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Masatake Kuranishi
Masatake Kuranishi (倉西 正武 ''Kuranishi Masatake''; July 19, 1924 – June 22, 2021) was a Japanese mathematician who worked on several complex variables, partial differential equations, and differential geometry. Education and career Kuranishi received in 1952 his Ph.D. from Nagoya University. He became a lecturer there in 1951, an associate professor in 1952, and a full professor in 1958. From 1955 to 1956 he was a visiting scholar at the Institute for Advanced Study in Princeton, New Jersey. From 1956 to 1961 he was a visiting professor at the University of Chicago, the Massachusetts Institute of Technology, and Princeton University. He became a professor at Columbia University in the summer of 1961. Kuranishi was an invited speaker at the International Congress of Mathematicians in 1962 at Stockholm with the talk ''On deformations of compact complex structures'' and in 1970 at Nice with the talk ''Convexity conditions related to 1/2 estimate on elliptic complexes''. He wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function Of Several Complex Variables
The theory of functions of several complex variables is the branch of mathematics dealing with complex-valued functions. The name of the field dealing with the properties of function of several complex variables is called several complex variables (and analytic space), that has become a common name for that whole field of study and Mathematics Subject Classification has, as a top-level heading. A function f:(z_1,z_2, \ldots, z_n) \rightarrow f(z_1,z_2, \ldots, z_n) is -tuples of complex numbers, classically studied on the complex coordinate space \Complex^n. As in complex analysis of functions of one variable, which is the case , the functions studied are ''holomorphic'' or ''complex analytic'' so that, locally, they are power series in the variables . Equivalently, they are locally uniform limits of polynomials; or locally square-integrable solutions to the -dimensional Cauchy–Riemann equations. For one complex variable, every domainThat is an open connected subset. (D \subs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartan–Kuranishi Prolongation Theorem
Given an exterior differential system defined on a manifold ''M'', the Cartan–Kuranishi prolongation theorem says that after a finite number of ''prolongations'' the system is either ''in involution'' (admits at least one 'large' integral manifold), or is impossible. History The theorem is named after Élie Cartan and Masatake Kuranishi. Applications This theorem is used in infinite-dimensional Lie theory In mathematics, the mathematician Sophus Lie ( ) initiated lines of study involving integration of differential equations, transformation groups, and contact of spheres that have come to be called Lie theory. For instance, the latter subject is L .... See also * Cartan-Kähler theorem References * M. Kuranishi, ''On É. Cartan's prolongation theorem of exterior differential systems'', Amer. J. Math., vol. 79, 1957, p. 1–47 * {{DEFAULTSORT:Cartan-Kuranishi prolongation theorem Partial differential equations Theorems in analysis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kuranishi Structure
In mathematics, especially in topology, a Kuranishi structure is a smooth analogue of scheme structure. If a topological space is endowed with a Kuranishi structure, then locally it can be identified with the zero set of a smooth map (f_1, \ldots, f_k)\colon \R^ \to \R^k, or the quotient of such a zero set by a finite group. Kuranishi structures were introduced by Japanese mathematicians Kenji Fukaya and Kaoru Ono in the study of Gromov–Witten invariants and Floer homology in symplectic geometry, and were named after Masatake Kuranishi. Definition Let X be a compact metrizable topological space. Let p \in X be a point. A Kuranishi neighborhood of p (of dimension k) is a 5-tuple ::: K_p = (U_p, E_p, S_p, F_p, \psi_p) where * U_p is a smooth orbifold; * E_p \to U_p is a smooth orbifold vector bundle; * S_p\colon U_p \to E_p is a smooth section; * F_p is an open neighborhood of p ; * \psi_p\colon S_p^(0) \to F_p is a homeomorphism. They should satisfy that \dim U_p - \operato ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heisuke Hironaka
is a Japanese mathematician who was awarded the Fields Medal in 1970 for his contributions to algebraic geometry. Career Hironaka entered Kyoto University in 1949. After completing his undergraduate studies at Kyoto University, he received his Ph.D. in 1960 from Harvard University while under the direction of Oscar Zariski. Hironaka held teaching positions at Brandeis University from 1960-1963, Columbia University in 1964, and Kyoto University from 1975 to 1988. He was a professor of mathematics at Harvard University from 1968 until becoming ''emeritus'' in 1992 and was a president of Yamaguchi University from 1996 to 2002. Research In 1964, Hironaka proved that singularities of algebraic varieties admit resolutions in characteristic zero. This means that any algebraic variety can be replaced by (more precisely is birationally equivalent to) a similar variety which has no singularities. He also introduced Hironaka's example showing that a deformation of Kähler manifolds need ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annales Henri Poincaré
The ''Annales Henri Poincaré'' (''A Journal of Theoretical and Mathematical Physics'') is a peer-reviewed scientific journal which collects and publishes original research papers in the field of theoretical and mathematical physics. The emphasis is on "analytical theoretical and mathematical physics" in a broad sense. The journal is named in honor of Henri Poincaré and it succeeds two former journals, ''Annales de l'Institut Henri Poincaré, physique théorique'' and ''Helvetica Physical Acta'' (). It is published by Birkhäuser Verlag. Its first Chief Editor was Vincent Rivasseau, followed by Krzysztof Gawedzki, and the current Chief Editor is Claude-Alain Pillet.Home page with relevant links, publisher, subjects covered, and bibliographic data. Springer. 2022-01 [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Memoirs Of The American Mathematical Society
