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81 relations: Academic Press, Alexander Goncharov, Alexandre Kirillov, American Academy of Arts and Sciences, American Mathematical Society, Andrei Zelevinsky, Andrey Kolmogorov, Atiyah–Singer index theorem, Automorphic form, Banach algebra, Boris Levitan, Calculus of variations, Cell biology, Distribution (mathematics), Edward Frenkel, Endre Szemerédi, Felix Berezin, Fellow of the Royal Society, Foliation, Functional analysis, Gelfand pair, Gelfand representation, Gelfand ring, Gelfand–Kirillov dimension, Gelfand–Mazur theorem, Gelfand–Naimark theorem, Gelfand–Naimark–Segal construction, Gelfand–Shilov space, General hypergeometric function, Generalized function, Georgiy Shilov, Georgy Adelson-Velsky, Group theory, Highland Park, New Jersey, History of the Jews in Ukraine, Integral geometry, Joseph Bernstein, Kherson Governorate, Kyoto Prize, Leroy P. Steele Prize, Leukemia, Lie group, Liouville–Bratu–Gelfand equation, London Mathematical Society, MacArthur Fellows Program, Marchenko equation, Mathematical analysis, Mathematician, Moscow Mathematical Society, Moscow State University, ..., National Academy of Sciences, New Brunswick, New Jersey, New Jersey, Okny, Order of Lenin, Ordinary differential equation, Parabolic induction, Pettis integral, Pontryagin class, Representation theory, Rigged Hilbert space, Robert Wood Johnson University Hospital, Royal Irish Academy, Russia, Russian Empire, Rutgers University, Semisimple Lie algebra, Sergei Fomin, Soliton, Soviet Union, Springer Science+Business Media, The New York Times, Theoretical physics, Tilting theory, Ukraine, United States, Verma module, Victor Ginzburg, Vitalii Ditkin, Wigner Medal, Wolf Prize. Expand index (31 more) »
Academic Press
Academic Press is an academic book publisher.
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Alexander Goncharov
Alexander B. Goncharov (born April 7, 1960) is a Russian American mathematician and professor at Yale University.
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Alexandre Kirillov
Alexandre Aleksandrovich Kirillov (Алекса́ндр Алекса́ндрович Кири́ллов, born 1936) is a Soviet and Russian mathematician, known for his works in the fields of representation theory, topological groups and Lie groups.
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American Academy of Arts and Sciences
The American Academy of Arts and Sciences is one of the oldest learned societies in the United States of America.
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American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
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Andrei Zelevinsky
Andrei Vladlenovich Zelevinsky (Андрей Владленович Зелевинский; 30 January 1953 – 10 April 2013) was a Russian-American mathematician who made important contributions to algebra, combinatorics, and representation theory, among other areas.
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Andrey Kolmogorov
Andrey Nikolaevich Kolmogorov (a, 25 April 1903 – 20 October 1987) was a 20th-century Soviet mathematician who made significant contributions to the mathematics of probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity.
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Atiyah–Singer index theorem
In differential geometry, the Atiyah–Singer index theorem, proved by, states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space of solutions) is equal to the topological index (defined in terms of some topological data).
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Automorphic form
In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group G to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup \Gamma \subset G of the topological group.
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Banach algebra
In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers (or over a non-Archimedean complete normed field) that at the same time is also a Banach space, i.e. a normed space and complete in the metric induced by the norm.
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Boris Levitan
Boris Levitan (7 June 1914 – 4 April 2004) was a mathematician known in particular for his work on almost periodic functions, and Sturm–Liouville operators, especially, on inverse scattering.
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Calculus of variations
Calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.
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Cell biology
Cell biology (also called cytology, from the Greek κυτος, kytos, "vessel") is a branch of biology that studies the structure and function of the cell, the basic unit of life.
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Distribution (mathematics)
Distributions (or generalized functions) are objects that generalize the classical notion of functions in mathematical analysis.
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Edward Frenkel
Edward Vladimirovich Frenkel (sometimes spelled Э́двард Фре́нкель; born May 2, 1968) is a Russian-American mathematician working in representation theory, algebraic geometry, and mathematical physics.
