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Victor Kac
Victor Gershevich (Grigorievich) Kac (; born 19 December 1943) is a Soviet and American mathematician at MIT, known for his work in representation theory. He co-discovered Kac–Moody algebras, and used the Weyl–Kac character formula for them to reprove the Macdonald identities. He classified the finite-dimensional simple Lie superalgebras, and found the Kac determinant formula for the Virasoro algebra. He is also known for the Kac–Weisfeiler conjectures with Boris Weisfeiler. Biography Kac studied mathematics at Moscow State University, receiving his MS in 1965 and his PhD in 1968. From 1968 to 1976, he held a teaching position at the Moscow Institute of Electronic Machine Building (MIEM). He left the Soviet Union in 1977, becoming an associate professor of mathematics at MIT. In 1981, he was promoted to full professor. Kac received a Sloan Fellowship and the Medal of the Collège de France, both in 1981, and a Guggenheim Fellowship in 1986. He received the Wigner ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Buguruslan
Buguruslan () is a town in Orenburg Oblast, Russia. Population: History It was founded at the end of 1748 as a settlement (Buguruslanskaya settlement) by Russian peasants and artisans who migrated to the Volga region, on the ancestral lands of the Bashkirs of the Kipchak parish of Nogai Daruga on the right bank of the Bolshoy Kinel River at the confluence of the Turkhanka River. In 1781, Sloboda received the status of the county town of Buguruslan, becoming the center of Buguruslan county as part of the Ufa region of the Ufa governorate. Administrative and municipal status Within the framework of administrative divisions, Buguruslan serves as the administrative center of Buguruslansky District, even though it is not a part of it. As an administrative division, it is, together with six rural localities, incorporated separately as the Town of BuguruslanLaw #1370/276-IV-OZ—an administrative unit with the status equal to that of the districts A district is a type of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. Since 1993, there has been a formal division into three categories. The prizes have been given since 1970, from a bequest of Leroy P. Steele, and were set up in honor of George David Birkhoff, William Fogg Osgood and William Caspar Graustein. The way the prizes are awarded was changed in 1976 and 1993, but the initial aim of honoring expository writing as well as research has been retained. The prizes of $5,000 are not given on a strict national basis, but relate to mathematical activity in the USA, and writing in English (originally, or in translation). Steele Prize for Lifetime Achievement *2025 Dusa McDuff *2024 Haïm Brezis *2023 Nicholas M. Katz *2022 Richard P. Stanley *2021 Spencer Bloch *2020 Karen Uhlenbeck *2019 Jeff Cheeger *2018 Jean Bourgain *2017 James G. Arthur *2016 Barry Simon *2015 Victor Kac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Congress Of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before 2022 as the Nevanlinna Prize), the Carl Friedrich Gauss Prize, Gauss Prize, and the Chern Medal are awarded during the congress's opening ceremony. Each congress is memorialized by a printed set of Proceedings recording academic papers based on invited talks intended to be relevant to current topics of general interest. Being List of International Congresses of Mathematicians Plenary and Invited Speakers, invited to talk at the ICM has been called "the equivalent ... of an induction to a hall of fame". History German mathematicians Felix Klein and Georg Cantor are credited with putting forward the idea of an international congress of mathematicians in the 1890s.A. John Coleman"Mathematics without borders": a book review. ''CMS Notes'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 List of natural phenomena, natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena. The advancement of science generally depends on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations.There is some debate as to whether or not theoretical physics uses mathematics to build intuition and illustrativeness to extract physical insight (especially when normal experience fails), rather than as a tool in formalizing theories. This links to the question of it using mathematics in a less formally rigorous, and more intuitive or heuristic way than, say, mathematical physics. For example, while developing special relativity, Albert E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lie Algebras
In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi identity. In other words, a Lie algebra is an algebra over a field for which the multiplication operation (called the Lie bracket) is alternating and satisfies the Jacobi identity. The Lie bracket of two vectors x and y is denoted ,y/math>. A Lie algebra is typically a non-associative algebra. However, every associative algebra gives rise to a Lie algebra, consisting of the same vector space with the commutator Lie bracket, ,y= xy - yx . Lie algebras are closely related to Lie groups, which are groups that are also smooth manifolds: every Lie group gives rise to a Lie algebra, which is the tangent space at the identity. (In this case, the Lie bracket measures the failure of commutativity for the Lie group.) Conversely, to any finite-dime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sloan Fellowship
The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. Fellowships were initially awarded in physics, chemistry, and mathematics. Awards were later added in neuroscience (1972), economics (1980), computer science (1993), computational and evolutionary molecular biology (2002), and ocean sciences or earth systems sciences (2012). Winners of these two-year fellowships are awarded $75,000, which may be spent on any expense supporting their research. From 2012 through 2020, the foundation awarded 126 research fellowship each year; in 2021, 128 were awarded, and 118 were awarded in 2022. Eligibility and selection To be eligible, a candidate must hold a Ph.D. or equivalent degree and must be a member of the faculty of a college, university, or other degree-granting institution in the United Sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soviet Union
