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Ivan Cherednik
Ivan Cherednik (Иван Владимирович Чередник) is a Russian-American mathematician. He introduced double affine Hecke algebras, and used them to prove Macdonald's constant term conjecture in . He has also dealt with algebraic geometry, number theory and Soliton equations. His research interests include representation theory, mathematical physics, and algebraic combinatorics. He is currently the Austin M. Carr Distinguished Professor of mathematics at the University of North Carolina at Chapel Hill. In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. See also *Dyson conjecture *Macdonald polynomials *Yangian In representation theory, a Yangian is an infinite-dimensional Hopf algebra, a type of a quantum group. Yangians first appeared in physics in the work of Ludvig Faddeev and his school in the late 1970s and early 1980s concerning the quantum inverse ... Publications * * * References *University of North Caroli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow
Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents within the city limits, over 19.1 million residents in the urban area, and over 21.5 million residents in Moscow metropolitan area, its metropolitan area. The city covers an area of , while the urban area covers , and the metropolitan area covers over . Moscow is among the world's List of largest cities, largest cities, being the List of European cities by population within city limits, most populous city entirely in Europe, the largest List of urban areas in Europe, urban and List of metropolitan areas in Europe, metropolitan area in Europe, and the largest city by land area on the European continent. First documented in 1147, Moscow became the capital of the Grand Principality of Moscow, which led the unification of the Russian lan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Physics
Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics, known as physical mathematics. Scope There are several distinct branches of mathematical physics, and these roughly correspond to particular historical parts of our world. Classical mechanics Applying the techniques of mathematical physics to classical mechanics typically involves the rigorous, abstract, and advanced reformulation of Newtonian mechanics in terms of Lagrangian mechanics and Hamiltonian mechanics (including both approaches in the presence of constraints). Both formulations are embodied in analytical mechanics and lead ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of North Carolina At Chapel Hill Faculty
A university () is an institution of tertiary education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase , which roughly means "community of teachers and scholars". Universities typically offer both undergraduate and postgraduate programs. The first universities in Europe were established by Catholic monks. The University of Bologna (), Italy, which was founded in 1088, is the first university in the sense of: *being a high degree-awarding institute. *using the word (which was coined at its foundation). *having independence from the ecclesiastic schools and issuing secular as well as non-secular degrees (with teaching conducted by both clergy and non-clergy): grammar, rhetoric, logic, theology, canon law and notarial law.Hunt Janin: "The university in medieval life, 1179–1499", McFarland, 2008, , p. 55f.de Ridder-Symoens, Hilde''A History of the University in Europe: Volume 1, Universities in the M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century American Mathematicians
File:1st century collage.png, From top left, clockwise: Jesus is crucified by Roman authorities in Judaea (17th century painting). Four different men ( Galba, Otho, Vitellius, and Vespasian) claim the title of Emperor within the span of a year; The Great Fire of Rome (18th-century painting) sees the destruction of two-thirds of the city, precipitating the empire's first persecution against Christians, who are blamed for the disaster; The Roman Colosseum is built and holds its inaugural games; Roman forces besiege Jerusalem during the First Jewish–Roman War (19th-century painting); The Trưng sisters lead a rebellion against the Chinese Han dynasty (anachronistic depiction); Boudica, queen of the British Iceni leads a rebellion against Rome (19th-century statue); Knife-shaped coin of the Xin dynasty., 335px rect 30 30 737 1077 Crucifixion of Jesus rect 767 30 1815 1077 Year of the Four Emperors rect 1846 30 3223 1077 Great Fire of Rome rect 30 1108 1106 2155 Boudic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russian Mathematicians