''Memoirs of the American Mathematical Society'' is a mathematical journal published in six volumes per year, totalling approximately 33 individually bound numbers, by the American Mathematical Society. It is intended to carry papers on new mathematical research between 80 and 200 pages in length. Usually, a bound number consists of a single paper, i.e., it is a monograph. The journal is indexed by Mathematical Reviews, Zentralblatt MATH, Science Citation Index, Research Alert, CompuMath Citation Index, and Current Contents. Other journals from the AMS * ''Bulletin of the American Mathematical Society'' * ''Journal of the American Mathematical Society'' * ''Notices of the American Mathematical Society ''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume appeared in 1953. Each issue of the magazine since ...'' * ''Proceedings of the Ame ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Von Neumann
John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest coverage of any mathematician of his time and was said to have been "the last representative of the great mathematicians who were equally at home in both pure and applied mathematics". He integrated pure and applied sciences. Von Neumann made major contributions to many fields, including mathematics (foundations of mathematics, measure theory, functional analysis, ergodic theory, group theory, lattice theory, representation theory, operator algebras, matrix theory, geometry, and numerical analysis), physics (quantum mechanics, hydrodynamics, ballistics, nuclear physics and quantum statistical mechanics), economics ( game theory and general equilibrium theory), computing ( Von Neumann architecture, linear programming, numerical meteo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Louis Nirenberg
Louis Nirenberg (February 28, 1925 – January 26, 2020) was a Canadian-American mathematician, considered one of the most outstanding mathematicians of the 20th century. Nearly all of his work was in the field of partial differential equations. Many of his contributions are now regarded as fundamental to the field, such as his strong maximum principle for second-order parabolic partial differential equations and the Newlander-Nirenberg theorem in complex geometry. He is regarded as a foundational figure in the field of geometric analysis, with many of his works being closely related to the study of complex analysis and differential geometry. Biography Nirenberg was born in Hamilton, Ontario to Ukrainian Jewish immigrants. He attended Baron Byng High School and McGill University, completing his BS in both mathematics and physics in 1945. Through a summer job at the National Research Council of Canada, he came to know Ernest Courant's wife Sara Paul. She spoke to Courant's f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph J
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] |
Charles B
Charles is a masculine given name predominantly found in English and French speaking countries. It is from the French form ''Charles'' of the Proto-Germanic name (in runic alphabet) or ''*karilaz'' (in Latin alphabet), whose meaning was "free man". The Old English descendant of this word was '' Ċearl'' or ''Ċeorl'', as the name of King Cearl of Mercia, that disappeared after the Norman conquest of England. The name was notably borne by Charlemagne (Charles the Great), and was at the time Latinized as ''Karolus'' (as in ''Vita Karoli Magni''), later also as '' Carolus''. Some Germanic languages, for example Dutch and German, have retained the word in two separate senses. In the particular case of Dutch, ''Karel'' refers to the given name, whereas the noun ''kerel'' means "a bloke, fellow, man". Etymology The name's etymology is a Common Germanic noun ''*karilaz'' meaning "free man", which survives in English as churl (< Old English ''ċeorl''), which developed its depr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CR Manifold
In mathematics, a CR manifold, or Cauchy–Riemann manifold, is a differentiable manifold together with a geometric structure modeled on that of a real hypersurface in a complex vector space, or more generally modeled on an edge of a wedge. Formally, a CR manifold is a differentiable manifold ''M'' together with a preferred complex distribution ''L'', or in other words a complex subbundle of the complexified tangent bundle \Complex TM = TM \otimes_\mathbb \Complex such that * ,Lsubseteq L (''L'' is formally integrable) * L\cap\bar=\. The subbundle ''L'' is called a CR structure on the manifold ''M''. The abbreviation CR stands for " Cauchy–Riemann" or "Complex-Real". Introduction and motivation The notion of a CR structure attempts to describe ''intrinsically'' the property of being a hypersurface (or certain real submanifolds of higher codimension) in complex space by studying the properties of holomorphic vector fields which are tangent to the hypersurface. Suppose for in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the founding editor-in-chief. It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering". It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two. This incarnation of the journal ceased publication after its tenth year, in 1883, giving as an explanation Hendricks' declining health, but Hendricks made arrangements to have it taken over by new management, and it was continued from March 1884 as the ''Annals of Mathematics''. The n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