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Endre Szemerédi
Endre Szemerédi (born August 21, 1940) is a Hungarian-American mathematician, working in the field of combinatorics and theoretical computer science.
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Felix Berezin
Felix Alexandrovich Berezin (Фе́ликс Алекса́ндрович Бере́зин; 25 April 1931 – 14 July 1980) was a Soviet Russian mathematician and physicist known for his contributions to the theory of supersymmetry and supermanifolds as well as to the path integral formulation of quantum field theory.
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Fellow of the Royal Society
Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted to individuals that the Royal Society judges to have made a "substantial contribution to the improvement of natural knowledge, including mathematics, engineering science and medical science".
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Foliation
In mathematics, a foliation is a geometric tool for understanding manifolds.
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Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense.
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Gelfand pair
In mathematics, the expression Gelfand pair is a pair (G,K) consisting of a group G and a subgroup K that satisfies a certain property on restricted representations.
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Gelfand representation
In mathematics, the Gelfand representation in functional analysis (named after I. M. Gelfand) has two related meanings.
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Gelfand ring
In mathematics, a Gelfand ring is an associative ring R with identity such that if I and J are distinct right ideals then there are elements i and j such that iRj.
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Gelfand–Kirillov dimension
In algebra, the Gelfand–Kirillov dimension (or GK dimension) of a right module M over a ''k''-algebra A is: where the sup is taken over all finite-dimensional subspaces V \subset A and M_0 \subset M. An algebra is said to have polynomial growth if its Gelfand–Kirillov dimension is finite.
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Gelfand–Mazur theorem
In operator theory, the Gelfand–Mazur theorem is a theorem named after Israel Gelfand and Stanisław Mazur which states that a Banach algebra with unit over the complex numbers in which every nonzero element is invertible is isometrically isomorphic to the complex numbers, i. e., the only complex Banach algebra that is a division algebra is the complex numbers C. The theorem follows from the fact that the spectrum of any element of a complex Banach algebra is nonempty: for every element a of a complex Banach algebra A there is some complex number λ such that λ1 − a is not invertible.
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Gelfand–Naimark theorem
In mathematics, the Gelfand–Naimark theorem states that an arbitrary C*-algebra A is isometrically *-isomorphic to a C*-algebra of bounded operators on a Hilbert space.
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Gelfand–Naimark–Segal construction
In functional analysis, a discipline within mathematics, given a C*-algebra A, the Gelfand–Naimark–Segal construction establishes a correspondence between cyclic *-representations of A and certain linear functionals on A (called states).
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Gelfand–Shilov space
In the mathematical field of functional analysis, a Gelfand–Shilov space S is a space of test functions for the theory of generalized functions, introduced by.
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General hypergeometric function
In mathematics, a general hypergeometric function or Aomoto–Gelfand hypergeometric function is a generalization of the hypergeometric function that was introduced by.
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Generalized function
In mathematics, generalized functions, or distributions, are objects extending the notion of functions.
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Georgiy Shilov
Georgi Evgen'evich Shilov (Гео́ргий Евге́ньевич Ши́лов; 3 February 1917 – 17 January 1975) was a Soviet mathematician and expert in the field of functional analysis, who contributed to the theory of normed rings and generalized functions.
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Georgy Adelson-Velsky
Georgy Maximovich Adelson-Velsky (Гео́ргий Макси́мович Адельсо́н-Ве́льский; name is sometimes transliterated as Georgii Adelson-Velskii) (8 January 1922 – 26 April 2014) was a Soviet and Israeli mathematician and computer scientist.
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Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.
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Highland Park, New Jersey
Highland Park is a borough in Middlesex County, New Jersey, United States.
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History of the Jews in Ukraine
Jewish communities have existed in the territory of Ukraine from the time of Kievan Rus' (one of Kiev city gates was called Judaic) and developed many of the most distinctive modern Jewish theological and cultural traditions such as Hasidism.
