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Edward Frenkel
Edward Vladimirovich Frenkel (; born May 2, 1968) is a Russian-American mathematician working in representation theory, algebraic geometry, and mathematical physics. He is a professor of mathematics at the University of California, Berkeley. Early life and education Edward Frenkel was born on May 2, 1968, in Kolomna, Russia, which was then part of the Soviet Union. His father is of Jewish descent and his mother is Russian. As a high school student he studied higher mathematics privately with Evgeny Evgenievich Petrov, although his initial interest was in quantum physics rather than mathematics. He was not admitted to Moscow State University and instead enrolled in the applied mathematics program at the Gubkin University of Oil and Gas. While a student there, he attended the seminar of Israel Gelfand and worked with Boris Feigin and Dmitry Fuchs. In 1989, upon receiving his undergraduate degree, he was invited to Harvard University and spent a year there as a visiting schola ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Kolomna
Kolomna (, ) is a historic types of inhabited localities in Russia, city in Moscow Oblast, Russia, situated at the confluence of the Moskva River, Moskva and Oka Rivers, (by rail) southeast of Moscow. Population: History Mentioned for the first time in 1177, Kolomna was founded in 1140–1160 according to the latest archaeological surveys. Kolomna's name may originate from the Old East Slavic, Old Russian term for "on the bend (in the river)", especially as the old city is located on a sharp bend in the Moskva River, Moscow River. In January 1238, Kolomna was Siege of Kolomna, destroyed by a Mongol invasion of Kievan Rus', Mongol invasion. In 1301, Kolomna became the first town to be incorporated into the Moscow Principality. Like some other ancient Russian cities, it has a Kolomna Kremlin, kremlin, which is a citadel similar to the Moscow Kremlin, more famous one in Moscow and also built of red brick. The stone Kolomna Kremlin was built from 1525–1531 under the Russian Tsar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Quantum Physics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot. Classical physics can describe many aspects of nature at an ordinary (macroscopic and Microscopic scale, (optical) microscopic) scale, but is not sufficient for describing them at very small submicroscopic (atomic and subatomic) scales. Classical mechanics can be derived from quantum mechanics as an approximation that is valid at ordinary scales. Quantum systems have Bound state, bound states that are Quantization (physics), quantized to Discrete mathematics, discrete values of energy, momentum, angular momentum, and ot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Geometric Langlands Correspondence
In mathematics, the geometric Langlands correspondence relates algebraic geometry and representation theory. It is a reformulation of the Langlands correspondence obtained by replacing the number fields appearing in the original number theoretic version by function fields and applying techniques from algebraic geometry. The correspondence is named for the Canadian mathematician Robert Langlands, who formulated the original form of it in the late 1960s. The geometric Langlands conjecture asserts the existence of the geometric Langlands correspondence. The existence of the geometric Langlands correspondence in the specific case of general linear groups over function fields was proven by Laurent Lafforgue in 2002, where it follows as a consequence of Lafforgue's theorem. Background In mathematics, the classical Langlands correspondence is a collection of results and conjectures relating number theory and representation theory. Formulated by Robert Langlands in the late 1960s, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Vladimir Drinfeld
Vladimir Gershonovich Drinfeld (; born February 14, 1954), surname also romanized as Drinfel'd, is a mathematician from Ukraine, who immigrated to the United States and works at the University of Chicago. Drinfeld's work connected algebraic geometry over finite fields with number theory, especially the theory of automorphic forms, through the notions of elliptic module and the theory of the geometric Langlands correspondence. Drinfeld introduced the notion of a quantum group (independently discovered by Michio Jimbo at the same time) and made important contributions to mathematical physics, including the ADHM construction of instantons, algebraic formalism of the quantum inverse scattering method, and the Drinfeld–Sokolov reduction in the theory of solitons. He was awarded the Fields Medal in 1990. In 2016, he was elected to the National Academy of Sciences. In 2018 he received the Wolf Prize in Mathematics. In 2023 he was awarded the Shaw Prize in Mathematical Sciences. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Alexander Beilinson
