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Shing-Tung Yau
Shing-Tung Yau (; ; born April 4, 1949) is a Chinese-American mathematician and the William Caspar Graustein Professor of Mathematics at Harvard University. In April 2022, Yau announced retirement from Harvard to become Chair Professor of mathematics at Tsinghua University. Yau was born in Shantou, China, moved to Hong Kong at a young age, and to the United States in 1969. He was awarded the Fields Medal in 1982, in recognition of his contributions to partial differential equations, the Calabi conjecture, the positive energy theorem, and the Monge–Ampère equation. Yau is considered one of the major contributors to the development of modern differential geometry and geometric analysis. The impact of Yau's work can be seen in the mathematical and physical fields of differential geometry, partial differential equations, convex geometry, algebraic geometry, enumerative geometry, mirror symmetry, general relativity, and string theory, while his work has also touched upon applied ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stephen Shing-Toung Yau
Stephen Shing-Toung Yau (; born 1952) is a Chinese-American mathematician. He is a Distinguished Professor Emeritus at the University of Illinois at Chicago, and currently teaches at Tsinghua University. He is a Fellow of the Institute of Electrical and Electronics Engineers and the American Mathematical Society. Biography Shing-Toung Yau was born in 1952 in British Hong Kong, with his ancestral home in Jiaoling County, Guangdong, China. He is the younger brother of Fields Medalist Shing-Tung Yau. After graduating from the Chinese University of Hong Kong, he studied mathematics at the State University of New York at Stony Brook, where he learnt after Henry Laufer and earned his M.A. in 1974 and Ph.D. in 1976. He was a member of Princeton University's Institute for Advanced Study from 1976 to 1977 and from 1981 to 1982, and was a Benjamin Pierce Assistant Professor at Harvard University from 1977 to 1980. He subsequently taught at the University of Illinois at Chicago for more ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mark Stern
Mark Stern is an American mathematician whose focus has been on geometric analysis, Yang–Mills theory, Hodge theory, and string theory. One of Stern's foremost accomplishments is his proof (joint with Leslie D. Saper) of the Zucker conjecture concerning locally symmetric spaces. Since about 2000, Stern has focused on geometric problems arising in physics, ranging from harmonic theory to string theory and supersymmetry. Stern has taught at Duke University since 1985, and was promoted to professor in 1992. He has been the mathematics department chairman but has focused primarily on research and teaching, with major grant support from the National Science Foundation. At Duke, he teaches such courses as multivariable calculus. Since 2010, Stern has spoken to advanced math audiences at the Newton Institute, CUNY Graduate Center, U.C. Irvine, Johns Hopkins, the University of Maryland, and multiple academic groups. Academic background Prior to Duke, Stern was a member of the Institu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bogomolov–Miyaoka–Yau Inequality
In mathematics, the Bogomolov–Miyaoka–Yau inequality is the inequality : c_1^2 \le 3 c_2 between Chern numbers of compact complex surfaces of general type. Its major interest is the way it restricts the possible topological types of the underlying real 4-manifold. It was proved independently by and , after and proved weaker versions with the constant 3 replaced by 8 and 4. Armand Borel and Friedrich Hirzebruch showed that the inequality is best possible by finding infinitely many cases where equality holds. The inequality is false in positive characteristic: and gave examples of surfaces in characteristic ''p'', such as generalized Raynaud surfaces, for which it fails. Formulation of the inequality The conventional formulation of the Bogomolov–Miyaoka–Yau inequality is as follows. Let ''X'' be a compact complex surface of general type, and let ''c''1 = ''c''1(''X'') and ''c''2 = ''c''2(''X'') be the first and second Chern class of the complex tangent bund ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximal Surface
In the mathematical field of differential geometry, a maximal surface is a certain kind of submanifold of a Lorentzian manifold. Precisely, given a Lorentzian manifold , a maximal surface is a spacelike submanifold of whose mean curvature is zero. As such, maximal surfaces in Lorentzian geometry are directly analogous to minimal surfaces in Riemannian geometry. The difference in terminology between the two settings has to do with the fact that small regions in maximal surfaces are local maximizers of the area functional, while small regions in minimal surfaces are local minimizers of the area functional. In 1976, Shiu-Yuen Cheng and Shing-Tung Yau resolved the "Bernstein problem" for maximal hypersurfaces of Minkowski space which are properly embedded, showing that any such hypersurface is a plane. This was part of the body of work for which Yau was awarded the Fields medal in 1982. The Bernstein problem was originally posed by Eugenio Calabi in 1970, who proved some special cases o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernstein's Problem
In differential geometry, Bernstein's problem is as follows: if the graph of a function on R''n''−1 is a minimal surface in R''n'', does this imply that the function is linear? This is true in dimensions ''n'' at most 8, but false in dimensions ''n'' at least 9. The problem is named for Sergei Natanovich Bernstein Sergei Natanovich Bernstein (russian: Серге́й Ната́нович Бернште́йн, sometimes Romanized as ; 5 March 1880 – 26 October 1968) was a Ukrainian and Russian mathematician of Jewish origin known for contributions to parti ... who solved the case ''n'' = 3 in 1914. Statement Suppose that ''f'' is a function of ''n'' − 1 real variables. The graph of ''f'' is a surface in R''n'', and the condition that this is a minimal surface is that ''f'' satisfies the minimal surface equation :\sum_^ \frac\frac = 0 Bernstein's problem asks whether an ''entire'' function (a function defined throughout R''n''−1 ) t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimal Surface