The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet Union, it dissolved in 1991. During its existence, it was the list of countries and dependencies by area, largest country by area, extending across Time in Russia, eleven time zones and sharing Geography of the Soviet Union#Borders and neighbors, borders with twelve countries, and the List of countries and dependencies by population, third-most populous country. An overall successor to the Russian Empire, it was nominally organized as a federal union of Republics of the Soviet Union, national republics, the largest and most populous of which was the Russian SFSR. In practice, Government of the Soviet Union, its government and Economy of the Soviet Union, economy were Soviet-type economic planning, highly centralized. As a one-party state go ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow Institute Of Electronic Machine Building
Moscow Institute of Electronics and Mathematics, MIEM (; also occasionally referred to as ''Moscow Institute of Electronic Engineering'') — a Russian higher educational institution in the field of electronics, computer engineering, and applied mathematics. History The institute was founded by the joint decree of the Communist Party Central Committee and the USSR government of 21 April 1962 as the ''Moscow Institute of Electronic Machine Building'' () from the ''Moscow Evening Machine Building Institute'' ( (founded in 1929). It was designed to educate personnel for the technologically advanced enterprises of the USSR's military industry. The institute changed over to the current name in 1993, retaining the same abbreviation. In 2011, the institute was incorporated into the National Research University Higher School of Economics. In December 2014, the institute moved to a new building located in the northwestern suburb of Moscow, Strogino, from its previous location at 3 Tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boris Weisfeiler
Boris Weisfeiler (born 19 April 1941 – disappeared 4–5 January 1985) was a Soviet-born mathematician and professor at Penn State University who lived in the United States before disappearing in Chile in 1985. Declassified US documents suggest a Chilean army patrol seized Weisfeiler and took him to Colonia Dignidad, a secretive Germanic agricultural commune set up in Chile in the 1960s. During the Chilean Pinochet military dictatorship Boris Weisfeiler allegedly drowned. He is known for the Weisfeiler filtration, Weisfeiler–Leman algorithm and Kac–Weisfeiler conjectures. Early life and career Weisfeiler, a Jew, was born in the Soviet Union. He received his Ph.D. in 1970 from the Steklov Institute of Mathematics Leningrad Department, as a student of Ernest Vinberg. In the early 1970s, Weisfeiler was asked to sign a letter against a colleague, and for his refusal was branded "anti-Soviet". Weisfeiler left the Soviet Union in 1975 to be free to advance his career and pra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kac Determinant Formula
In mathematics, the Virasoro algebra is a complex Lie algebra and the unique nontrivial central extension of the Witt algebra. It is widely used in two-dimensional conformal field theory and in string theory. It is named after Miguel Ángel Virasoro. Structure The Virasoro algebra is spanned by generators for and the central charge . These generators satisfy ,L_n0 and The factor of \frac is merely a matter of convention. For a derivation of the algebra as the unique central extension of the Witt algebra, see derivation of the Virasoro algebra or Schottenloher, Thm. 5.1, pp. 79. The Virasoro algebra has a presentation in terms of two generators (e.g. 3 and −2) and six relations. The generators L_ are called annihilation modes, while L_ are creation modes. A basis of creation generators of the Virasoro algebra's universal enveloping algebra is the set : \mathcal = \Big\_ For L\in \mathcal, let , L, = \sum_^k n_i, then _0,L= , L, L. Representation theory In any i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lie Superalgebra
In mathematics, a Lie superalgebra is a generalisation of a Lie algebra to include a \Z/2\Z grading. Lie superalgebras are important in theoretical physics where they are used to describe the mathematics of supersymmetry. The notion of \Z/2\Z grading used here is distinct from a second \Z/2\Z grading having cohomological origins. A graded Lie algebra (say, graded by \Z or \N) that is anticommutative and has a graded Jacobi identity also has a \Z/2\Z grading; this is the "rolling up" of the algebra into odd and even parts. This rolling-up is not normally referred to as "super". Thus, supergraded Lie superalgebras carry a ''pair'' of \Z/2\Zgradations: one of which is supersymmetric, and the other is classical. Pierre Deligne calls the supersymmetric one the ''super gradation'', and the classical one the ''cohomological gradation''. These two gradations must be compatible, and there is often disagreement as to how they should be regarded. Definition Formally, a Lie superalgebra is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Macdonald Identities
In mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ..., the Macdonald identities are some infinite product identities associated to affine root systems, introduced by . They include as special cases the Jacobi triple product identity, Watson's quintuple product identity, several identities found by , and a 10-fold product identity found by . and pointed out that the Macdonald identities are the analogs of the Weyl denominator formula for affine Kac–Moody algebras and superalgebras. References * * * * * *{{Citation , last1=Winquist , first1=Lasse , title=An elementary proof of p(11m+6) ≡ 0 mod 11 , mr=0236136 , year=1969 , journal=Journal of Combinatorial Theory , volume=6 , pages=56–59 , doi=10.1016/s0021-9800(69)80105-5, doi-access=free Lie al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