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Integral geometry
In mathematics, integral geometry is the theory of measures on a geometrical space invariant under the symmetry group of that space.
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Joseph Bernstein
Joseph Bernstein (sometimes spelled I. N. Bernshtein; יוס(י)ף נאומוביץ ברנשטיין; Иосиф Наумович Бернштейн, Iosif Naumovič Bernštejn; born 18 April 1945) is an Israeli mathematician working at Tel Aviv University.
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Kherson Governorate
The Kherson Governorate (1802–1922) (Херсонская губерния, translit.: Khersonskaya guberniya; Херсонська губернія, translit.: Khersons`ka huberniya) or Government of Kherson was a guberniya, or administrative territorial unit, between the Dnieper and Dniester Rivers, of the Russian Empire.
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Kyoto Prize
The is Japan's highest private award for global achievement.
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Leroy P. Steele Prize
The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics.
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Leukemia
Leukemia, also spelled leukaemia, is a group of cancers that usually begin in the bone marrow and result in high numbers of abnormal white blood cells.
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Lie group
In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.
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Liouville–Bratu–Gelfand equation
In mathematics, Liouville–Bratu–Gelfand equation or Liouville's equation is a non-linear eigenvalue Poisson equation, named after the mathematicians Joseph Liouville, G. Bratu and Israel Gelfand.
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London Mathematical Society
The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS) and the Institute of Mathematics and its Applications (IMA)).
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MacArthur Fellows Program
The MacArthur Fellows Program, MacArthur Fellowship, or "Genius Grant", is a prize awarded annually by the John D. and Catherine T. MacArthur Foundation typically to between 20 and 30 individuals, working in any field, who have shown "extraordinary originality and dedication in their creative pursuits and a marked capacity for self-direction" and are citizens or residents of the United States.
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Marchenko equation
In mathematical physics, more specific in the one-dimensional inverse scattering problem, the Marchenko equation (or Gelfand-Levitan-Marchenko equation or GLM equation), named after Israel Gelfand, Boris Levitan and Vladimir Marchenko, is derived by computing the Fourier transform of the scattering relation: K(r,r^\prime) + g(r,r^\prime) + \int_r^ K(r,r^) g(r^,r^\prime) \mathrmr^.
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Mathematical analysis
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
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Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.
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Moscow Mathematical Society
The Moscow Mathematical Society (MMS) is a society of Moscow mathematicians aimed at the development of mathematics in Russia.
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Moscow State University
Lomonosov Moscow State University (MSU; Московский государственный университет имени М. В. Ломоносова, often abbreviated МГУ) is a coeducational and public research university located in Moscow, Russia.
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National Academy of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization.
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New Brunswick, New Jersey
New Brunswick is a city in Middlesex County, New Jersey, United States, in the New York City metropolitan area.
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New Jersey
New Jersey is a state in the Mid-Atlantic region of the Northeastern United States.
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Okny
Okny (Окни, Окны) is an urban-type settlement in the west of Odessa Oblast, Ukraine.
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Order of Lenin
The Order of Lenin (Orden Lenina), named after the leader of the Russian October Revolution, was established by the Central Executive Committee on April 6, 1930.
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Ordinary differential equation
In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.
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Parabolic induction
In mathematics, parabolic induction is a method of constructing representations of a reductive group from representations of its parabolic subgroups.
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Pettis integral
In mathematics, the Pettis integral or Gelfand–Pettis integral, named after I. M. Gelfand and B. J. Pettis, extends the definition of the Lebesgue integral to vector-valued functions on a measure space, by exploiting duality.
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Pontryagin class
In mathematics, the Pontryagin classes, named for Lev Pontryagin, are certain characteristic classes.
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Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures.
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Rigged Hilbert space
In mathematics, a rigged Hilbert space (Gelfand triple, nested Hilbert space, equipped Hilbert space) is a construction designed to link the distribution and square-integrable aspects of functional analysis.
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Robert Wood Johnson University Hospital
The Robert Wood Johnson University Hospital (RWJUH) is an American 965-bed hospital with campuses in New Brunswick (Robert Wood Johnson University Hospital New Brunswick), and Somerville, New Jersey (Somerset Medical Center), and serves as a flagship hospital of RWJBarnabas Health.
