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Customer Reviews (19)

Review of The Shape of Inner Space
A really interesting book. While it deals with very high-level mathematics, Yau and Nadis are able to explain it so that it is comprehensible to the average reader who does not have a PhD in mathematics. Much of it also deals with a historical look at the mathematics of the last 20 years or so, and how it has led to advances in string theory. In addition it also explains the interactions between the complex math of high-level geometry and its relationship to string theory, and how the two have worked together to advance each other. Would highly recommend it.

"An Extraordinary Journey"
The "Shape of Inner Space" by Shing-Tung Yau and Steve Nardis is an extraordinary journey of the hidden dimensions of the universe. The authors take us on an exhilarating ride through terrains of mathematics and physics. Calabi-Yau manifolds are topological structures and are central to superstring theory. These compacted multi-dimensional structures are rolled up into small shapes, which are unobservable by humans.

As an artist, I found this book fascinating. My work is interdisciplinary and has bridged the disciplines of mathematics, science and art. It will serve as an inspiration for years to come.
I strongly recommend this book.
Irene Rousseau MFA, Ph.D.

Math Simplified
An immensely complex subject, simplified in every day terms and made readable for non mathematicians like myself.

A Beautiful Book
This book gives a very clear explanation of how geometrical ideas can influence physics.There are almost no math equations in the book, so it is a very good read for anyone who would like to get an idea of some of the core math ideas behind string theory.Lately, there have been a lot of articles and books that would give the lay person the idea that maybe string theory should be ignored.But this book makes it very clear why some of the ideas behind higher dimensional spaces open upfruitful areas which generate a lot of thought.The broken symmetry that we see in the standard model as well as its failure to account for gravity suggest that Calabi-Yau spaces are either a part of the explanation, or are at least a fruitful direction in which to look.

A fantastic journey into mathematics of string theory
This book is not only unique for elegantly explaining complicated concepts of geometry, and its `DNA' imprint on physics via string theory, but it is said from the vantage point of the world renowned geometer who has played a major role in all
these developments.Through
the collaboration of the two authors, the book is very down to earth and has
a style which not only explains how different ideas have unfolded in the past
couple of decades, but how beautifully natural they all fit with one another.
Black holes, curved space, topology and a human struggle to understand the inner
workings of nature through beautiful mathematical reasoning shines very clearly
through the book and provides the reader with a front row seat for an exciting
journey into the interaction of modern physics and mathematics.I strongly recommend this book to all those interested in seeing the power of elegant mathematics
applied to the most enigmatic questions in modern physics. ... Read more

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In the Spring of 1984, the authors gave a series of lectures in the Institute for Advanced Studies in Princeton. These lectures, which continued throughout the 1984-1985 academic year, are published in this volume. Lectures on Differential Geometry was originally printed in Chinese, and widely circulated in China. This greatly anticipated English translation is an essential reference tool for Differential Geometry. Differential Geometry has progressed rapidly in this century. This book describes the major achievements in this field. ... Read more

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The International Congress of Mathematicians was an historical event that was held at the Morningside Center of Mathematics of the Chinese Academy of Sciences (Beijing). It was the first occasion where Chinese mathematicians from all over the world gathered to present their research.

The Morningside Mathematics lectures were given by R. Borcherds, J. Coates, R. Graham, and D. Stroock. Other distinguished speakers included J.-P. Bourguignon, J. Jöst, M. Taylor, and S. L. Lee. Topics covered in the volume include algebra and representation theory, algebraic geometry, number theory and automorphic forms, Riemannian geometry and geometric analysis, mathematical physics, topology, complex analysis and complex geometry, computational mathematics, and combinatorics. ... Read more

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This volume is an updated edition of Essays on Mirror Manifolds, the first book of papers published after the phenomenon of mirror symmetry was discovered. The two major groups who made the discovery reported their papers here.

Greene, Plesser, and Candelas gave details on their findings; Witten gave his interpretation which was vital for future development. Vafa introduced the concept of quantum cohomology. Several mathematicians, including Katz, Morrison, Wilson, Roan, Tian, Hübsch, Yau, and Borcea discussed current knowledge about Calabi-Yau manifolds. Ferrara and his coauthors addressed special geometry and $N=2$ supergravity. Rocek proposed possible mirrors for Calabi-Yau manifolds with torsion. This collection continues to be an important book on this spectacular achievement in algebraic geometry and mathematical physics. ... Read more

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new paperback reissue ... Read more

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This book presents surveys from a workshop held during the theme year in geometry and topology at the Centre de recherches mathématiques (CRM, University of Montréal). The volume is in some sense a sequel to Mirror Symmetry I (1998) and Mirror Symmetry II (1996), copublished by the AMS and International Press.

