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Jack Morava
Jack Johnson Morava is an American homotopy theorist at Johns Hopkins University. Education Of Czech and Appalachian descent, he was raised in Texas' lower Rio Grande valley. An early interest in topology was strongly encouraged by his parents. He enrolled at Rice University in 1962 as a physics major, but (with the help of Jim Douglas) entered the graduate mathematics program in 1964. His advisor Eldon Dyer arranged, with the support of Michael Atiyah, a one-year fellowship at the University of Oxford, followed by a year in Princeton at the Institute for Advanced Study. Work Morava brought ideas from arithmetic geometry into the realm of algebraic topology. Under Atiyah's tutelage Morava concentrated on the relation between K-theory and cobordism, and when Daniel Quillen's work on that subject appeared he saw that ideas of Sergei Novikov implied close connections between the stable homotopy category and the derived category of quasicoherent sheaves on the moduli stack of on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ellen Contini-Morava
Ellen Contini-Morava is an anthropological linguist, interested in the meanings of linguistic forms, discourse analysis, functional linguistics and (noun) classification; in particular, in the relationship between lexicon and grammar. She specializes in Bantu languages in general, and Swahili in particular. Education and career Contini-Morava received her PhD from Columbia University in 1983 under William Diver and Erica Garcia. She is a professor emerita at the University of Virginia. Books Contini-Morava is the author of the book ''Discourse Pragmatics and Semantic Categorization: The Case of Negation and Tense-Aspect with Special Reference to Swahili'' (Mouton de Gruyter, 1989). Her edited volume Editing is the process of selecting and preparing written language, written, Image editing, visual, Audio engineer, audible, or Film editing, cinematic material used by a person or an entity to convey a message or information. The editing p ...s include ''Between Grammar and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sergei Novikov (mathematician)
Sergei Petrovich Novikov ( Russian: Серге́й Петро́вич Но́виков ; 20 March 19386 June 2024) was a Soviet and Russian mathematician, noted for work in both algebraic topology and soliton theory. He became the first Soviet mathematician to receive the Fields Medal in 1970. Biography Novikov was born on 20 March 1938 in Gorky, Soviet Union (now Nizhny Novgorod, Russia). He grew up in a family of talented mathematicians. His father was Pyotr Sergeyevich Novikov, who gave a negative solution to the word problem for groups. His mother, Lyudmila Vsevolodovna Keldysh, and maternal uncle, Mstislav Vsevolodovich Keldysh, were also important mathematicians. Novikov entered Moscow State University in 1955 and graduated in 1960. In 1964, he received the Moscow Mathematical Society Award for young mathematicians and defended a dissertation for the ''Candidate of Science in Physics and Mathematics'' degree (equivalent to the PhD) under Mikhail Postnikov at Moscow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yuri I
Yuri I Vladimirovich (; ; c. 1099 – 15 May 1157), commonly known as Yuri Dolgorukiy (, ) or the Long Arm, was a Monomakhovichi prince of Rostov and Suzdal, acquiring the name ''Suzdalia'' during his reign. Noted for successfully curbing the privileges of the landowning ''boyar'' class in Rostov-Suzdal and his ambitious building programme, Yuri transformed this principality into the independent power that would evolve into early modern Muscovy. Yuri Dolgorukiy was the progenitor of the Yurievichi ( ), a branch of the Monomakhovichi. Yuri spent much of his life in internecine strife with the other Rus' princes for suzerainty over the Kievan Rus, which had been held by his father ( Vladimir Monomakh) and his elder brother before him. Although he twice managed to briefly hold Kiev (in September 1149 – April 1151, again in March 1155 – May 1157) and rule as Grand Prince of Kiev, his autocratic rule and perceived foreigner status made him unpopular with the powerful Kieva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Israel Gelfand
Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand (, , ; – 5 October 2009) was a prominent Soviet and American mathematician, one of the greatest mathematicians of the 20th century, biologist, teacher and organizer of mathematical education. He made significant contributions to many branches of mathematics, including group theory, representation theory and functional analysis. The recipient of many awards, including the Order of Lenin and the first Wolf Prize, he was a Foreign Fellow of the Royal Society and professor at Moscow State University and, after immigrating to the United States shortly before his 76th birthday, at Rutgers University. Gelfand is also a 1994 MacArthur Fellow. His legacy continues through his students, who include Endre Szemerédi, Alexandre Kirillov, Edward Frenkel, Joseph Bernstein, David Kazhdan, as well as his own son, Sergei Gelfand. Early years A native of Kherson Governorate, Russian Empire (now, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vladimir Arnold
Vladimir Igorevich Arnold (or Arnol'd; , ; 12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician. He is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, and contributed to several areas, including geometrical theory of dynamical systems, algebra, catastrophe theory, topology, real algebraic geometry, symplectic geometry, differential equations, classical mechanics, differential-geometric approach to hydrodynamics, geometric analysis and singularity theory, including posing the ADE classification problem. His first main result was the solution of Hilbert's thirteenth problem in 1957 when he was 19. He co-founded three new branches of mathematics: topological Galois theory (with his student Askold Khovanskii), symplectic topology and KAM theory. Arnold was also a populariser of mathematics. Through his lectures, seminars, and as the author of several textbooks (such as '' Mathematical Methods of Clas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steklov Institute Of Mathematics
