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Drinfeld
Vladimir Gershonovich Drinfeld ( uk, Володи́мир Ге́ршонович Дрінфельд; russian: Влади́мир Ге́ршонович Дри́нфельд; born February 14, 1954), surname also romanized as Drinfel'd, is a renowned mathematician from the former USSR, who emigrated to the United States and is currently working 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 w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic Module
In mathematics, a Drinfeld module (or elliptic module) is roughly a special kind of module over a ring of functions on a curve over a finite field, generalizing the Carlitz module. Loosely speaking, they provide a function field analogue of complex multiplication theory. A shtuka (also called F-sheaf or chtouca) is a sort of generalization of a Drinfeld module, consisting roughly of a vector bundle over a curve, together with some extra structure identifying a "Frobenius twist" of the bundle with a "modification" of it. Drinfeld modules were introduced by , who used them to prove the Langlands conjectures for GL2 of an algebraic function field in some special cases. He later invented shtukas and used shtukas of rank 2 to prove the remaining cases of the Langlands conjectures for GL2. Laurent Lafforgue proved the Langlands conjectures for GL''n'' of a function field by studying the moduli stack of shtukas of rank ''n''. "Shtuka" is a Russian word штука meaning "a single cop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Group
In mathematics and theoretical physics, the term quantum group denotes one of a few different kinds of noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix quantum groups (which are structures on unital separable C*-algebras), and bicrossproduct quantum groups. Despite their name, they do not themselves have a natural group structure, though they are in some sense 'close' to a group. The term "quantum group" first appeared in the theory of quantum integrable systems, which was then formalized by Vladimir Drinfeld and Michio Jimbo as a particular class of Hopf algebra. The same term is also used for other Hopf algebras that deform or are close to classical Lie groups or Lie algebras, such as a "bicrossproduct" class of quantum groups introduced by Shahn Majid a little after the work of Drinfeld and Jimbo. In Drinfeld's approach, quantum groups arise as Hopf algebras depe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fields Medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award honours the Canadian mathematician John Charles Fields. The Fields Medal is regarded as one of the highest honors a mathematician can receive, and has been described as the Nobel Prize of Mathematics, although there are several major differences, including frequency of award, number of awards, age limits, monetary value, and award criteria. According to the annual Academic Excellence Survey by ARWU, the Fields Medal is consistently regarded as the top award in the field of mathematics worldwide, and in another reputation survey conducted by IREG in 2013–14, the Fields Medal came closely after the Abel Prize as the second most prestigious international award in mathematics. The prize includes a monetary award which, since 2006, has bee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Group
In mathematics and theoretical physics, the term quantum group denotes one of a few different kinds of noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix quantum groups (which are structures on unital separable C*-algebras), and bicrossproduct quantum groups. Despite their name, they do not themselves have a natural group structure, though they are in some sense 'close' to a group. The term "quantum group" first appeared in the theory of quantum integrable systems, which was then formalized by Vladimir Drinfeld and Michio Jimbo as a particular class of Hopf algebra. The same term is also used for other Hopf algebras that deform or are close to classical Lie groups or Lie algebras, such as a "bicrossproduct" class of quantum groups introduced by Shahn Majid a little after the work of Drinfeld and Jimbo. In Drinfeld's approach, quantum groups arise as Hopf algebras depe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oper (mathematics)
In mathematics, an Oper is a principal connection, or in more elementary terms a type of differential operator. They were first defined and used by Vladimir Drinfeld and Vladimir Sokolov to study how the KdV equation and related integrable PDEs correspond to algebraic structures known as Kac–Moody algebras. Their modern formulation is due to Drinfeld and Alexander Beilinson. History Opers were first defined, although not named, in a 1981 Russian paper by Drinfeld and Sokolov on ''Equations of Korteweg–de Vries type, and simple Lie algebras''. They were later generalized by Drinfeld and Beilinson in 1993, later published as an e-print in 2005. Formulation Abstract Let G be a connected reductive group over the complex plane \mathbb, with a distinguished Borel subgroup B = B_G \subset G. Set N = ,B/math>, so that H = B/N is the Cartan group. Denote by \mathfrak < \mathfrak < \mathfrak and the corresponding |
