications to Dvoretzky and Central-Limit-type results. The study of spectral properties of various systems, matrices, operators and potentials is another central theme in this volume. As expected, probabilistic tools play a significant role and probabilistic questions regarding Gaussian noise stability, the Gaussian Free Field and First Passage Percolation are also addressed. The historical connection to the field of Classical Convexity is also well represented with new properties and applications of mixed-volumes. The interplay between the real convex and complex pluri-subharmonic settings continues to manifest itself in several additional articles. All contributions are original research papers and were subject to the usual refereeing standards.

Editors and Affiliations

  • School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

    Bo'az Klartag

  • Technion - Israel Institute of Technology, Haifa, Israel

    Emanuel Milman

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