The Cube-A Window to Convex and Discrete Geometry

ISBN-13: 9780521855358 / Angielski / Twarda / 2006 / 186 str.

Chuanming Zong; B. Bollobas; W. Fulton

Opis

Eight topics about the unit cubes are introduced within this textbook: cross sections, projections, inscribed simplices, triangulations, 0/1 polytopes, Minkowski's conjecture, Furtwangler's conjecture, and Keller's conjecture. In particular Chuanming Zong 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.

Recenzje

"Because this book is a love letter to the unity of mathematics, readers can hardly but come to share Zong's undisguised enthusiasm...Highly recommended." -- Choice

Spis treści

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.