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Geometric Aspects of Functional Analysis - Israel Seminar (GAFA) 2017-2019 Volume II (Paperback, 1st ed. 2020)
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Geometric Aspects of Functional Analysis - Israel Seminar (GAFA) 2017-2019 Volume II (Paperback, 1st ed. 2020)
Series: Lecture Notes in Mathematics, 2266
Expected to ship within 12 - 17 working days
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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 Poincare 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.
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