(This volume presents lectures, given by Richard Schoen an...)
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.
(From the beginning, harmonic maps were studied in connect...)
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. The book presents some of the latest research on this topic from two of the foremost researchers in the field.
(A collection of lectures, given by the author, and numero...)
A collection of lectures, given by the author, and numerous contributors at Tsing Hua University, Taiwan. Topics covered include: energy in general relativity; existence and convergence of solutions; closed geodesics; and mean curvature evolution.
The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions
(String theory says we live in a ten-dimensional universe,...)
String theory says we live in a ten-dimensional universe, but that only four are accessible to our everyday senses. According to theorists, the missing six are curled up in bizarre structures, known as Calabi-Yau manifolds. In "The Shape of Inner Space", Shing-Tung Yau, the man, who mathematically proved, that these manifolds exist, argues, that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe.
From the Great Wall to the Great Collider: China and the Quest to Uncover the Inner Workings of the Universe
(This book explains how an ambitious new machine — on the ...)
This book explains how an ambitious new machine — on the scale of China's proposed "Great Collider" — could provide us with a fuller understanding of the origins of our universe and its most basic constituents.
The Shape of a Life: One Mathematician's Search for the Universe's Hidden Geometry
(Harvard geometer and Fields medalist Shing-Tung Yau has p...)
Harvard geometer and Fields medalist Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians.
Shing-Tung Yau is a Chinese-born American mathematician, educator and researcher. He is mostly known for his work in differential geometry. Yau also gained prominence for his work in algebraic and Kähler geometry, general relativity and string theory.
Background
Shing-Tung Yau was born on April 4, 1949, in Shantou, Guangdong, China, the fifth of the eight children of Chen Ying Chiou and Yeuk-Lam (Leung) Chiou. Within the year, Communists had overthrown the government and the family fled to Hong Kong, where Yau's father, a respected economist and philosopher, obtained a position at a college, which would later be part of Hong Kong University. Yau's mother knit and created goods by hand to help support the family, for professors were poorly paid.
Education
During his early years, Yau acquired broad knowledge of classical Chinese Literature and History from his father. He studied at Pui Ching Middle School in Hong Kong. Later, he attended a high school in Hong Kong and during those years, much emphasis was placed on Mathematics, partly because the laboratories for the sciences were ill-equipped. Between 1966 and 1969, Shing-Tung studied Mathematics at the Chinese University of Hong Kong, where he earned his undergraduate degree.
One of Yau's professors at the Chinese University of Hong Kong had attended the University of California at Berkeley and suggested he study there. An IBM fellowship made it possible for Yau to attend Berkeley. He studied there with Shiing-Shen Chern, a legendary geometrician (Yau would later edit a collection of papers, honoring his teacher). Yau completed his Doctor of Philosophy degree in Mathematics in 1971.
During his lifetime, Shing-Tung received numerous honorary degrees from different educational establishments, including an Honorary Degree of Doctor of Science from the Chinese University of Hong Kong in 1980, an Honorary Master of Arts from Harvard University in 1987, an Honorary Degree of Doctor of Science from National Chiao Tung University, Taiwan, in 1997, a Doctor of Science honoris causa from the University of Macau in 2002, an Honorary Doctorate from Zhejiang University on March 25, 2003 and many others.
In 1971, after receiving his doctorate degree, Yau spent a year as a fellow at the Institute for Advanced Study in Princeton, and then, in 1972, he accepted a position as an Assistant Professor of Mathematics at the State University of New York at Stony Brook, where he remained until 1973.
Between 1973 and 1974, Yau served as a Visiting Assistant Professor at Stanford University in California. In 1974, he became a full Professor of Mathematics at the same university, a post he continued to hold until 1979.
After leaving Stanford in 1979, Yau returned to the Institute for Advanced Study as an educator. He left the institute in 1984 to become a Professor of Mathematics and Chairman of the Department at the University of California, San Diego.
Differential geometry, which is Yau’s field, was developed during the 1800's, and it uses derivatives and integrals to describe geometric objects, such as surfaces and curves. Differential geometry is particularly concerned with geometrical calculations across many dimensions. The simplest kind of geometry would be one and two dimensional, analyzing figures, such as squares or circles. The geometry of a three-dimensional figure, such as a cube or a cylinder, is more complicated. Differential geometry is primarily concerned with calculations about geometrical figures in four or more dimensions. An example of a four-dimensional figure would be a three-dimensional one, changing over time — the stretching and snapping of a rubber band, for instance, or a drop of water splashing on a surface.
One of the most important applications of differential geometry is Einstein’s theory of relativity: Einstein used differential geometry in his original calculations and it was central to his theory of gravity. The general theory of relativity includes a conjecture — that is, an unproven postulate — which proposes, that in an isolated physical system the total energy, including gravity and matter, would be positive. Called the positive mass conjecture, this was fundamental to the theory of relativity, but no one had been able to prove it.