Alexander A. Beilinson (born 1957) is the David and Mary Winton Green University professor at the University of Chicago and works on mathematics. His research has spanned representation theory, algebraic geometry and mathematical physics. In 1999, Beilinson was awarded the Ostrowski Prize with Helmut Hofer. In 2017, he was elected to the National Academy of Sciences. In 2018, he received the Wolf Prize in Mathematics and in 2020 the Shaw Prize in Mathematics. Early life and education Beilinson was born in Moscow of mostly Russian descent while his paternal grandfather was Jewish. Nevertheless he was discriminated because of his Jewish surname, and was not admitted to Moscow State University. He went to Pedagogical Institute instead and transferred to Moscow State University when he was a third year student. Work In 1978, Beilinson published a paper on coherent sheaves and several problems in linear algebra. His two-page note in the journal ''Functional Analysis and Its ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Harish-Chandra Isomorphism
In mathematics, the Harish-Chandra isomorphism, introduced by , is an isomorphism of commutative rings constructed in the theory of Lie algebras. The isomorphism maps the center \mathcal(U(\mathfrak)) of the universal enveloping algebra U(\mathfrak) of a reductive Lie algebra \mathfrak to the elements S(\mathfrak)^W of the symmetric algebra S(\mathfrak) of a Cartan subalgebra \mathfrak that are invariant under the Weyl group W. Introduction and setting Let \mathfrak be a semisimple Lie algebra, \mathfrak its Cartan subalgebra and \lambda, \mu \in \mathfrak^* be two elements of the weight space (where \mathfrak^* is the dual of \mathfrak) and assume that a set of positive roots \Phi_+ have been fixed. Let V_\lambda and V_\mu be highest weight modules with highest weights \lambda and \mu respectively. Central characters The \mathfrak-modules V_\lambda and V_\mu are representations of the universal enveloping algebra U(\mathfrak) and its center acts on the modules by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Universal Enveloping Algebra
In mathematics, the universal enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal enveloping algebras are used in the representation theory of Lie groups and Lie algebras. For example, Verma modules can be constructed as quotients of the universal enveloping algebra. In addition, the enveloping algebra gives a precise definition for the Casimir operators. Because Casimir operators commute with all elements of a Lie algebra, they can be used to classify representations. The precise definition also allows the importation of Casimir operators into other areas of mathematics, specifically, those that have a differential algebra. They also play a central role in some recent developments in mathematics. In particular, their dual provides a commutative example of the objects studied in non-commutative geometry, the quantum groups. This dual can be shown, by the Gelf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Wakimoto Module
Wakimoto (written: 脇本) is a Japanese surname. Notable people with the surname include: *Kosei Wakimoto (born 1994), Japanese footballer *Roger Wakimoto Roger M. Wakimoto (born December 11, 1953) is an atmospheric scientist specializing in research on mesoscale meteorology, particularly severe convective storms and radar meteorology. A former director of the National Center for Atmospheric Resear ... (born 1953), American atmospheric scientist *, Japanese cyclist {{surname Japanese-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Affine Lie Algebra
In mathematics, an affine Lie algebra is an infinite-dimensional Lie algebra that is constructed in a canonical fashion out of a finite-dimensional simple Lie algebra. Given an affine Lie algebra, one can also form the associated affine Kac-Moody algebra, as described below. From a purely mathematical point of view, affine Lie algebras are interesting because their representation theory, like representation theory of finite-dimensional semisimple Lie algebras, is much better understood than that of general Kac–Moody algebras. As observed by Victor Kac, the character formula for representations of affine Lie algebras implies certain combinatorial identities, the Macdonald identities. Affine Lie algebras play an important role in string theory and two-dimensional conformal field theory due to the way they are constructed: starting from a simple Lie algebra \mathfrak, one considers the loop algebra, L\mathfrak, formed by the \mathfrak-valued functions on a circle (interpreted as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Harvard Society Of Fellows
The Society of Fellows is a group of scholars selected at the beginnings of their careers by Harvard University for their potential to advance academic wisdom, upon whom are bestowed distinctive opportunities to foster their individual and intellectual growth. Junior fellows are appointed by senior fellows based upon previous academic accomplishments and receive generous financial support for three years while they conduct independent research at Harvard University in any discipline, without being required to meet formal degree requirements or to be graded in any way. The only stipulation is that they maintain primary residence in Cambridge, Massachusetts, for the duration of their fellowship. Membership in the society is for life. The society has contributed numerous scholars to the Harvard faculty and thus significantly influenced the tenor of discourse at the university. Among its best-known members are philosopher W. V. O. Quine, Jf '36; behaviorist B. F. Skinner, Jf '36; doubl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