This list of Russian mathematicians includes the famous mathematicians from the Russian Empire, the Soviet Union and the Russian Federation. Alphabetical list __NOTOC__ A *Georgy Adelson-Velsky, inventor of AVL tree algorithm, developer of Kaissa, the first world computer chess champion *Sergei Adian, known for his work in group theory, especially on the Burnside problem *Aleksandr Danilovich Aleksandrov, Aleksandr Aleksandrov, developer of CAT(k) space and Alexandrov's uniqueness theorem in geometry *Pavel Alexandrov, author of the Alexandroff compactification and the Alexandrov topology *Dmitri Anosov, developed Anosov diffeomorphism *Vladimir Arnold, an author of the Kolmogorov–Arnold–Moser theorem in dynamical systems, solved Hilbert's 13th problem, raised the ADE classification and Arnold's rouble problems B *Alexander Beilinson, influential mathematician in representation theory, algebraic geometry and mathematical physics *Sergey Bernstein, developed the Bernstein p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessment to form Cambridge University Press and Assessment under Queen Elizabeth II's approval in August 2021. With a global sales presence, publishing hubs, and offices in more than 40 countries, it published over 50,000 titles by authors from over 100 countries. Its publications include more than 420 academic journals, monographs, reference works, school and university textbooks, and English language teaching and learning publications. It also published Bibles, runs a bookshop in Cambridge, sells through Amazon, and has a conference venues business in Cambridge at the Pitt Building and the Sir Geoffrey Cass Sports and Social Centre. It also served as the King's Printer. Cambridge University Press, as part of the University of Cambridge, was a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the founding editor-in-chief. It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering". It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two. This incarnation of the journal ceased publication after its tenth year, in 1883, giving as an explanation Hendricks' declining health, but Hendricks made arrangements to have it taken over by new management, and it was continued from March 1884 as the ''Annals of Mathematics''. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yangian
In representation theory, a Yangian is an infinite-dimensional Hopf algebra, a type of a quantum group. Yangians first appeared in physics in the work of Ludvig Faddeev and his school in the late 1970s and early 1980s concerning the quantum inverse scattering method. The name ''Yangian'' was introduced by Vladimir Drinfeld in 1985 in honor of C.N. Yang. Initially, they were considered a convenient tool to generate the solutions of the quantum Yang–Baxter equation. The center of the Yangian can be described by the quantum determinant. The Yangian is a degeneration of the quantum loop algebra (i.e. the quantum affine algebra at vanishing central charge). Description For any finite-dimensional semisimple Lie algebra ''a'', Drinfeld defined an infinite-dimensional Hopf algebra ''Y''(''a''), called the Yangian of ''a''. This Hopf algebra is a deformation of the universal enveloping algebra ''U''(''a'' 'z'' of the Lie algebra of polynomial loops of ''a'' given by explicit generat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Macdonald Polynomials
In mathematics, Macdonald polynomials ''P''λ(''x''; ''t'',''q'') are a family of orthogonal symmetric polynomials in several variables, introduced by Macdonald in 1987. He later introduced a non-symmetric generalization in 1995. Macdonald originally associated his polynomials with weights λ of finite root systems and used just one variable ''t'', but later realized that it is more natural to associate them with affine root systems rather than finite root systems, in which case the variable ''t'' can be replaced by several different variables ''t''=(''t''1,...,''tk''), one for each of the ''k'' orbits of roots in the affine root system. The Macdonald polynomials are polynomials in ''n'' variables ''x''=(''x''1,...,''xn''), where ''n'' is the rank of the affine root system. They generalize many other families of orthogonal polynomials, such as Jack polynomials and Hall–Littlewood polynomials and Askey–Wilson polynomials, which in turn include most of the named orthogona ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dyson Conjecture
In mathematics, the Dyson conjecture is a conjecture about the constant term of certain Laurent polynomials, proved independently in 1962 by Wilson and Gunson. Andrews generalized it to the q-Dyson conjecture, proved by Zeilberger and Bressoud and sometimes called the Zeilberger–Bressoud theorem. Macdonald generalized it further to more general root systems with the Macdonald constant term conjecture, proved by Cherednik. Dyson conjecture The Dyson conjecture states that the Laurent polynomial :\prod_(1-t_i/t_j)^ has constant term :\frac. The conjecture was first proved independently by and . later found a short proof, by observing that the Laurent polynomials, and therefore their constant terms, satisfy the recursion relations :F(a_1,\dots,a_n) = \sum_^nF(a_1,\dots,a_i-1,\dots,a_n). The case ''n'' = 3 of Dyson's conjecture follows from the Dixon identity. and used a computer to find expressions for non-constant coefficients of Dyson's Laurent poly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
