78th  Top University of California, Berkeley alumni 
3rd  Top Zhejiang University faculty 
13rd  Top people by Erd%C5%91s number: #2 
10th  Top National Medal of Science laureates 
ShingTung Yau  

ShingTung Yau at Harvard Law School dining hall


Born  April 4, 1949 Shantou, Guangdong Province, China 
Residence  U.S. 
Fields  Mathematics 
Institutions  Harvard University, Chinese University of Hong Kong Zhejiang University 
Alma mater  Chinese University of Hong Kong (B.A. 1969) UC Berkeley (Ph. D 1971) 
Doctoral advisor  ShiingShen Chern 
Doctoral students  Richard Schoen (Stanford, 1977) HuaiDong Cao (Princeton, 1986) Gang Tian (Harvard, 1988) Lizhen Ji (Northeastern, 1991) Kefeng Liu (Harvard, 1993) 
Notable awards  Fields Medal (1982) Veblen Prize (1981) Crafoord Prize (1994) National Medal of Science (1997) Wolf Prize (2010) 
ShingTung Yau (Chinese: 丘成桐; born April 4, 1949) is a Chinese American mathematician working in differential geometry. He was born in Shantou, Guangdong Province, China into a family of scholars from Jiaoling, Guangdong Province. His work has led to the important CalabiYau manifolds, which are the basic building blocks of the universe, according to String Theory. He developed and put the field of differential equations on manifolds into the mainstream of mathematics, and his work on minimal manifolds has applications to topology and general relativity theory.
Yau has made lasting impacts on both physics and mathematics. CalabiYau manifolds are among the ‘standard toolkit’ for string theorists today. He has been very active in the exciting interface between geometry and theoretical physics. His proof of the positive energy theorem in general relativity finally demonstrated—sixty years after its discovery—that Einstein’s theory is consistent and stable. His proof of the Calabi conjecture allowed physicists—using CalabiYau compactification—to show that string theory is a viable candidate for a unified theory of nature.
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Yau was born in Shantou, Guangdong Province, China with an ancestry in Jiaoling (also in Guangdong) in a family of eight children. When he was only a few months old, his family moved to Yuen Long and then 5 years later to Shatin in New Territory. When Yau was fourteen, his father, a philosophy professor, died.
Yau moved to Hong Kong with his family where, after graduating from Pui Ching Middle School, he studied mathematics at the Chinese University of Hong Kong from 1966 to 1969. Yau went to UC Berkeley in the fall of 1969. At the age of 22, Yau was awarded the Ph.D. degree under the supervision of ShiingShen Chern at Berkeley in two years. He spent a year as a member of the Institute for Advanced Study, Princeton, New Jersey, and two years at the State University of New York at Stony Brook. Then he went to Stanford University.
Since 1987, he has been at Harvard University ^{[1]}, where he has had numerous Ph.D. students. He is also involved in the activities of research institutes in Hong Kong and China. He takes an interest in the state of K12 mathematics education in China, and his criticisms of the Chinese education system, corruption in the academic world in China, and the quality of mathematical research and education, have been widely publicized.
Duong Hong Phong of Columbia University has commented on the wide influence of Yau's research in geometric analysis.^{[2]}
Yau's solution of the Calabi conjecture, concerning the existence of an EinsteinKähler metric, has farreaching consequences. The existence of such a canonical unique metric allows one to give explicit representatives of characteristic classes. CalabiYau manifolds are now fundamental in string theory, where the Calabi conjecture provides an essential piece in the model.
In algebraic geometry, the Calabi conjecture implies the MiyaokaYau inequality on Chern numbers of surfaces, a characterization of the complex projective plane and quotients of the twodimensional complex unit ball, an important class of Shimura varieties.
Yau also made a contribution in the case that the first Chern number c_{1} > 0, and conjectured its relation to the stability in the sense of geometric invariant theory in algebraic geometry. This has motivated the work of Simon Donaldson on scalar curvature and stability. Another important result of DonaldsonUhlenbeckYau is that a holomorphic vector bundle is stable (in the sense of David Mumford) if and only if there exists an HermitianYangMills metric on it. This has many consequences in algebraic geometry, for example, the characterization of certain symmetric spaces, Chern number inequalities for stable bundles, and the restriction of the fundamental groups of a Kähler manifold.
Yau pioneered the method of using minimal surfaces to study geometry and topology. By an analysis of how minimal surfaces behave in spacetime, Yau and Richard Schoen proved the long standing conjecture that the total mass in general relativity is positive.
