Book Description
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

Product Description
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

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

Greene, Plesser, and Candelas gave details on their findings;Witten gave his interpretation which was vital for futuredevelopment. Vafa introduced the concept of quantum cohomology.Several mathematicians, including Katz, Morrison, Wilson, Roan,Tian, Hübsch, Yau, and Borcea discussed current knowledgeabout Calabi-Yau manifolds. Ferrara and his coauthors addressedspecial geometry and $N=2$ supergravity. Rocek proposed possiblemirrors for Calabi-Yau manifolds with torsion. This collectioncontinues to be an important book on this spectacularachievement in algebraic geometry and mathematical physics. ... Read more

Book Description
The Surveys in Differential Geometry are supplements to the Journal of Differential Geometry, which are published by International Press. They include significant invited papers combining original research and overviews of the most current research in specific areas of interest to the growing Journal of Differential Geometry community.The survey volumes serve as continuing references, inspirations for new research, and introductions to the variety of topics of interest to differential geometers. These supplements are published annually since 1999.

As a service to the mathematics community, the editors of the Journal of Differential Geometry decided to organize a conference to be held every three years. Among the speakers at our first conference were people working in algebraic geometry, mathematical physics and other interesting fields. These speakers are prominent specialists in their respective areas who are able to give a broad overview of recent trends and make predictions and suggestions for future research. We believe that these conferences are important gatherings that inspire experts and non-experts alike. Our first conference was held at Harvard University from April 27-29, 1990, was made possible by the generous funding of the Journal of Differential Geometry. Central to the success of this conference were the speakers who prepared not only two hours' worth of lectures, but also the manuscripts published here. Their lectures were enthusiastically received by several hundred participants. ... Read more

Book Description
From the beginning harmonic maps were studied in connection with the theory of minimal surfaces.

In 1985, the authors presented a series of lectures at the University of California at San Diego on the subject of harmonic maps. Most of these lectures are collected here as Part I. Part I of the book is devoted to harmonic maps defined on Riemann surfaces. Part II was added much more recently, and comprises part of the thesis of the first author, the work of N. Korevaar and the second author, and applications to geometry by the authors. The final chapter is due to J. Jost and the second author. This book presents some of the latest research on this topic from two of the foremost researchers in the field. ... Read more

Book Description
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

Book Description
These three parts contain the proceedings of the AMS SummerInstitute on Differential Geometry, held at the UniversityCalifornia, Los Angeles in July 1990. This was the largest AMSSummer Institute ever, reflecting the wide-ranging and intenseresearch activity in the subject. The parts contain manyextensive survey articles presenting perspectives on relativelybroad topics; these articles would be accessible to advancedgraduate students. In addition, the authors of the researcharticles were encouraged to survey the relevant literature. Thethree parts together offer the deepest and most comprehensivesurvey of recent research in differential geometry availabletoday. ... Read more

Book Description
The International Congress of Mathematicians was an historicalevent that was held at the Morningside Center of Mathematics ofthe Chinese Academy of Sciences (Beijing). It was the firstoccasion where Chinese mathematicians from all over the worldgathered to present their research.

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

Book Description
In 1992, many of the world's most distinquished scientists gathered to honor Professor and Nobel Laureate, Chen Ning Yang on the occasion of his seventieth birthday. This volume documents the scientific contributions that resulted from that conference. Additionally, it has several biographical and historical contributions that discuss the impact C.N. Yang has made on the research and lives of his students, colleagues, and friends. ... Read more

Book Description
This book presents surveys from a workshop held during the themeyear in geometry and topology at the Centre de recherchesmathématiques (CRM, University of Montréal). Thevolume is in some sense a sequel to Mirror Symmetry I (1998) andMirror Symmetry II (1996), copublished by the AMS andInternational Press.

Included are recent developments in the theory of mirrormanifolds and the related areas of complex and symplecticgeometry. The long introductory articles explain the keyphysical 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 broadaudience of mathematicians and physicists to reach the frontierof research in this fast expanding area.

Features:

Crucial research pertaining to future developments in algebraicand symplectic geometry and to the physics of unified stringtheories

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 bothmathematics and physics ... Read more