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Chern Song
Shiing-Shen Chern (; , ; October 28, 1911 – December 3, 2004) was a Chinese-American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geometry" and is widely regarded as a leader in geometry and one of the greatest mathematicians of the twentieth century, winning numerous awards and recognition including the Wolf Prize and the inaugural Shaw Prize. In memory of Shiing-Shen Chern, the International Mathematical Union established the Chern Medal in 2010 to recognize "an individual whose accomplishments warrant the highest level of recognition for outstanding achievements in the field of mathematics". Chern worked at the Institute for Advanced Study (1943–45), spent about a decade at the University of Chicago (1949-1960), and then moved to University of California, Berkeley, where he co-founded the Mathematical Sciences Research Institute in 1982 and was the institute's foun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chen (surname)
Chen () () is a common Chinese-language surname and one of the most common surnames in Asia. It is the most common surname in Taiwan (2010) and Singapore (2000). Chen is also the most common family name in Guangdong, Zhejiang, Fujian, Macau, and Hong Kong. It is the most common surname in Xiamen, the ancestral hometown of many overseas Hoklo. Chen was listed 10th in the ''Hundred Family Surnames'' poem, in the verse 馮陳褚衛 (Feng Chen Chu Wei). In Cantonese, it is usually romanized as Chan (as in Jackie Chan), most widely used by those from Hong Kong. Chan is also widely used in Macao and Malaysia. It is also sometimes spelled Chun. In many Southern Min dialects (including dialects of Hainan, Fujian, and Taiwan), the name is pronounced Tan, while in Teochew, it is pronounced Tang. In Hakka and Taishanese, the name is spelled Chin. In Wu it is pronounced Zen or Tchen. In Vietnam, this surname is written as Trần (in Quốc Ngữ) and is 2nd most common. In Thailand, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Francis Pohl
William Francis Pohl (16 September 1937 – 9 December 1988) was an American mathematician, specializing in differential geometry and known for the Clifton–Pohl torus. Pohl received from the University of Chicago his B.A in 1957 and his M.A.1958. He completed his Ph.D. at Berkeley in 1961 under the direction of Shiing-Shen Chern with dissertation ''Differential Geometry of Higher Order''. His dissertation was published in 1962 in the journal ''Topology'' and has received over 120 citations in the mathematical literature. He was a member of the mathematics faculty at the University of Minnesota from September 1964 until his untimely death. Pohl engaged in a famous controversy arguing against Francis Crick Francis Harry Compton Crick (8 June 1916 – 28 July 2004) was an English molecular biologist, biophysicist, and neuroscientist. He, James Watson, Rosalind Franklin, and Maurice Wilkins played crucial roles in deciphering the helical struc ... but, in view of additiona ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chern–Simons Form
In mathematics, the Chern–Simons forms are certain secondary characteristic classes. The theory is named for Shiing-Shen Chern and James Harris Simons, co-authors of a 1974 paper entitled "Characteristic Forms and Geometric Invariants," from which the theory arose. Definition Given a manifold and a Lie algebra valued 1-form \mathbf over it, we can define a family of ''p''-forms: In one dimension, the Chern–Simons 1-form is given by :\operatorname \mathbf In three dimensions, the Chern–Simons 3-form is given by :\operatorname \left \mathbf \wedge \mathbf-\frac \mathbf \wedge \mathbf \wedge \mathbf \right= \operatorname \left d\mathbf \wedge \mathbf + \frac \mathbf \wedge \mathbf \wedge \mathbf\right In five dimensions, the Chern–Simons 5-form is given by : \begin & \operatorname \left \mathbf\wedge\mathbf \wedge \mathbf-\frac \mathbf \wedge\mathbf\wedge\mathbf\wedge\mathbf +\frac \mathbf \wedge \mathbf \wedge \mathbf \wedge \mathbf \wedge\mathbf \right\\ pt= & \oper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chern–Simons Theory
The Chern–Simons theory is a 3-dimensional topological quantum field theory of Schwarz type developed by Edward Witten. It was discovered first by mathematical physicist Albert Schwarz. It is named after mathematicians Shiing-Shen Chern and James Harris Simons, who introduced the Chern–Simons 3-form. In the Chern–Simons theory, the action is proportional to the integral of the Chern–Simons 3-form. In condensed-matter physics, Chern–Simons theory describes the topological order in fractional quantum Hall effect states. In mathematics, it has been used to calculate knot invariants and three-manifold invariants such as the Jones polynomial. Particularly, Chern–Simons theory is specified by a choice of simple Lie group G known as the gauge group of the theory and also a number referred to as the ''level'' of the theory, which is a constant that multiplies the action. The action is gauge dependent, however the partition function of the quantum theory is well-defined wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chern–Gauss–Bonnet Theorem
In mathematics, the Chern theorem (or the Chern–Gauss–Bonnet theorem after Shiing-Shen Chern, Carl Friedrich Gauss, and Pierre Ossian Bonnet) states that the Euler–Poincaré characteristic (a topological invariant defined as the alternating sum of the Betti numbers of a topological space) of a closed even-dimensional Riemannian manifold is equal to the integral of a certain polynomial (the Euler class) of its curvature form (an analytical invariant). It is a highly non-trivial generalization of the classic Gauss–Bonnet theorem (for 2-dimensional manifolds / surfaces) to higher even-dimensional Riemannian manifolds. In 1943, Carl B. Allendoerfer and André Weil proved a special case for extrinsic manifolds. In a classic paper published in 1944, Shiing-Shen Chern proved the theorem in full generality connecting global topology with local geometry. Riemann–Roch and Atiyah–Singer are other generalizations of the Gauss–Bonnet theorem. Statement One useful form o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chern Class
