Ebook: Geometric Aspects of Functional Analysis: Israel Seminar 2006–2010

This collection of original papers related to the Israeli GAFA seminar (on Geometric Aspects of Functional Analysis) from the years 2006 to 2011 continues the long tradition of the previous volumes, which reflect the general trends of Asymptotic Geometric Analysis, understood in a broad sense, and are a source of inspiration for new research. Most of the papers deal with various aspects of the theory, including classical topics in the geometry of convex bodies, inequalities involving volumes of such bodies or more generally, logarithmically-concave measures, valuation theory, probabilistic and isoperimetric problems in the combinatorial setting, volume distribution on high-dimensional spaces and characterization of classical constructions in Geometry and Analysis (like the Legendre and Fourier transforms, derivation and others). All the papers here are original research papers.

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In these meetings, which were held in honour of Professor Tosio Kato on his retirement, the focus was on the interplay of functional analysis and partial differential equations. Thus, the study of Schrodinger operators, from the viewpoints of evolution equations and spectral theory, is one major subject, while functional analytic studies of nonlinear PDEs, including Navier-Stokes, KdV and other equations, constitutes another main theme. Papers on these linear and nonlinear problems are linked through their methods and types of approach The [alpha]-Cosine transform and intertwining integrals on real Grassmannians / Semyon Alesker -- On modules over valuations / Semyon Alesker -- On multiplicative maps of continuous and smooth functions / Shiri Artstein-Avidan, Dmitry Faifman, and Vitali Milman -- Order isomorphisms on convex functions in windows / Shiri Artstein-Avidan, Dan Florentin, and Vitali Milman -- Finite transitive graph embeddings into a hyperbolic metric space must stretch or squeeze / Itai Benjamini and Oded Schramm -- Tightness of fluctuations of first passage percolation on some large graphs / Itai Benjamini and Ofer Zeitouni -- Finitely supported measures on SL₂[real number] which are absolutely continuous at infinity / Jean Bourgain -- Moebius Schrödinger / Jean Bourgain -- Interpolations, convexity and geometric inequalities / Dario Cordero-Erausquin and Bo'az Klartag -- Hypercontractive measures, Talagrand's inequality, and influences / Dario Cordero-Erausquin and Michel Ledoux -- A family of unitary operators satisfying a poisson-type summation formula / Dmitry Faifman -- Stability of order preserving transforms / Dan Florentin and Alexander Segal -- On the distribution of the [psi]₂-norm of linear functionals on isotropic convex bodies / Apostolos Giannopoulos, Grigoris Paouris, and Petros Valettas -- A remark on vertex index of the convex bodies / Efim D. Gluskin and Alexander E. Litvak -- Inner regularization of log-concave measures and small-ball estimates / Bo'az Klartag and Emanuel Milman -- An operator equation generalizing the Leibniz rule for the second derivative / Hermann König and Vitali Milman -- Moments of unconditional logarithmically concave vectors / Rafal Latala -- Projections of probability distributions: a measure-theoretic Dvoretzky theorem / Elizabeth Meckes -- On a Loomis-Whitney type inequality for permutationally invariant unconditional convex bodies / Piotr Nayar and Tomasz Tkocz -- The Hörmander proof of the Bourgain-Milman theorem / Fedor Nazarov -- On some extension of Feige's inequality / Krzysztof Oleszkiewicz -- On the mean width of log-concave functions / Liran Rotem -- Approximate Gaussian isoperimetry for k sets / Gideon Schechtman -- Remarks on stability of Brunn-Minkowski and isoperimetric inequalities for convex bodies / Alexander Segal -- On contact points of convex bodies / Nikhil Srivastava -- A: Related conference and seminar talks