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Cube-A Window to Convex and Discrete Geometry

Cube-A Window to Convex and Discrete Geometry - 06 edition

ISBN13: 978-0511138317

Cover of Cube-A Window to Convex and Discrete Geometry 06 (ISBN 978-0511138317)
ISBN13: 978-0511138317
ISBN10: 0511138318
Edition: 06
Copyright: 2006
Publisher: Cambridge University Press
Published: 2006
International: No

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Cube-A Window to Convex and Discrete Geometry - 06 edition

ISBN13: 978-0511138317

Chuanming Zong

ISBN13: 978-0511138317
ISBN10: 0511138318
Edition: 06
Copyright: 2006
Publisher: Cambridge University Press
Published: 2006
International: No
Summary

This tract has two purposes: to show what is known about the n-dimensional unit cubes and to demonstrate how Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory, can be applied to the study of them. The unit cubes, from any point of view, are among the most important and fascinating objects in an n-dimensional Euclidean space. However, our knowledge about them is still quite limited and many basic problems remain unsolved. In this Tract eight topics about the unit cubes are introduced: cross sections, projections, inscribed simplices, triangulations, 0/1 polytopes, Minkowski's conjecture, Furtwangler's conjecture, and Keller's conjecture. In particular the author demonstrates how deep analysis like log concave measure and the Brascamp-Lieb inequality can deal with the cross section problem, how Hyperbolic Geometry helps with the triangulation problem, how group rings can deal with Minkowski's conjecture and Furtwangler's conjecture, and how Graph Theory handles Keller's conjecture.

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