Yau’s first major contribution to differential geometry was his proof of another conjecture, called the Calabi conjecture, which concerns how volume and distance can be measured not in four, but in five or more dimensions. In 1979, Yau and Richard Schoen proved Einstein’s positive mass conjecture by applying methods Yau devised. The proof was based on their work with minimal surfaces. A minimal surface is one, in which a small deformation creates a surface with a larger area — soap films are often used as an example of minimal surfaces. The mathematic equations, that must be used to describe minimal surfaces, differ from those, used for most problems in differential geometry. The latter use differential equations to describe curves and surfaces, while mathematicians, working with minimal surfaces, use partial, nonlinear differential equations, which are far more difficult to work with. Schoen and Yau’s proof analyzed how such surfaces behave in space and time, and showed, that Einstein had correctly defined mass. Their methods allowed for the development of a new theory of minimal surfaces in higher dimensions, and they have had an impact on topology, algebraic geometry and general relativity.
In 1987, Yau joined the faculty of Harvard University as a Professor of Mathematics. During 1991 and 1992 (concurrent with his position at Harvard), he served as the Wilson T. S. Wang Distinguished Visiting Professor at the Chinese University of Hong Kong and Special Chair of National Tsing Hua University in Hsinchu, Taiwan.
During his career, Yau has published over 150 scientific papers and served as an editor-in-chief of the Journal of Differential Geometry, as well as editor of both Communications in Mathematical Physics and Letters in Mathematical Physics.
In addition, Shing-Tung is also involved in the activities of Mathematics research institutes in Hong Kong and the mainland People's Republic of China (PRC). Also, he is active in educational reform initiatives for primary and secondary-school Mathematics in China, and his criticisms of the Chinese mainland education system, corruption in the academic world in the Chinese mainland and the quality of mathematical research and education have been widely publicized.
Currently, Yau continues to teach at Harvard University, serving as the William Caspar Graustein Professor of Mathematics.
Shing-Tung Yau has made fundamental contributions to differential geometry, which have influenced a wide range of scientific disciplines, including Astronomy and Theoretical Physics. With Richard Schoen, Yau solved a long-standing question in Albert Einsteins’s theory of relativity by proving, that the sum of the energy in the universe is positive. Their proof provided an important tool for understanding how black holes form.
Also, one of his main contributions was his proof of Calabi conjecture. The theorem was significant not only for pure Mathematics, but also Mathematical Physics, having become the basis for string theory.
Shing-Tung received numerous awards, including the John J. Carty Award for the Advancement of Science in 1981, Oswald Veblen Prize in Geometry in 1981, Fields Medal in 1982, National Medal of Science in 1997 and many others.
Moreover, during his career, Shing-Tung was named an Honorary Professor at different educational establishments, including Fudan University (1983), Hangzhou University (1987), Nankai University (1993), Zhejiang University (1998), the University of Science and Technology of China (1999), Northwest University (July 15, 2009), among others.
(From the beginning, harmonic maps were studied in connect...)
1997
Membership
foreign member
Indian National Science Academy
,
India
2008
foreign member
Lincean Academy
,
Italy
2005
foreign member
Russian Academy of Sciences
,
Russian Federation
2003
foreign member
Chinese Academy of Sciences
,
China
1994
member
National Academy of Science
,
United States
1993
member
American Academy of Arts and Sciences
,
United States
1982
fellow
American Association for the Advancement of Science
,
United States
fellow
American Mathematical Society
,
United States
2012
Connections
Yau married Yu Yun Kuo in 1976. Their marriage produced two children — Isaac and Michael.
Father:
Chen Ying Chiou
Mother:
Yeuk-Lam (Leung) Chiou
child:
Michael Yau
child:
Isaac Yau
Wife:
Yu Yun Kuo
mentor:
Shiing-Shen Chern
colleague:
Richard Schoen
Doctoral student:
Tian Gang
Doctoral student:
Kefeng Liu
References
Impressions of Shing-Tung Yau and His Mathematical World
This volume presents collected impressions of Yau and his mathematical world, written by his friends, students and colleagues from past and present. Together, these impressions paint a vivid portrait of an extraordinary kind of scholar.
in 1982, for "his contributions to partial differential equations, to the Calabi conjecture in algebraic geometry, to the positive mass conjecture of general relativity theory and to real and complex Monge–Ampère equations"
in 1982, for "his contributions to partial differential equations, to the Calabi conjecture in algebraic geometry, to the positive mass conjecture of general relativity theory and to real and complex Monge–Ampère equations"
China International Scientific and Technological Cooperation Award,
China
in 2003, for "his outstanding contribution to PRC in aspects of making progress in sciences and technology, training researchers"
in 2003, for "his outstanding contribution to PRC in aspects of making progress in sciences and technology, training researchers"
Wolf Prize in Mathematics,
Israel
in 2010, for "his work in geometric analysis and mathematical physics"
in 2010, for "his work in geometric analysis and mathematical physics"
Wolf Prize in Mathematics
2010
2010
Marcel Grossmann Award
in 2018, "for the proof of the positivity of total mass in the theory of general relativity and perfecting as well the concept of quasi-local mass, for his proof of the Calabi conjecture, for his continuous inspiring role in the study of black holes physics"
in 2018, "for the proof of the positivity of total mass in the theory of general relativity and perfecting as well the concept of quasi-local mass, for his proof of the Calabi conjecture, for his continuous inspiring role in the study of black holes physics"