In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of area-minimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film, which is a minimal surface whose boundary is the wire frame. However, the term is used for more general surfaces that may self-intersect or do not have constraints. For a given constraint there may also exist several minimal surfaces with different areas (for example, see minimal surface of revolution): the standard definitions only relate to a local optimum, not a global optimum. Definitions Minimal surfaces can be defined in several equivalent ways in R3. The fact that they are equivalent serves to demonstrate how minimal surface theory lies at the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plateau Problem
In mathematics, Plateau's problem is to show the existence of a minimal surface with a given boundary, a problem raised by Joseph-Louis Lagrange in 1760. However, it is named after Joseph Plateau who experimented with soap films. The problem is considered part of the calculus of variations. The existence and regularity problems are part of geometric measure theory. History Various specialized forms of the problem were solved, but it was only in 1930 that general solutions were found in the context of mappings (immersions) independently by Jesse Douglas and Tibor Radó. Their methods were quite different; Radó's work built on the previous work of René Garnier and held only for rectifiable simple closed curves, whereas Douglas used completely new ideas with his result holding for an arbitrary simple closed curve. Both relied on setting up minimization problems; Douglas minimized the now-named Douglas integral while Radó minimized the "energy". Douglas went on to be awarded ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chiu-Chu Melissa Liu
Chiu-Chu Melissa Liu (; born December 15, 1974) is a Taiwanese mathematician who works as a professor of mathematics at Columbia University. Her research interests include algebraic geometry and symplectic geometry.Curriculum vitae , retrieved 2015-01-12. Education Liu graduated from in 1996, and earned her Ph.D. in 2002 from under the supervision of |
Mu-Tao Wang
Mu-Tao Wang () is a Taiwanese mathematician and current Professor of Mathematics at Columbia University. Education He entered National Taiwan University in 1984, originally for international business, but after a year he switched to mathematics. He earned his BS in Mathematics at National Taiwan University in 1988 and his MS from the same institution in 1992. He received a PhD in Mathematics in 1998 from Harvard University with a thesis entitled ''"Generalized harmonic maps and representations of discrete groups."'' His thesis adviser at Harvard was Chinese Fields Medalist and differential geometer Shing-Tung Yau. Career Wang joined the Columbia faculty as an assistant professor in 2001, and was appointed full professor in 2009. Before joining the faculty at Columbia, Wang was Szego Assistant Professor at Stanford University. He was a Sloan Research Fellow from 2003–2005. In 2007, he was named a Kavli Fellow of the National Academy of Sciences and was awarded the Chern Prize. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kefeng Liu
Kefeng Liu (Chinese: 刘克峰; born 12 December 1965), is a Chinese-American mathematician who is known for his contributions to geometric analysis, particularly the geometry, topology and analysis of moduli spaces of Riemann surfaces and Calabi–Yau manifolds. He is a professor of mathematics at University of California, Los Angeles, as well as the executive director of the Center of Mathematical Sciences at Zhejiang University. He is best known for his collaboration with Bong Lian and Shing-Tung Yau in which they establish some enumerative geometry conjectures motivated by mirror symmetry. Biography Liu was born in Kaifeng, Henan province, China. In 1985, Liu received his B.A. in mathematics from the Department of Mathematics of Peking University in Beijing. In 1988, Liu obtained his M.A. from the Institute of Mathematics of the Chinese Academy of Sciences (CAS) in Beijing. Liu then went to study in the United States, obtaining a Ph.D. from Harvard University in 1993 under ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lizhen Ji
Lizhen Ji (Chinese: 季理真; born 1964), is a Chinese-American mathematician. He is a professor of mathematics at the University of Michigan, Ann Arbor. Biography April 1964, Ji was born in Wenzhou, Zhejiang Province, China. Ji graduated BS from Hangzhou University (previous and current Zhejiang University) in Hangzhou in 1984. From 1984 to 1985, Ji was a master student at the Department of Mathematics of Hangzhou University. Ji went to United States to continue his study in 1985, and in 1987 Ji obtained MS from the Department of Mathematics of the University of California, San Diego. In 1991, Ji obtained PhD from the Northeastern University (doctoral advisors: R. Mark Goresky and Shing-Tung Yau). From 1991 to 1994, Ji was C.L.E. Moore instructor at the Department of Mathematics of MIT. From 1994 to 1995, Ji was a member of the Institute for Advanced Study School of Mathematics in Princeton, New Jersey. From 1995 to 1999, Ji was an assistant professor at the Department of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wanxiong Shi
Wanxiong Shi (; 6 October 1963 - 30 September 2021) was a Chinese mathematician. He was known for his fundamental work in the theory of Ricci flow. Education Shi was a native of Quanzhou, Fujian. In 1978, Shi graduated from Quanzhou No. 5 Middle School, and entered the University of Science and Technology of China. Shi earned his bachelor's degree in mathematics in 1982, then he went to the Institute of Mathematics of Chinese Academy of Sciences and obtained his master's degree in mathematics in 1985 under the guidance of Lu Qikeng () and Zhong Jiaqing (). Then Shi was recruited by Shing-Tung Yau to study under him at the University of California, San Diego. In 1987, Shi followed Yau to Harvard University and obtained his Ph.D. there in 1990. Since Shi was stronger in geometric analysis than other Chinese students, having an impressive ability to carry out highly technical arguments, he was assigned by Yau to investigate Ricci flow in the challenging case of noncompact manifo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
