An Elementary Introduction to Modern Convex Geometry

By Ball, Keith

Book Id: WPLBN0000661940
Format Type: PDF eBook:
File Size: 0.6 MB
Reproduction Date: 2005

Title:	An Elementary Introduction to Modern Convex Geometry
Author:	Ball, Keith
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Language:	English
Subject:	Science., Mathematics, Logic
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Citation APA MLA Chicago Ball, B. K. (n.d.). An Elementary Introduction to Modern Convex Geometry. Retrieved from http://gutenberg.us/

Description
Mathematics document containing theorems and formulas.

Excerpt
Excerpt: These notes are based, somewhat loosely, on three series of lectures given by myself, J. Lindenstrauss and G. Schechtman, during the Introductory Workshop in Convex Geometry held at the Mathematical Sciences Research Institute in Berkeley, early in 1996. A fourth series was given by B. Bollob as, on rapid mixing and random volume algorithms; they are found elsewhere in this book. The material discussed in these notes is not, for the most part, very new, but the presentation has been strongly influenced by recent developments: among other things, it has been possible to simplify many of the arguments in the light of later discoveries. Instead of giving a comprehensive description of the state of the art, I have tried to describe two or three of the more important ideas that have shaped the modern view of convex geometry, and to make them as accessible...

Table of Contents
Contents Preface 1 Lecture 1. Basic Notions 2 Lecture 2. Spherical Sections of the Cube 8 Lecture 3. Fritz John's Theorem 13 Lecture 4. Volume Ratios and Spherical Sections of the Octahedron 19 Lecture 5. The Brunn{Minkowski Inequality and Its Extensions 25 Lecture 6. Convolutions and Volume Ratios: The Reverse Isoperimetric Problem 32 Lecture 7. The Central Limit Theorem and Large Deviation Inequalities 37 Lecture 8. Concentration of Measure in Geometry 41 Lecture 9. Dvoretzky's Theorem 47 Acknowledgements 53 References 53 Index 55