This theorem implies that flat spacetime is stable, a fundamental issue for the theory of general relativity. Briefly, the positive mass conjecture says that if a threedimensional manifold has positive scalar curvature and is asymptotically flat, then a constant that appears in the asymptotic expansion of the metric is positive. A continuation of the above work gives another result in relativity proved by Yau, an existence theorem for black holes. Yau and Schoen continued their work on manifolds with positive scalar curvature, which led to Schoen's final solution of the Yamabe problem.
Yau and William H. Meeks solved the wellknown question whether the Douglas solution of a minimal disk for an external Jordan curve, the Plateau problem, in three space, is always embedded if the boundary curve is a subset of a convex boundary. They then went on to prove that these embedded minimal surfaces are equivariant for finite group actions. Combining this work with a result of William Thurston, Cameron Gordon assembled a proof of the Smith conjecture: for any cyclic group acting on a sphere, the set of fixed points is not a knotted curve.
Yau and Karen Uhlenbeck proved the existence and uniqueness of HermitianEinstein metrics (or equivalently Hermitian YangMills connections) for stable bundles on any compact Kähler manifold, extending an earlier result of Donaldson for projective algebraic surfaces, and M. S. Narasimhan and C. S. Seshadri for algebraic curves. Both the results and methods of this paper have been influential in parts of both algebraic geometry and string theory. This result is now usually called the DonaldsonUhlenbeckYau Theorem.
Yau and YumTong Siu proved the 1981 Frankel conjecture in complex geometry, stating that any compact positivelycurved Kähler manifold is biholomorphic to complex projective space. An independent proof was given by Shigefumi Mori, using methods of algebraic geometry in positive characteristic.
With Bong Lian and Kefeng Liu, Yau proved mirror formulas conjectured by string theorists. These formulas give the explicit numbers of rational curves of all degrees in a large class of CalabiYau manifolds, in terms of the PicardFuchs equations of the corresponding mirror manifolds.
Yau developed the method of gradient estimates for Harnack's inequalities. This method has been used and refined by him and other people to attack for example, bounds on the heat kernel. Early in 1981, Yau suggested to Richard Hamilton that he use the Ricci flow to realize naturally the canonical decomposition of a threedimensional manifold into pieces, each of which has a geometric structure, in the Thurston program. Hamilton amplified their results, to what is now called the LiYauHamilton inequality for the Ricci flow equations.
Gradient estimates were also used crucially in Yau's joint work with S. Y. Cheng to give a complete proof of the higher dimensional Hermann Minkowski problem and the Dirichlet problem for the real Monge–Ampère equation, and other results on the KählerEinstein metric of bounded pseudoconvex domains.
When Yau was a graduate student, he started to generalize the uniformization theorem of Riemann surfaces to higherdimensional complex Kähler manifolds. For a compact manifold with Positive bisectional curvature, the Frankel conjecture proved by Siu and Yau, and independently by Mori, shows that it is complex projective space. Yau proposed a series of conjectures when the manifold is noncompact, and made contributions towards their solutions. For example, when the bisectional curvature is positive, it must be biholomorphic to C^{n}. Some aspects of work on these conjectures were used in the solution of the Poincaré conjecture by Perelman.
When Yau was working on his thesis about manifolds with nonpositive curvature and their fundamental groups, he realized that it is possible to use harmonic maps to give alternative proofs of some results there. He was aware of the Mostow rigidity theorem for locally symmetric spaces, which was used by him to prove the uniqueness of complex structure of quotients of complex balls. Naturally he proposed that harmonic maps be used to prove rigidity of the complex structure for Kähler manifolds with strongly negative curvature, a program that was successfully carried out by YumTong Siu. This method, the socalled SiuYau method, has been extended to prove strong and superrigidities of many locally symmetric spaces.
Minimal submanifolds have been used by Yau in the solutions of the Positive Mass Conjecture, the Smith conjecture, the Frankel conjecture, and else. Many people others have since applied minimal surfaces to other problems. Mikhail Gromov's introduction of pseudoholomorphic curves in symplectic geometry has also had an important impact on that field.
Yau has compiled an influential set of open problems in geometry.
One of Yau’s problems is about bounded harmonic functions, and harmonic functions on noncompact manifolds of polynomial growth. After proving nonexistence of bounded harmonic functions on manifolds with positive curvatures, he turned around and proposed the Dirichlet problem at infinity for bounded harmonic functions on negatively curved manifolds, and then proceeded to harmonic functions of polynomial growth. Dennis Sullivan tells a story about Yau's geometric intuition, and how it led him to reject an analytical proof of Sullivan's. Michael Anderson independently found the same result about bounded harmonic function on simply connected negatively curved manifolds using a geometric convexity construction.^{[2]}
Again otivated by Mostow's strong rigidity theorem, Yau called for a notion of rank for general manifolds extending the one for locally symmetric spaces, and asked for rigidity properties for higher rank metrics. Advances in this direction have been made by Ballmann, Brin and Eberlein in their work on nonpositive curved manifolds, Gromov's and Eberlein's metric rigidity theorems for higher rank locally symmetric spaces and the classification of closed higher rank manifolds of nonpositive curvature by Ballmann and BurnsSpatzier. This leaves rank 1 manifolds of nonpositive curvature as the focus of research. They behave more like manifolds of negative curvature, but remain poorly understood in many regards.