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Royal Irish Academy
The Royal Irish Academy (RIA) (Acadamh Ríoga na hÉireann), based in Dublin, is an all-Ireland independent academic body that promotes study and excellence in the sciences, and humanities and social sciences.
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Russia
Russia (rɐˈsʲijə), officially the Russian Federation (p), is a country in Eurasia. At, Russia is the largest country in the world by area, covering more than one-eighth of the Earth's inhabited land area, and the ninth most populous, with over 144 million people as of December 2017, excluding Crimea. About 77% of the population live in the western, European part of the country. Russia's capital Moscow is one of the largest cities in the world; other major cities include Saint Petersburg, Novosibirsk, Yekaterinburg and Nizhny Novgorod. Extending across the entirety of Northern Asia and much of Eastern Europe, Russia spans eleven time zones and incorporates a wide range of environments and landforms. From northwest to southeast, Russia shares land borders with Norway, Finland, Estonia, Latvia, Lithuania and Poland (both with Kaliningrad Oblast), Belarus, Ukraine, Georgia, Azerbaijan, Kazakhstan, China, Mongolia and North Korea. It shares maritime borders with Japan by the Sea of Okhotsk and the U.S. state of Alaska across the Bering Strait. The East Slavs emerged as a recognizable group in Europe between the 3rd and 8th centuries AD. Founded and ruled by a Varangian warrior elite and their descendants, the medieval state of Rus arose in the 9th century. In 988 it adopted Orthodox Christianity from the Byzantine Empire, beginning the synthesis of Byzantine and Slavic cultures that defined Russian culture for the next millennium. Rus' ultimately disintegrated into a number of smaller states; most of the Rus' lands were overrun by the Mongol invasion and became tributaries of the nomadic Golden Horde in the 13th century. The Grand Duchy of Moscow gradually reunified the surrounding Russian principalities, achieved independence from the Golden Horde. By the 18th century, the nation had greatly expanded through conquest, annexation, and exploration to become the Russian Empire, which was the third largest empire in history, stretching from Poland on the west to Alaska on the east. Following the Russian Revolution, the Russian Soviet Federative Socialist Republic became the largest and leading constituent of the Union of Soviet Socialist Republics, the world's first constitutionally socialist state. The Soviet Union played a decisive role in the Allied victory in World War II, and emerged as a recognized superpower and rival to the United States during the Cold War. The Soviet era saw some of the most significant technological achievements of the 20th century, including the world's first human-made satellite and the launching of the first humans in space. By the end of 1990, the Soviet Union had the world's second largest economy, largest standing military in the world and the largest stockpile of weapons of mass destruction. Following the dissolution of the Soviet Union in 1991, twelve independent republics emerged from the USSR: Russia, Ukraine, Belarus, Kazakhstan, Uzbekistan, Armenia, Azerbaijan, Georgia, Kyrgyzstan, Moldova, Tajikistan, Turkmenistan and the Baltic states regained independence: Estonia, Latvia, Lithuania; the Russian SFSR reconstituted itself as the Russian Federation and is recognized as the continuing legal personality and a successor of the Soviet Union. It is governed as a federal semi-presidential republic. The Russian economy ranks as the twelfth largest by nominal GDP and sixth largest by purchasing power parity in 2015. Russia's extensive mineral and energy resources are the largest such reserves in the world, making it one of the leading producers of oil and natural gas globally. The country is one of the five recognized nuclear weapons states and possesses the largest stockpile of weapons of mass destruction. Russia is a great power as well as a regional power and has been characterised as a potential superpower. It is a permanent member of the United Nations Security Council and an active global partner of ASEAN, as well as a member of the G20, the Shanghai Cooperation Organisation (SCO), the Council of Europe, the Asia-Pacific Economic Cooperation (APEC), the Organization for Security and Co-operation in Europe (OSCE), and the World Trade Organization (WTO), as well as being the leading member of the Commonwealth of Independent States (CIS), the Collective Security Treaty Organization (CSTO) and one of the five members of the Eurasian Economic Union (EEU), along with Armenia, Belarus, Kazakhstan and Kyrgyzstan.
