The Cube : A Window to Convex and Discrete Geometry

Chuanming Zong - Collection Cambridge Tracts in Mathematics

174 pages, parution le 17/01/2006

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Résumé

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.

Demonstrates how Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, and Number Theory, can be applied to the study of unit cubes
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 applications of deep analysis like log concave measure and the Brascamp-Lieb inequality

Sommaire

Basic notation
Introduction
Cross sections
Projections
Inscribed simplices
Triangulations
0/1 polytopes
Minkowski's conjecture
Furtwangler's conjecture
Keller's conjecture

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Chuanming Zong
Collection	Cambridge Tracts in Mathematics
Parution	17/01/2006
Nb. de pages	174
Format	16 x 23,5
Couverture	Relié
Poids	390g
Intérieur	Noir et Blanc
EAN13	9780521855358
ISBN13	978-0-521-85535-8