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Chern
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 fou ... [...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 ho ... [...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-define ... [...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 ... [...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= & \ope ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nankai University
Nankai University (NKU or Nankai; ) is a national public research university located in Tianjin, China. It is a prestigious Chinese state Class A Double First Class University approved by the central government of China, and a member of the former project 985 and project 211 group of universities. It was founded in 1919, by educators Yan Xiu and Zhang Boling. During the Sino-Japanese War (1937–1945), Nankai University, Peking University and Tsinghua University merged and formed the National Changsha Provisional University, which later moved to Kunming and was renamed the National Southwestern Associated University (西南联大). On December 25, 2000, the State Ministry of Education signed an agreement with Tianjin Municipal Government to jointly establish and develop Nankai University. Since then, Nankai has been listed among the universities to receive priority development investments from the Chinese government in the twenty-first century. Nankai has long been ... [...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 com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Brown Gardner
Robert Brown (Robby) Gardner (February 27, 1939 – May 5, 1998) was an American mathematician who worked on differential geometry, a field in which he obtained several novel results. He was the author and co-author of three influential books, produced more than fifty papers, eighteen masters students and thirteen Ph.D students. His 1991 book, ''Exterior Differential Systems'', coauthored with R. Bryant, S. S. Chern, H. Goldschmidt, and P. Griffiths, is the standard reference for the subject. Robert Bryant, Duke University's Professor of Mathematics and the president of the American Mathematical Society (2015-2017) was a student of his. He is better known in the United States for his improvements and popularization of the methods of Élie Cartan (most notably, Cartan's equivalence method, an algorithmic procedure for determining if two geometric shapes are different). The works of Cartan were hard to grasp for most students, and Gardner worked to explain them in more access ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liao Shantao
Liao Shantao (; 4 January 1920 - 6 June 1997) was a Chinese mathematician. Biography Liao was born into a family of farming background on January 4, 1920, in Hengshan County, Hunan. His father was Liao Zihao () and his mother was Zeng Ping (). He attended Mingde Middle School and Changsha No. 1 High School in Changsha, capital of Hunan province. In 1938 he was accepted to National Southwestern Associated University and graduated in 1941. After graduation, he taught at Mingde Middle School. He moved to Peking University in 1946 as an associate professor and then to Academia Sinica as a research assistant in 1948. He pursued advanced studies in the United States, earning his doctor's degree from the University of Chicago in 1952. His doctoral dissertation was directed by Shiing-Shen Chern. He did post-doctoral research at Princeton University from 1953 to 1955. Liao gave up the job that mathematician Norman Steenrod had arranged for him in scientific research at Princeton Universi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Louis Auslander
Louis Auslander (July 12, 1928 – February 25, 1997) was a Jewish American mathematician. He had wide-ranging interests both in pure and applied mathematics and worked on Finsler geometry, geometry of solvmanifolds and nilmanifolds, locally affine spaces, many aspects of harmonic analysis, representation theory of solvable Lie groups, and multidimensional Fourier transforms and the design of signal sets for communications and radar. He is the author of more than one hundred papers and ten books. Education and career Auslander received his Ph.D. at the University of Chicago in 1955 under Shiing-Shen Chern. He was a visiting scholar at the Institute for Advanced Study in 1955-57 and again in 1971-72. After holding a variety of faculty positions at US universities, in 1965 Auslander joined the faculty at City University of New York, Graduate Center and since 1971 he had been a Distinguished Professor of Mathematics and Computer Science there. Personal life Louis Auslander was mar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manfredo Do Carmo
Manfredo Perdigão do Carmo (15 August 1928, Maceió – 30 April 2018, Rio de Janeiro) was a Brazilian mathematician. He spent most of his career at IMPA and is seen as the doyen of differential geometry in Brazil. Education and career Do Carmo studied civil engineering at the University of Recife from 1947 to 1951. After working a few years as engineer, he accepted a teaching position at the newly created Institute of Physics and Mathematics at Recife. On suggestion of Elon Lima, in 1959 he went to Instituto Nacional de Matemática Pura e Aplicada to improve his background and in 1960 he moved to the USA to pursue a Ph.D. in mathematics at the University of California, Berkeley under the supervision of Shiing-Shen Chern. He defended his thesis, entitled "''The Cohomology Ring of Certain Kahlerian Manifolds''", in 1963. After working again at University of Recife and at the University of Brasilia, in 1966 he became professor at Instituto Nacional de Matemática Pu ... [...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 h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
