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The Cube-A Window to Convex and Discrete Geometry

The Cube-A Window to Convex and Discrete Geometry

£99.99

Part of Cambridge Tracts in Mathematics

  • Date Published: February 2006
  • availability: Available
  • format: Hardback
  • isbn: 9780521855358

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About the Authors
  • 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
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    Product details

    • Date Published: February 2006
    • format: Hardback
    • isbn: 9780521855358
    • length: 184 pages
    • dimensions: 235 x 152 x 15 mm
    • weight: 0.394kg
    • contains: 6 b/w illus.
    • availability: Available
  • Table of Contents

    Preface
    Basic notation
    0. Introduction
    1. Cross sections
    2. Projections
    3. Inscribed simplices
    4. Triangulations
    5. 0/1 polytopes
    6. Minkowski's conjecture
    7. Furtwangler's conjecture
    8. Keller's conjecture
    Bibliography
    Index.

  • Author

    Chuanming Zong, Peking University, Beijing
    Chuanming Zong is a Professor of Mathematics at Peking University.

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