In mathematics, in particular in algebraic topology, differential geometry and algebraic geometry, the Chern classes are characteristic classes associated with complex vector bundles. They have since found applications in physics, Calabi–Yau manifolds, string theory, Chern–Simons theory, knot theory, Gromov–Witten invariants, topological quantum field theory, the Chern theorem etc. Chern classes were introduced by . Geometric approach Basic idea and motivation Chern classes are characteristic classes. They are topological invariants associated with vector bundles on a smooth manifold. The question of whether two ostensibly different vector bundles are the same can be quite hard to answer. The Chern classes provide a simple test: if the Chern classes of a pair of vector bundles do not agree, then the vector bundles are different. The converse, however, is not true. In topology, differential geometry, and algebraic geometry, it is often important to count how many l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Wai-Kwong Li
Peter Wai-Kwong Li (born 18 April 1952) is a mathematician whose research interests include differential geometry and partial differential equations, in particular geometric analysis. After undergraduate work at California State University, Fresno, he received his Ph.D. at University of California, Berkeley under Shiing-Shen Chern in 1979. Presently he is Professor Emeritus at University of California, Irvine, where he has been located since 1991. His most notable work includes the discovery of the Li–Yau differential Harnack inequalities, and the proof of the Willmore conjecture in the case of non-embedded surfaces, both done in collaboration with Shing-Tung Yau. He is an expert on the subject of function theory on complete Riemannian manifolds. He has been the recipient of a Guggenheim Fellowship in 1989 and a Sloan Research Fellowship. In 2002, he was an invited speaker in the Differential Geometry section of the International Congress of Mathematicians in Beijing, where he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shiu-Yuen Cheng
Shiu-Yuen Cheng (鄭紹遠) is a Hong Kong mathematician. He is currently the Chair Professor of Mathematics at the Hong Kong University of Science and Technology. Cheng received his Ph.D. in 1974, under the supervision of Shiing-Shen Chern, from University of California at Berkeley. Cheng then spent some years as a post-doctoral fellow and assistant professor at Princeton University and the State University of New York at Stony Brook. Then he became a full professor at University of California at Los Angeles. Cheng chaired the Mathematics departments of both the Chinese University of Hong Kong and the Hong Kong University of Science and Technology in the 1990s. In 2004, he became the Dean of Science at HKUST. In 2012, he became a fellow of the American Mathematical Society. He is well known for contributions to differential geometry and partial differential equations, including Cheng's eigenvalue comparison theorem, Cheng's maximal diameter theorem, and a number of works with Sh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Joseph A
Joseph is a common male given name, derived from the Hebrew Yosef (יוֹסֵף). "Joseph" is used, along with "Josef", mostly in English, French and partially German languages. This spelling is also found as a variant in the languages of the modern-day Nordic countries. In Portuguese and Spanish, the name is "José". In Arabic, including in the Quran, the name is spelled '' Yūsuf''. In Persian, the name is "Yousef". The name has enjoyed significant popularity in its many forms in numerous countries, and ''Joseph'' was one of the two names, along with ''Robert'', to have remained in the top 10 boys' names list in the US from 1925 to 1972. It is especially common in contemporary Israel, as either "Yossi" or "Yossef", and in Italy, where the name "Giuseppe" was the most common male name in the 20th century. In the first century CE, Joseph was the second most popular male name for Palestine Jews. In the Book of Genesis Joseph is Jacob's eleventh son and Rachel's first son, and k ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alan Weinstein
Alan David Weinstein (17 June, 1943, New York City) is a professor of mathematics at the University of California, Berkeley, working in the field of differential geometry, and especially in Poisson geometry. Education and career Weinstein obtained a bachelor's degree at the Massachusetts Institute of Technology in 1964. He received a PhD at University of California, Berkeley in 1967 under the direction of Shiing-Shen Chern. His dissertation was entitled "''The cut locus and conjugate locus of a Riemannian manifold''". He worked then at MIT on 1967 (as Moore instructor) and at Bonn University in 1968/69. In 1969 he became assistant professor at Berkeley, and from 1976 he is full professor. During 1978/79 he was visiting professor at Rice University. Weinstein was awarded in 1971 a Sloan Research Fellowship and in 1985 a Guggenheim Fellowship. In 1978 he was invited speaker at the International Congress of Mathematicians in Helsinki. In 1992 he was elected Fellow of the Ame ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sidney Martin Webster
Sidney Martin Webster (born 12 November 1945 in Danville, Illinois) is an American mathematician, specializing in multidimensional complex analysis. After military service, Webster attended the University of California, Berkeley as an undergraduate and then as a graduate student, receiving a PhD in 1975 under the supervision of Shiing-Shen Chern with thesis ''Real hypersurfaces in complex space''. Webster was a faculty member at Princeton University from 1975 to 1980 and at the University of Minnesota from 1980 to 1989. In 1989 he became a full professor at the University of Chicago. He has held visiting positions at the University of Wuppertal, Rice University, and ETH Zurich. Webster was a Sloan Fellow for the academic year 1979–1980. In 1994 in Zurich he was an invited speaker of the International Congress of Mathematicians. In 2001 he received, jointly with László Lempert, the Stefan Bergman Prize from the American Mathematical Society. In 2012 Webster was elected a Fellow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
