Shing-Tung Yau

YauS.-T. YauYau, Shing-TungS. T. YauS.T. YauShing–Tung YauYau Shing Tung丘成桐
Shing-Tung Yau (born April 4, 1949) is a Chinese-born naturalized American mathematician who was awarded the Fields Medal in 1982.wikipedia
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Pui Ching Middle School (Hong Kong)

Pui Ching Middle School
After graduating from Pui Ching Middle School, he studied mathematics at the Chinese University of Hong Kong from 1966 to 1969.

String theory

string theoriststringstring theories
Calabi–Yau manifolds are now fundamental in string theory, where the Calabi conjecture provides an essential piece in the model.
It is named after mathematicians Eugenio Calabi and Shing-Tung Yau.

Calabi–Yau manifold

Calabi–YauCalabi-Yau manifoldCalabi-Yau manifolds
Calabi–Yau manifolds are now fundamental in string theory, where the Calabi conjecture provides an essential piece in the model. Calabi–Yau manifolds are part of the standard toolkit for string theorists today.
The motivational definition given by Shing-Tung Yau is of a compact Kähler manifold with a vanishing first Chern class, that is, also Ricci flat.

Fields Medal

Fields MedalistFields Prize in MathematicsFields Medalists
Shing-Tung Yau (born April 4, 1949) is a Chinese-born naturalized American mathematician who was awarded the Fields Medal in 1982.

Scalar curvature

Ricci scalarcurvaturecurvature scalar
This has motivated the work of Simon Donaldson on scalar curvature and stability.
One such result is the positive mass theorem of Schoen, Yau and Witten.

Shiing-Shen Chern

S. S. ChernChernChen Xingshen
Yau left for the University of California, Berkeley in the fall of 1969, where he received his Ph.D. in mathematics two years later, under the supervision of Shiing-Shen Chern.
Shing-Tung Yau was one of his PhD students during this period, and he later won the Fields Medal.

Stephen Shing-Toung Yau

Yau, Stephen Shing-Toung
He has seven siblings, including Stephen Shing-Toung Yau, also a mathematician.
He is the younger brother of Fields Medalist Shing-Tung Yau.

Richard Schoen

Richard M. SchoenRichard Melvin SchoenRick Schoen
By analyzing how minimal surfaces behave in space-time, Yau and Richard Schoen proved the long-standing conjecture that the total mass in general relativity is positive.
In 1979, together with his former doctoral supervisor, Shing-Tung Yau, he proved the fundamental positive energy theorem in general relativity.

Calabi conjecture

Calabi–Yau theoremComplex Monge–Ampère equation
His proof of the Calabi conjecture allowed physicists to show, using Calabi–Yau compactification, that string theory is a viable candidate for a unified theory of nature.
This was proved for negative first Chern classes independently by Thierry Aubin and Shing-Tung Yau in 1976.

Kefeng Liu

Liu, Kefeng
With Bong Lian and Kefeng Liu, Yau proved the mirror formulas conjectured by string theorists in a paper posted in December 1997.
Liu then went to study in the United States, obtaining a Ph.D. from Harvard University in 1993 under Shing-Tung Yau.

Institute for Advanced Study

Institute for Advanced StudiesInstitute for Advanced Study, PrincetonIAS
He spent a year as a member of the Institute for Advanced Study at Princeton before joining Stony Brook University in 1972 as an assistant professor.
Among them are James Waddell Alexander II, Michael Atiyah, Enrico Bombieri, Shiing-Shen Chern, Pierre Deligne, Freeman J. Dyson, Albert Einstein, Clifford Geertz, Kurt Gödel, Albert Hirschman, George F. Kennan, Tsung-Dao Lee, J. Robert Oppenheimer, Erwin Panofsky, Atle Selberg, John von Neumann, André Weil, Hermann Weyl, Frank Wilczek, Edward Witten, Chen-Ning Yang and Shing-Tung Yau.

Geometric analysis

Geometricgeometrical analysisglobal analysis
Yau's work is mainly in differential geometry, especially in geometric analysis.
In the 1980s fundamental contributions by Karen Uhlenbeck, Clifford Taubes, Shing-Tung Yau, Richard Schoen, and Richard Hamilton launched a particularly exciting and productive era of geometric analysis that continues to this day.

