Geometric aspects of functional analysis : Israel Seminar (GAFA) 2017-2019 / Bo'az Klartag, Emanuel Milman, editors.

Format:

Book

Conference/Event

Contributor:

Klartag, Bo'az, editor.

Milman, Emanuel, 1977- editor.

Conference Name:

Israel Seminar on Geometrical Aspects of Functional Analysis (2017-2019)

Series:

Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 2256.

Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 2266.

Lecture notes in mathematics, 0075-8434 ; volume 2256, 2266

Language:

English

Subjects (All):

Functional analysis--Congresses.

Functional analysis.

Banach spaces--Congresses.

Banach spaces.

Convex domains--Congresses.

Convex domains.

Geometry--Congresses.

Geometry.

Functional differential equations--Asymptotic theory--Congresses.

Functional differential equations.

Functional differential equations--Asymptotic theory.

Genre:

Conference papers and proceedings.

Physical Description:

<1-2> volumes : illustrations ; 24 cm.

Place of Publication:

Cham : Springer, [2020]

Summary:

Continuing the theme of the previous volumes, 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.

Notes:

Includes bibliographical references.

Current copyright fee: GBP19.00 42\0.

ISBN:

9783030360191

3030360199

9783030467616

3030467619

OCLC:

1184114185