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Russian Empire
The Russian Empire (Российская Империя) or Russia was an empire that existed across Eurasia and North America from 1721, following the end of the Great Northern War, until the Republic was proclaimed by the Provisional Government that took power after the February Revolution of 1917.
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Rutgers University
Rutgers, The State University of New Jersey, commonly referred to as Rutgers University, Rutgers, or RU, is an American public research university and is the largest institution of higher education in New Jersey.
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Semisimple Lie algebra
In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras, i.e., non-abelian Lie algebras \mathfrak g whose only ideals are and \mathfrak g itself.
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Sergei Fomin
Sergei Vasilyevich Fomin (Серге́й Васи́льевич Фоми́н; 9 December 1917 – 17 August 1975) was a Soviet mathematician who was co-author with Kolmogorov of Introductory real analysis, and co-author with I.M. Gelfand of Calculus of Variations (1963), both books that are widely read in Russian and in English.
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Soliton
In mathematics and physics, a soliton is a self-reinforcing solitary wave packet that maintains its shape while it propagates at a constant velocity.
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Soviet Union
The Soviet Union, officially the Union of Soviet Socialist Republics (USSR) was a socialist state in Eurasia that existed from 1922 to 1991.
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Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
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The New York Times
The New York Times (sometimes abbreviated as The NYT or The Times) is an American newspaper based in New York City with worldwide influence and readership.
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Theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena.
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Tilting theory
In mathematics, specifically representation theory, tilting theory describes a way to relate the module categories of two algebras using so-called tilting modules and associated tilting functors.
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Ukraine
Ukraine (Ukrayina), sometimes called the Ukraine, is a sovereign state in Eastern Europe, bordered by Russia to the east and northeast; Belarus to the northwest; Poland, Hungary, and Slovakia to the west; Romania and Moldova to the southwest; and the Black Sea and Sea of Azov to the south and southeast, respectively.
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United States
The United States of America (USA), commonly known as the United States (U.S.) or America, is a federal republic composed of 50 states, a federal district, five major self-governing territories, and various possessions.
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Verma module
Verma modules, named after Daya-Nand Verma, are objects in the representation theory of Lie algebras, a branch of mathematics.
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Victor Ginzburg
Victor Ginzburg (born 1957) is a Russian American mathematician who works in representation theory and in noncommutative geometry.
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Vitalii Ditkin
Vitalii Arsenievich Ditkin (2 May 1910, Bogorodsk (now Noginsk), Russia – 17 October 1987, Moscow) was a Russian mathematician who introduced Ditkin sets.
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Wigner Medal
The Wigner Medal is an award designed "to recognize outstanding contributions to the understanding of physics through Group Theory".
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Wolf Prize
The Wolf Prize is an international award granted in Israel, that has been presented most years since 1978 to living scientists and artists for "achievements in the interest of mankind and friendly relations among people...
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I. Gelfand, I. M. Gel'fand, I. M. Gelfand, I.M. Gel'fand, I.M. Gelfand, Israel Gel'fand, Israel M. Gel'fand, Israel M. Gelfand, Israel Moiseevich Gel'fand, Israel Moiseevich Gelfand, Israel Moiseevitch Gelfand, Israil Gelfand, Israil Moiseivich Gelfand, Israël Moïseevitch Gelfand, Israïl Moiseevich Gelfand, Israïl Moyseyovich Gel'fand, Isreal Gel'fand, Izrael Moiseivich Gelfand, Izrail Gel'fand, Izrail Gelfand, Izrail M. Gelfand, Izrail Moiseevich Gel'fand, Izrail Moiseevich Gelfand, Izrail Moyseyovich Gel'fand, Izrail Moyseyovich Gelfand, Изра́иль Моисе́евич Ге́льфанд, ישראל געלפֿאַנד.
References
[1] https://en.wikipedia.org/wiki/Israel_Gelfand