Harvard University

HarvardHarvard CollegeUniversity of Harvard
He is currently the William Caspar Graustein Professor of Mathematics at Harvard University.
Harvard's faculty includes scholars such as biologist E. O. Wilson, psychologist Steven Pinker, physicists Lisa Randall and Roy Glauber, chemists Elias Corey, Dudley R. Herschbach and George M. Whitesides, computer scientists Michael O. Rabin and Leslie Valiant, Shakespeare scholar Stephen Greenblatt, writer Louis Menand, critic Helen Vendler, historians Henry Louis Gates, Jr. and Niall Ferguson, economists Amartya Sen, N. Gregory Mankiw, Robert Barro, Stephen A. Marglin, Don M. Wilson III and Martin Feldstein, political philosophers Harvey Mansfield, Baroness Shirley Williams and Michael Sandel, Fields Medalist mathematician Shing-Tung Yau, political scientists Robert Putnam, Joseph Nye, and Stanley Hoffmann, scholar/composers Robert Levin and Bernard Rands, astrophysicist Alyssa A. Goodman, and legal scholars Alan Dershowitz and Lawrence Lessig.

Chinese University of Hong Kong

The Chinese University of Hong KongCUHKChinese University
After graduating from Pui Ching Middle School, he studied mathematics at the Chinese University of Hong Kong from 1966 to 1969.
Other notable faculty members include mathematician Shing-Tung Yau, laureate of the Fields Medal and the Veblen Prize, and computational theorist Andrew Yao, laureate of the Turing Award, and surgeon James Ware.

Positive energy theorem

positive mass conjecturepositive mass theorem
His proof of the positive energy theorem in general relativity demonstrated—sixty years after its discovery—that Einstein's theory is consistent and stable.
The original proof of the theorem for ADM mass was provided by Richard Schoen and Shing-Tung Yau in 1979 using variational methods.

Mirror symmetry (string theory)

mirror symmetrymirror manifoldmirror conjecture
These formulas give the explicit numbers of rational curves of all degrees in a large class of Calabi–Yau manifolds, in terms of the Picard–Fuchs equations of the corresponding mirror manifolds.
Major approaches to mirror symmetry include the homological mirror symmetry program of Maxim Kontsevich and the SYZ conjecture of Andrew Strominger, Shing-Tung Yau, and Eric Zaslow.

Simon Donaldson

DonaldsonSimon Kirwan DonaldsonSimon K. Donaldson
This has motivated the work of Simon Donaldson on scalar curvature and stability.
It had been one of the most actively investigated topics in geometry since its proposal in the 1980s by Shing-Tung Yau after he proved the Calabi conjecture.

Karen Uhlenbeck

Karen K. UhlenbeckUhlenbeck, Karen
Yau and Karen Uhlenbeck proved the existence and uniqueness of Hermitian–Einstein metrics (or equivalently Hermitian Yang–Mills 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.
A wider survey of her contributions to the field of calculus of variations was published by Simon Donaldson in the March 2019 issue of Notices of the American Mathematical Society; Donaldson describes the work of Uhlenbeck, along with Shing-Tung Yau, Richard Schoen and several others, as developing a... "...whole circle of ideas and techniques involving the dimension of singular sets, monotonicity, 'small energy' results, tangent cones, etc. [that] has had a wide-ranging impact in many branches of differential geometry over the past few decades and forms the focus of much current research activity."

Smith conjecture

Combining this work with a result by 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.
The proof of the general case was described by and depended on several major advances in 3-manifold theory, in particular the work of William Thurston on hyperbolic structures on 3-manifolds, and results by William Meeks and Shing-Tung Yau on minimal surfaces in 3-manifolds, with some additional help from Bass, Cameron Gordon, Peter Shalen, and Rick Litherland.

Edward Witten

Ed WittenWittenE. Witten
He has collaborated with string theorists including Strominger, Vafa and Witten, and as post-doctorals from theoretical physics with Brian Greene, Eric Zaslow and A. Klemm.
While the original proof of this result due to Richard Schoen and Shing-Tung Yau used variational methods, Witten's proof used ideas from supergravity theory to simplify the argument.

André Neves

Andre NevesAndré Arroja NevesNeves, André
Kei Irie, Fernando Codá Marques, and André Neves solved this problem in the generic case and later Antoine Song claimed it in full generality.
In 2017, jointly with Kei Irie and Fernando Codá Marques, they solved Yau's conjecture (formulated by Shing-Tung Yau in 1982) in the generic case.

Fernando Codá Marques

Fernando C. MarquesMarques, Fernando Codá
Kei Irie, Fernando Codá Marques, and André Neves solved this problem in the generic case and later Antoine Song claimed it in full generality.
In December 2017, in cooperation with Kei Irie and André Neves, he solved Yau's conjecture (Yau, 1982) in the generic case.

Almgren–Pitts min-max theory

Almgren–Pitts min-max theory of minimal surfaces
At the time it was known from Almgren–Pitts min-max theory the existence of at least one minimal surface.
It has played roles in the solutions to a number of conjectures in geometry and topology found by Almgren and Pitts themselves and also by other mathematicians, such as Mikhail Gromov, Richard Schoen, Shing-Tung Yau, Fernando Codá Marques, André Neves, Ian Agol, among others.