Toshikazu Sunada's Books

Topological Crystallography

With a View Towards Discrete Geometric Analysis

By: Toshikazu Sunada

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Topological Crystallography

With a View Towards Discrete Geometric Analysis

By: Toshikazu Sunada

Geometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhedra addressed in the final volume of Euclid’s Elements. Since then, geometry has taken its own path and the study of crystals has not been a central theme in mathematics, with the exception of Kepler’s work on snowflakes. Only in the nineteenth century did mathematics begin to play a role in crystallography as group theory came to be applied to the morphology of crystals. This monograph follows the Greek tradition in seeking beautiful shapes such as regular convex polyhedra. The primary aim is to convey to the reader how algebraic topology is effectively used to explore the rich world of crystal structures. Graph theory, homology theory, and the theory of covering maps are employed to introduce the notion of the topological crystal which retains, in the abstract, all the information on the connectivity of atoms in the crystal. For that reason the title Topological Crystallography has been chosen. Topological crystals can be described as “living in the logical world, not in space,” leading to the question of how to place or realize them “canonically” in space. Proposed here is the notion of standard realizations of topological crystals in space, including as typical examples the crystal structures of diamond and lonsdaleite. A mathematical view of the standard realizations is also provided by relating them to asymptotic behaviors of random walks and harmonic maps. Furthermore, it can be seen that a discrete analogue of algebraic geometry is linked to the standard realizations. Applications of the discussions in this volume include not only a systematic enumeration of crystal structures, an area of considerable scientific interest for many years, but also the architectural design of lightweight rigid structures. The reader therefore can see the agreement of theory and practice.

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Page Count

236

Publisher

Springer Science & Business Media

Published Date

ISBN 10

4431541772

ISBN 13

9784431541776

A Mathematical Gift, III

The interplay between topology, functions, geometry, and algebra

By: Koji Shiga,Toshikazu Sunada

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A Mathematical Gift, III

The interplay between topology, functions, geometry, and algebra

By: Koji Shiga,Toshikazu Sunada

This book brings the beauty and fun of mathematics to the classroom. It offers serious mathematics in a lively, reader-friendly style. Included are exercises and many figures illustrating the main concepts. The first chapter talks about the theory of manifolds. It includes discussion of smoothness, differentiability, and analyticity, the idea of local coordinates and coordinate transformation, and a detailed explanation of the Whitney imbedding theorem (both in weak and in strong form).The second chapter discusses the notion of the area of a figure on the plane and the volume of a solid body in space. It includes the proof of the Bolyai-Gerwien theorem about scissors-congruent polynomials and Dehn's solution of the Third Hilbert Problem. This is the third volume originating from a series of lectures given at Kyoto University (Japan). It is suitable for classroom use for high school mathematics teachers and for undergraduate mathematics courses in the sciences and liberal arts. The first and second volumes are available as Volume 19 and Volume 20 in the AMS series, ""Mathematical World"".

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Page Count

141

Publisher

American Mathematical Society

Published Date

ISBN 10

0821832840

ISBN 13

9780821832844

Proceedings of the Third Asian Mathematical Conference 2000

University of the Philippines, Diliman, Philippines, 23-27 October 2000

By: Toshikazu Sunada

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Proceedings of the Third Asian Mathematical Conference 2000

University of the Philippines, Diliman, Philippines, 23-27 October 2000

By: Toshikazu Sunada

This proceedings volume contains 55 research and expository articles on a wide range of currently active and interesting areas in pure and applied mathematics. The research articles report on the current research accomplishments and the significance of the results. Every expository article aims to make the subject interesting by including the state of the subject, description and motivation of the problems, the relevance of the results, and open problems for future research directions. This book serves as a good reference not only for researchers but also for graduate students.

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Page Count

633

Publisher

World Scientific

Published Date

ISBN 10

9812777466

ISBN 13

9789812777461

Topological Crystallography

With a View Towards Discrete Geometric Analysis

By: Toshikazu Sunada

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Topological Crystallography

With a View Towards Discrete Geometric Analysis

By: Toshikazu Sunada

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Page Count

236

Publisher

Springer Science & Business Media

Published Date

ISBN 10

4431541772

ISBN 13

9784431541776

Discrete Geometric Analysis

Proceedings of the First JAMS Symposium on Discrete Geometric Analysis, December 12-20, 2002, Sendai, Japan

By: Motoko Kotani

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Discrete Geometric Analysis

Proceedings of the First JAMS Symposium on Discrete Geometric Analysis, December 12-20, 2002, Sendai, Japan

By: Motoko Kotani

Collects papers from the proceedings of the first symposium of the Japan Association for Mathematical Sciences. This book covers topics that center around problems of geometric analysis in relation to heat kernels, random walks, and Poisson boundaries on discrete groups, graphs, and other combinatorial objects.

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Page Count

274

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821833510

ISBN 13

9780821833513

Book's by Toshikazu Sunada

Topological Crystallography

Topological Crystallography

A Mathematical Gift, III

A Mathematical Gift, III

Proceedings of the Third Asian Mathematical Conference 2000

Proceedings of the Third Asian Mathematical Conference 2000

Topological Crystallography

Topological Crystallography

Discrete Geometric Analysis

Discrete Geometric Analysis

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