Drinfeld–Sokolov–Wilson Equation
The Drinfeld–Sokolov–Wilson (DSW) equations are an integrable system of two coupled nonlinear partial differential equations proposed by Vladimir Drinfeld Vladimir Gershonovich Drinfeld ( uk, Володи́мир Ге́ршонович Дрінфельд; russian: Влади́мир Ге́ршонович Дри́нфельд; born February 14, 1954), surname also romanized as Drinfel'd, is a renowne ... and Vladimir Sokolov, and independently by George Wilson: : \begin &\frac+3v\frac=0\\ pt&\frac=2\frac+\frac v+2u \frac \end Notes References *Graham W. Griffiths, William E. Shiesser ''Traveling Wave Analysis of Partial Differential Equations'', p. 135 Academy Press *Richard H. Enns, George C. McCGuire, ''Nonlinear Physics Birkhauser'', 1997 *Inna Shingareva, Carlos Lizárraga-Celaya, ''Solving Nonlinear Partial Differential Equations with Maple'' Springer. *Eryk Infeld and George Rowlands, ''Nonlinear Waves,Solitons and Chaos'', Cambridge 2000 *Saber Elaydi, ''An In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manin–Drinfeld Theorem
In mathematics, the Manin–Drinfeld theorem, proved by and , states that the difference of two cusps of a modular curve has finite order in the Jacobian variety In mathematics, the Jacobian variety ''J''(''C'') of a non-singular algebraic curve ''C'' of genus ''g'' is the moduli space of degree 0 line bundles. It is the connected component of the identity in the Picard group of ''C'', hence an abelian vari .... References * * Modular forms Theorems in number theory {{numtheory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lie-* Algebra
In mathematics, a Lie-* algebra is a D-module with a Lie* bracket. They were introduced by Alexander Beilinson and Vladimir Drinfeld Vladimir Gershonovich Drinfeld ( uk, Володи́мир Ге́ршонович Дрінфельд; russian: Влади́мир Ге́ршонович Дри́нфельд; born February 14, 1954), surname also romanized as Drinfel'd, is a renowne ... (), and are similar to the conformal algebras discussed by and to vertex Lie algebras. References * * {{algebra-stub Lie algebras ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ADHM Construction
In mathematical physics and gauge theory, the ADHM construction or monad construction is the construction of all instantons using methods of linear algebra by Michael Atiyah, Vladimir Drinfeld, Nigel Hitchin, Yuri I. Manin in their paper "Construction of Instantons." ADHM data The ADHM construction uses the following data: * complex vector spaces ''V'' and ''W'' of dimension ''k'' and ''N'', * ''k'' × ''k'' complex matrices ''B''1, ''B''2, a ''k'' × ''N'' complex matrix ''I'' and a ''N'' × ''k'' complex matrix ''J'', * a real moment map \mu_r = _1,B_1^\dagger _2,B_2^\daggerII^\dagger-J^\dagger J, * a complex moment map \displaystyle\mu_c = _1,B_2IJ. Then the ADHM construction claims that, given certain regularity conditions, * Given ''B''1, ''B''2, ''I'', ''J'' such that \mu_r=\mu_c=0, an anti-self-dual instanton in a SU(''N'') gauge theory with instanton number ''k'' can be constructed, * All anti-self-dual instantons c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kharkov
Kharkiv ( uk, Ха́рків, ), also known as Kharkov (russian: Харькoв, ), is the second-largest city and municipality in Ukraine.Kharkiv "never had eastern-western conflicts" '''' (23 October 2014) Located in the northeast of the country, it is the largest city of the historic region. Kharkiv is the of |
Moscow State University
M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious university in the country. The university includes 15 research institutes, 43 faculties, more than 300 departments, and six branches (including five foreign ones in the Commonwealth of Independent States countries). Alumni of the university include past leaders of the Soviet Union and other governments. As of 2019, 13 List of Nobel laureates, Nobel laureates, six Fields Medal winners, and one Turing Award winner had been affiliated with the university. The university was ranked 18th by ''The Three University Missions Ranking'' in 2022, and 76th by the ''QS World University Rankings'' in 2022, #293 in the world by the global ''Times Higher World University Rankings'', and #326 by ''U.S. News & World Report'' in 2022. It was the highest-ran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolf Prize In Mathematics
The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts. According to a reputation survey conducted in 2013 and 2014, the Wolf Prize in Mathematics is the third most prestigious international academic award in mathematics, after the Abel Prize and the Fields Medal. Until the establishment of the Abel Prize, it was probably the closest equivalent of a "Nobel Prize in Mathematics", since the Fields Medal is awarded every four years only to mathematicians under the age of 40. Laureates Laureates per country Below is a chart of all laureates per country (updated to 2022 laureates). Some laureates are counted more than once if have multiple citizenship. Notes See also * List of mathematics awards References External links * * * Israel-Wolf-Prizes 2015Jerusalempost Wolf Prizes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