Included are recent developments in the theory of mirror manifolds and the related areas of complex and symplectic geometry. The long introductory articles explain the key physical ideas and motivation, namely conformal field theory, supersymmetry, and string theory. Open problems are emphasized. Thus the book provides an efficient way for a very broad audience of mathematicians and physicists to reach the frontier of research in this fast expanding area.

Features:

Crucial research pertaining to future developments in algebraic and symplectic geometry and to the physics of unified string theories

Well-known authors who are leaders in the field

Introductory article by Greene and Yau

A solid and even blend of ideas and techniques from both mathematics and physics ... Read more

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In the summer of 1990, S.Y. Cheng and S.-T. Yau organized a conference in honour of their professor S.S. Chern on the occasion of his 79th birthday. This volume contains personal reminiscences from some of his friends and students. The lectures reflect his wisdom and warmth toward young geometers. ... Read more

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Lie groups are fundamental objects in mathematics. They occur naturally in differential geometry, algebraic geometry, representation theory, number theory, and other areas. Closely related are arithmetic subgroups, locally symmetric spaces and the spectral theory of automorphic forms.This book consists of five chapters which give comprehensive introductions to Lie groups, Lie algebras, arithmetic groups and reduction theories, cohomology of arithmetic groups, and the Petersson and Kuznetsov trace formulas. ... Read more

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Proceedings of a conference at the Chinese University of Hong Kong, held in response to Andrew Wile's conjecture that every elliptic curve over Q is modular. The survey article describing Wile's work is included as the first article in the present edition. ... Read more

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Table of contents

The Evolution Problem in General Relativity (Mihalis Dafermos)
Very Large Graphs (Lázló Lovász)
On the Classification of Topological Field Theories (Jacob Lurie)
Properly embedded minimal planar domains with infinite topology are Riemann minimal examples (William H. Meeks III and Joaquín Pérez)
Unearthing the Visions of a Master: Harmonic Maass Forms and Number Theory (Ken Ono) ... Read more

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Since its discovery in the early 1990s, mirror symmetry, or more generally, string theory, has exploded onto the mathematical landscape. This topic touches upon many branches of mathematics and mathematical physics, and has revealed deep connections between subjects previously considered unrelated. The papers in this volume treat mirror symmetry from the perspectives of both mathematics and physics. The articles can be roughly grouped into four sub-categories within the topic of mirror symmetry: arithmetic aspects, geometric aspects, differential geometric and mathematical physics aspects, and geometric analytic aspects. In these works, the reader will find mathematics addressing, and in some cases solving, problems inspired and influenced by string theory.Titles in this series are co-published with International Press, Cambridge, MA. ... Read more

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This digital document, covering the life and work of Shing-Tung Yau, is an entry from Contemporary Authors, a reference volume published by Thompson Gale. The length of the entry is 1541 words. The page length listed above is based on a typical 300-word page. Although the exact content of each entry from this volume can vary, typical entries include the following information:

• Place and date of birth and death (if deceased)
• Family members
• Education
• Professional associations and honors
• Employment
• Writings, including books and periodicals
• A description of the author's work
• References to further readings about the author

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In 1993, a conference was held honoring Raoul Bott on his 70th birthday. Many of his friends and students came from all over the world to celebrate this special occasion. Raoul Bott is a valued member of the Harvard University Department of Mathematics, and a great mathematician. The conference in his honor attracted a large audience over the course of three days. The lectures given during the conference, along with other important mathematical contributions, are presented in this volume in honor of Raoul Bott. ... Read more

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This text contains highlights from two conferences on mathematical physics: "Interface Between Mathematics and Physics", held in 1992 at the Academy Sinica, in Taiwan; and "Topics in Geometry and Physics". ... Read more

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The collection of articles in this volume are based on lectures presented during the Winter School on Mirror Symmetry held at Harvard University. There are many new directions suggested by mirror symmetry which could potentially have very rich connections in physics and mathematics.

This book brings together the latest research in a major area of mathematical physics, including the recent progress in mirror manifolds and Lagrangian submanifolds. In particular, several articles describing homological approach and related topics are included.

Other AMS titles edited by S.-T Yau published in the AMS/IP Studies in Advanced Mathematics series include, Mirror Symmetry III, Volume 10, Mirror symmetry II, Volume 1, and Mirror Symmetry I, Volume 9. ... Read more

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This volume represents selected proceedings of the Fourth International Congress of Chinese Mathematicians, held in Hangzhou, China. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. Approximately fifteen hundred mathematicians participated in the Congress.Included in this volume are the complete Morningside Lectures, the complete plenary lectures, and selected invited lectures.Titles in this series are co-published with International Press, Cambridge, MA. ... Read more

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This volume presents lectures given by Richard Schoen and Shing-Tung Yau at the Institute for Advanced Studies at Princeton University in 1984 and 1985. The lectures describe the major advances in differential geometry, which progressed rapidly in the twentieth century. ... Read more