Steklov Institute of Mathematics or Steklov Mathematical Institute () is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Steklov, who in 1919 founded the Institute of Physics and Mathematics in Saint Petersburg, Leningrad. In 1934, this institute was split into separate parts for physics and mathematics, and the mathematical part became the Steklov Institute. At the same time, it was moved to Moscow. The first director of the Steklov Institute was Ivan Matveyevich Vinogradov. From 19611964, the institute's director was the notable mathematician Sergei Chernikov. The old building of the Institute in Leningrad became its Department in Leningrad. Today, that department has become a separate institute, called the ''St. Petersburg Department of Steklov Mathematical Institute of the Russian Academy of Sciences'' or PDMI RAS, located in Saint Petersburg, Russia. The n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
DARPA
The Defense Advanced Research Projects Agency (DARPA) is a research and development agency of the United States Department of Defense responsible for the development of emerging technologies for use by the military. Originally known as the Advanced Research Projects Agency (ARPA), the agency was created on February 7, 1958, by President Dwight D. Eisenhower in response to the Soviet Union, Soviet launching of Sputnik 1 in 1957. By collaborating with academia, industry, and government partners, DARPA formulates and executes research and development projects to expand the frontiers of technology and science, often beyond immediate U.S. military requirements.Dwight D. Eisenhower and Science & Technology, (2008). Dwight D. Eisenhower Memorial CommissionSource The name of the organization first changed from its founding name, ARPA, to DARPA, in March 1972, changing back to ARPA in February 1993, then reverted to DARPA in March 1996. ''The Economist'' has called DARPA "the agency that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ArXiv
arXiv (pronounced as "archive"—the X represents the Chi (letter), Greek letter chi ⟨χ⟩) is an open-access repository of electronic preprints and postprints (known as e-prints) approved for posting after moderation, but not Scholarly peer review, peer reviewed. It consists of scientific papers in the fields of mathematics, physics, astronomy, electrical engineering, computer science, quantitative biology, statistics, mathematical finance, and economics, which can be accessed online. In many fields of mathematics and physics, almost all scientific papers are self-archiving, self-archived on the arXiv repository before publication in a peer-reviewed journal. Some publishers also grant permission for authors to archive the peer-reviewed postprint. Begun on August 14, 1991, arXiv.org passed the half-million-article milestone on October 3, 2008, had hit a million by the end of 2014 and two million by the end of 2021. As of November 2024, the submission rate is about 24,000 arti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Class Field Theory
In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field. Hilbert is credited as one of pioneers of the notion of a class field. However, this notion was already familiar to Kronecker and it was actually Weber who coined the term before Hilbert's fundamental papers came out. The relevant ideas were developed in the period of several decades, giving rise to a set of conjectures by Hilbert that were subsequently proved by Takagi and Artin (with the help of Chebotarev's theorem). One of the major results is: given a number field ''F'', and writing ''K'' for the maximal abelian unramified extension of ''F'', the Galois group of ''K'' over ''F'' is canonically isomorphic to the ideal class group of ''F''. This statement was generalized to the so called Artin reciprocity law; in the idelic language, writing '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Division Algebra
In the field of mathematics called abstract algebra, a division algebra is, roughly speaking, an algebra over a field in which division, except by zero, is always possible. Definitions Formally, we start with a non-zero algebra ''D'' over a field. We call ''D'' a division algebra if for any element ''a'' in ''D'' and any non-zero element ''b'' in ''D'' there exists precisely one element ''x'' in ''D'' with ''a'' = ''bx'' and precisely one element ''y'' in ''D'' such that . For associative algebras, the definition can be simplified as follows: a non-zero associative algebra over a field is a division algebra if and only if it has a multiplicative identity element 1 and every non-zero element ''a'' has a multiplicative inverse (i.e. an element ''x'' with ). Associative division algebras The best-known examples of associative division algebras are the finite-dimensional real ones (that is, algebras over the field R of real numbers, which are finite- dimensional as a vector space ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ravenel Conjectures
In mathematics, the Ravenel conjectures are a set of mathematical conjectures in the field of stable homotopy theory posed by Douglas Ravenel at the end of a paper published in 1984. It was earlier circulated in preprint. The problems involved have largely been resolved, with all but the "telescope conjecture" being proved in later papers by others. Ravenel's conjectures exerted influence on the field through the founding of the approach of chromatic homotopy theory. The first of the seven conjectures, then the ''nilpotence conjecture'', was proved in 1988 and is now known as the nilpotence theorem. The telescope conjecture, which was fourth on the original list, remains of substantial interest because of its connection with the convergence of an Adams–Novikov spectral sequence. While opinion has been generally against the truth of the original statement, investigations of associated phenomena (for a triangulated category in general) have become a research area in its own right ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Douglas Ravenel
Douglas Conner Ravenel (born February 17, 1947) is an American mathematician known for work in algebraic topology. Life Ravenel received his PhD from Brandeis University in 1972 under the direction of Edgar H. Brown, Jr. with a thesis on exotic characteristic classes of spherical fibrations. From 1971 to 1973 he was a C. L. E. Moore instructor at the Massachusetts Institute of Technology, and in 1974/75 he visited the Institute for Advanced Study. He became an assistant professor at Columbia University in 1973 and at the University of Washington in Seattle in 1976, where he was promoted to associate professor in 1978 and professor in 1981. From 1977 to 1979 he was a Sloan Fellow. Since 1988 he has been a professor at the University of Rochester. He was an invited speaker at the International Congress of Mathematicians in Helsinki, 1978, and is an editor of The New York Journal of Mathematics since 1994. In 2012 he became a fellow of the American Mathematical Society. In 2022 he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
