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Geometric Aspects of Functional Analysis
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As in the previous Seminar Notes, the current volume reflects general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. A classical theme in the Local Theory of Banach Spaces which is well represented in this volume is the identification of lower-dimensional structures in high-dimensional objects. More recent applications of high-dimensionality are manifested by contributions in Random Matrix Theory, Concentration of Measure and Empirical Processes. Naturally, the Gaussian measure plays a central role in many of these topics, and is also studied in this volume; in particular, the recent breakthrough proof of the Gaussian Correlation Conjecture is revisited. The interplay of the theory with Harmonic and Spectral Analysis is also well apparent in several contributions. The classical relation to both the primal and dual Brunn-Minkowski theories is also well represented, and related algebraic structures pertaining to valuations and valent functions are discussed. All contributions are original research papers and were subject to the usual refereeing standards.
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Alesker, S.: On repeated sequential closures of constructible functions in valuations.- Ben-Efraim L., Milman, V., Segal, A.: Orbit point of view on some results of asymp-totic theory; Orbit type and cotype.- Bobkov, S. G., Nayar, P., Tetali, P.: Concentration Properties of Restricted Measures with Applications to Non-Lipschitz Functions.- Bourgain, J.:On random walks in large compact Lie groups.- Bourgain, J.: On a problem of Farrell and Vershynin in random matrix theory..- Colesanti, A., Lombardi, N.: Valutations on the space of quasi-concave functions.- Dafnis, N., Paouris, G.: An inequality for moments of log-concave functions on Gaus-sian random vectors.- Friedland, O., Yomdin, Y.:(s; p)-valent functions.- Gluskin, E. D., Ostrover, Y.: A remark on projections of the rotated cube to complex lines.- Guedon, O., Hinrichs, A., Litvak, A. E., Prochno, J.: On the expectation of operatornorms of random matrices.- Haviv, I., Regev, O.: The Restricted Isometry Property of Subsampled Fourier Ma-trices.- Huang, H., Wei, F.: Upper bound for the Dvoretzky dimension in Milman-Schechtman theorem.- Klartag, B.: Super-Gaussian directions of random vectors.- Koldobsky, A., Pajor, A.: A remark on measures of sections of Lp-balls.- Kolesnikov, A. V., Milman, E.: Sharp Poincare-type inequality for the Gaussian mea-sure on the boundary of convex sets.- K onig, H., Milman, V.: Rigidity of the chain rule and nearly submultiplicative functions.- Lata la, R., Matlak, D.: Royen's proof of the Gaussian correlation inequality.- Liaw, C., Mehrabian, A., Plan, Y., Vershynin, R.: A simple tool for bounding the deviation of random matrices on geometric sets.- Mendelson, S.: On multiplier processes under weak moment assumptions.- Milman, V., Rotem, L.: Characterizing the radial sum for star bodies.- Oleskiewicz, K.: On mimicking Rademacher sums in tail spaces.- Rossi, A., Salani, P.: Stability for Borell-Brascamp-Lieb inequalities.pan>

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