LEADER 03508nam 22005895 450 001 996418280103316 005 20200709101457.0 010 $a3-030-46762-7 024 7 $a10.1007/978-3-030-46762-3 035 $a(CKB)4100000011343403 035 $a(DE-He213)978-3-030-46762-3 035 $a(MiAaPQ)EBC6273205 035 $a(PPN)251090345 035 $a(EXLCZ)994100000011343403 100 $a20200708d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric Aspects of Functional Analysis$b[electronic resource] $eIsrael Seminar (GAFA) 2017-2019 Volume II /$fedited by Bo'az Klartag, Emanuel Milman 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (X, 348 p. 8 illus., 1 illus. in color.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2266 311 $a3-030-46761-9 330 $aContinuing the theme of the previous volume, these seminar notes reflect general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. Two classical topics represented are the Concentration of Measure Phenomenon in the Local Theory of Banach Spaces, which has recently had triumphs in Random Matrix Theory, and the Central Limit Theorem, one of the earliest examples of regularity and order in high dimensions. Central to the text is the study of the Poincaré and log-Sobolev functional inequalities, their reverses, and other inequalities, in which a crucial role is often played by convexity assumptions such as Log-Concavity. The concept and properties of Entropy form an important subject, with Bourgain's slicing problem and its variants drawing much attention. Constructions related to Convexity Theory are proposed and revisited, as well as inequalities that go beyond the Brunn?Minkowski theory. One of the major current research directions addressed is the identification of lower-dimensional structures with remarkable properties in rather arbitrary high-dimensional objects. In addition to functional analytic results, connections to Computer Science and to Differential Geometry are also discussed. . 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2266 606 $aFunctional analysis 606 $aConvex geometry  606 $aDiscrete geometry 606 $aProbabilities 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aConvex and Discrete Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21014 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 615 0$aFunctional analysis. 615 0$aConvex geometry . 615 0$aDiscrete geometry. 615 0$aProbabilities. 615 14$aFunctional Analysis. 615 24$aConvex and Discrete Geometry. 615 24$aProbability Theory and Stochastic Processes. 676 $a515.7 702 $aKlartag$b Bo'az$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aMilman$b Emanuel$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418280103316 996 $aGeometric aspects of functional analysis$980193 997 $aUNISA