Overview
- Contains more than 40 open research problems proposed to help further research
- Ideal for graduate students as well as researchers in mathematics and computer science
- Acts as a short introduction to important and modern parts of discrete geometry
- Ideal book for a one semester course at an advanced undergraduate or graduate level course
- Features proofs that cover a broad range of methods of discrete geometry, often presentable in short talks
- Includes supplementary material: sn.pub/extras
Part of the book series: Fields Institute Monographs (FIM, volume 32)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This monograph gives a short introduction to the relevant modern parts of discrete geometry, in addition to leading the reader to the frontiers of geometric research on sphere arrangements. The readership is aimed at advanced undergraduate and early graduate students, as well as interested researchers. It contains more than 40 open research problems ideal for graduate students and researchers in mathematics and computer science. Additionally, this book may be considered ideal for a one-semester advanced undergraduate or graduate level course.
The core part of this book is based on three lectures given by the author at the Fields Institute during the thematic program on “Discrete Geometry and Applications” and contains four core topics. The first two topics surround active areas that have been outstanding from the birth of discrete geometry, namely dense sphere packings and tilings. Sphere packings and tilings have a very strong connection to number theory, coding, groups, and mathematical programming. Extending the tradition of studying packings of spheres, is the investigation of the monotonicity of volume under contractions of arbitrary arrangements of spheres. The third major topic of this book can be found under the sections on ball-polyhedra that study the possibility of extending the theory of convex polytopes to the family of intersections of congruent balls. This section of the text is connected in many ways to the above-mentioned major topics and it is also connected to some other important research areas as the one on coverings by planks (with close ties to geometric analysis). This fourth core topic is discussed under covering balls by cylinders.
Reviews
From the reviews:
“This is an exciting book aimed at graduate students and researchers as it contains a multitude of open problems after leading the reader to the research frontier.” (Kelly J. Pearson, zbMATH, Vol. 1281, 2014)
Authors and Affiliations
Bibliographic Information
Book Title: Lectures on Sphere Arrangements – the Discrete Geometric Side
Authors: Károly Bezdek
Series Title: Fields Institute Monographs
DOI: https://doi.org/10.1007/978-1-4614-8118-8
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2013
Hardcover ISBN: 978-1-4614-8117-1Published: 05 August 2013
Softcover ISBN: 978-1-4939-0032-9Published: 26 August 2015
eBook ISBN: 978-1-4614-8118-8Published: 04 August 2013
Series ISSN: 1069-5273
Series E-ISSN: 2194-3079
Edition Number: 1
Number of Pages: XII, 175
Topics: Convex and Discrete Geometry, Polytopes