It is known that if a complex manifold has a Kähler–Einstein metric, then its tangent bundle is stable. Yau realized early in 1980s that the existence of special metrics on Kähler manifolds is equivalent to the stability of the manifolds. Various people such as S.Donaldson, a Fields medalist, have made progress to understand such a relation.
He has collaborated with string theorists including Strominger, Vafa and Witten, and as postdoctorals from theoretical physics with B. Greene, E. Zaslow and A. Klemm . The StromingerYauZaslow program is to construct explicitly mirror manifolds. David Gieseker wrote of the seminal role of the Calabi conjecture in relating string theory with algebraic geometry, in particular for the developments of the SYZ program, mirror conjecture and YauZaslow conjecture.^{[2]}
Yau was born in China but grew up in Hong Kong. After the door of China was opened to the west in the late 1970s, Yau revisited China in 1979 on the invitation of Hua Luogeng. To help develop Chinese mathematics, Yau started by educating students from China, then establishing mathematics research institutes and centers, organizing conferences at all levels, initiating outreach programs, and raising private funds for these purposes. John Coates has commented on Yau's success as fundraiser.^{[2]} The first of Yau's initiatives is The Institute of Mathematical Sciences at The Chinese University of Hong Kong in 1993. The goal is to “organize activities related to a broad variety of fields including both pure and Applied mathematics, scientific computation, image processing, mathematical physics and statistics. The emphasis is on interaction and linkages with the physical sciences, engineering, industry and commerce.”
The second one is the Morningside Center of Mathematics in Beijing, established in 1996. Part of the money for the building and regular operations was raised by Yau from the Morningside Foundation in Hong Kong. Yau proposed organizing the International Congress of Chinese Mathematicians, now held every three years. The first congress was held at the Morningside Center from December 12 to 18, 1998. The third is the Center of Mathematical Sciences at Zhejiang University. It was established in 2002. Yau is the director of all these three math institutes and visits them on a regular basis.
Yau went came to Taiwan to attend a conference in 1985 thematics. In 1990, he was invited by Dr. C.S. Liu, then the President of National Tsinghua University, to visit the university for a year. A few years later, he convinced Liu, by then the chairman of National Science Council, to create the National Center of Theoretical Sciences (NCTS), which was established at Hsinchu in 1998. He was the chairman of the Advisory Board of the NCTS until 2005 and was followed by H. T. Yau of Harvard University.
His classmate at college Y.C.Siu speaks of Yau as an ambassador of mathematics.^{[2]} In Hong Kong, with the support of Ronnie Chan, Yau set up the Hang Lung Award for high school students. He has also organized and participated in meetings for high school and college students, for example, the panel discussions Why Math? Ask Masters! in Hangzhou, July 2004, and The Wonder of Mathematics in Hong Kong, December 2004. Yau organized the JDG conference surveying developments in geometry and related fields, and the annual Current development of mathematics conference. Yau also coinitiated a series of books on popular mathematics, "Mathematics and Mathematical People".
Yau has received numerous honors and awards in his life^{[3]}, including:
In August 2006, a New Yorker article on the Poincaré conjecture, "Manifold Destiny", discussed Yau's relationship to that famous problem.^{[15]} Yau claims this article is defamatory, and in September 2006 he established a public relations website, managed by the PR firm Spector and Associates, to dispute points in it and demand an apology. By April 5, 2007, fifteen mathematics professors, including two quoted in the New Yorker article, had posted letters of support on Yau's website.^{[16]} The New Yorker reportedly stands by its article.^{[17]}
On October 17, 2006, a more sympathetic profile of Yau appeared, along with photographs from different stages of his life, in the New York Times.^{[18]} After recounting Yau's humble beginnings and rise to academic stardom, it devotes about half its length to the Perelman affair. The article acknowledges that Yau's egotism and highprofile activities, including criticism of Chinese academia,^{[19]} have alienated some of his colleagues and that Yau's promotion of the CaoZhu paper "annoyed many mathematicians, who felt that Dr. Yau had slighted Dr. Perelman." In contrast to the "Manifold Destiny" article, it paints Yau as ultimately more concerned with the development of mathematics than with his reputation. In regards to the Perelman affair, the article focuses on Yau's position, which is that Perelman's proof was not understood by all, and he "had a duty to dig out the truth of the proof."


