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Grigori Margulis
Grigory Aleksandrovich Margulis (russian: Григо́рий Алекса́ндрович Маргу́лис, first name often given as Gregory, Grigori or Gregori; born February 24, 1946) is a Russian-American mathematician known for his work on lattices in Lie groups, and the introduction of methods from ergodic theory into diophantine approximation. He was awarded a Fields Medal in 1978, a Wolf Prize in Mathematics in 2005, and an Abel Prize in 2020, becoming the fifth mathematician to receive the three prizes. In 1991, he joined the faculty of Yale University, where he is currently the Erastus L. De Forest Professor of Mathematics. Biography Margulis was born to a Russian family of Lithuanian Jewish descent in Moscow, Soviet Union. At age 16 in 1962 he won the silver medal at the International Mathematical Olympiad. He received his PhD in 1970 from the Moscow State University, starting research in ergodic theory under the supervision of Yakov Sinai. Early work with Da ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow
Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million residents within the city limits, over 17 million residents in the urban area, and over 21.5 million residents in the 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 largest cities; being the most populous city entirely in Europe, the largest urban and metropolitan area in Europe, and the largest city by land area on the European continent. First documented in 1147, Moscow grew to become a prosperous and powerful city that served as the capital of the Grand Duchy that bears its name. When the Grand Duchy of Moscow evolved into the Tsardom of Russia, Moscow remained the political and economic center for most of the Tsardom's history. When th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oppenheim Conjecture
In Diophantine approximation, the Oppenheim conjecture concerns representations of numbers by real quadratic forms in several variables. It was formulated in 1929 by Alexander Oppenheim and later the conjectured property was further strengthened by Harold Davenport and Oppenheim. Initial research on this problem took the number ''n'' of variables to be large, and applied a version of the Hardy-Littlewood circle method. The definitive work of Grigory Margulis, Margulis, settling the conjecture in the affirmative, used methods arising from ergodic theory and the study of discrete subgroups of semisimple Lie groups. Short description Meyer's theorem states that an indefinite integral quadratic form ''Q'' in ''n'' variables, ''n'' ≥ 5, nontrivially represents zero, i.e. there exists a non-zero vector ''x'' with integer components such that ''Q''(''x'') = 0. The Oppenheim conjecture can be viewed as an analogue of this statement for forms ''Q'' that are not multi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Mathematical Olympiad
The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except in 1980. More than 100 countries, representing over 90% of the world's population, send teams of up to six students, plus one team leader, one deputy leader, and observers. The content ranges from extremely difficult algebra and pre-calculus problems to problems on branches of mathematics not conventionally covered in secondary or high school and often not at university level either, such as projective and complex geometry, functional equations, combinatorics, and well-grounded number theory, of which extensive knowledge of theorems is required. Calculus, though allowed in solutions, is never required, as there is a principle that anyone with a basic understanding of mathematics should understand the problems, even if the solutions require ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lithuanian Jews
Lithuanian Jews or Litvaks () are Jews with roots in the territory of the former Grand Duchy of Lithuania (covering present-day Lithuania, Belarus, Latvia, the northeastern Suwałki and Białystok regions of Poland, as well as adjacent areas of modern-day Russia and Ukraine). The term is sometimes used to cover all Haredi Jews who follow a " Lithuanian" ( Ashkenazi, non- Hasidic) style of life and learning, whatever their ethnic background. The area where Lithuanian Jews lived is referred to in Yiddish as , hence the Hebrew term (). No other famous Jew is more closely linked to a specifically Lithuanian city than Vilna Gaon (in Yiddish, "the genius of Vilna"). Rabbi Elijah ben Solomon Zalman (1720–1797) to give his rarely used full name, helped make Vilna (modern-day Vilnius) a world center for Talmudic learning. Chaim Grade (1910–1982) was born in Vilna, the city about which he would write. The inter-war Republic of Lithuania was home to a large and influential Jewish ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russians
, native_name_lang = ru , image = , caption = , population = , popplace = 118 million Russians in the Russian Federation (2002 ''Winkler Prins'' estimate) , region1 = , pop1 = approx. 7,500,000 (including Russian Jews and Russian Germans) , ref1 = , region2 = , pop2 = 7,170,000 (2018) ''including Crimea'' , ref2 = , region3 = , pop3 = 3,512,925 (2020) , ref3 = , region4 = , pop4 = 3,072,756 (2009)(including Russian Jews and Russian Germans) , ref4 = , region5 = , pop5 = 1,800,000 (2010)(Russian ancestry and Russian Germans and Jews) , ref5 = 35,000 (2018)(born in Russia) , region6 = , pop6 = 938,500 (2011)(including Russian Jews) , ref6 = , region7 = , pop7 = 809,530 (2019) , ref7 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erastus L
Erastus is a masculine given name which may refer to: Biblical figures: * Erastus of Corinth, in the New Testament of the Bible People: * Erastus of Scepsis, 4th century BC student of Plato * Erastus Newton Bates (1828–1898), American politician and Civil War brigadier general * Erastus Flavel Beadle (1821–1894), American printer and pioneer publisher of pulp fiction * Erastus C. Benedict (1800–1880), American lawyer and politician * Erastus Brigham Bigelow (1814–1879), inventor of weaving machines * Erastus Brooks (1815–1886), American newspaper editor and politician * Erastus Corning (1794–1872), businessman and politician * Erastus Corning 2nd (1909–1983), mayor of Albany, New York, great-grandson of the above * Erastus Milo Cravath (1833–1900), American abolitionist, field secretary with the American Missionary Association, co-founder and president of Fisk University and founder of numerous other historically black colleges * Erastus D. Culver (1803–1889), A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diophantine Approximation
In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria. The first problem was to know how well a real number can be approximated by rational numbers. For this problem, a rational number ''a''/''b'' is a "good" approximation of a real number ''α'' if the absolute value of the difference between ''a''/''b'' and ''α'' may not decrease if ''a''/''b'' is replaced by another rational number with a smaller denominator. This problem was solved during the 18th century by means of continued fractions. Knowing the "best" approximations of a given number, the main problem of the field is to find sharp upper and lower bounds of the above difference, expressed as a function of the denominator. It appears that these bounds depend on the nature of the real numbers to be approximated: the lower bound for the approximation of a rational number by another rational number is larger than ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ergodic Theory
Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expressed through the behavior of time averages of various functions along trajectories of dynamical systems. The notion of deterministic dynamical systems assumes that the equations determining the dynamics do not contain any random perturbations, noise, etc. Thus, the statistics with which we are concerned are properties of the dynamics. Ergodic theory, like probability theory, is based on general notions of measure theory. Its initial development was motivated by problems of statistical physics. A central concern of ergodic theory is the behavior of a dynamical system when it is allowed to run for a long time. The first result in this direction is the Poincaré recurrence theorem, which claims that almost all points in any subset of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice (discrete Subgroup)
In Lie theory and related areas of mathematics, a lattice in a locally compact group is a discrete subgroup with the property that the quotient space has finite invariant measure. In the special case of subgroups of R''n'', this amounts to the usual geometric notion of a lattice as a periodic subset of points, and both the algebraic structure of lattices and the geometry of the space of all lattices are relatively well understood. The theory is particularly rich for lattices in semisimple Lie groups or more generally in semisimple algebraic groups over local fields. In particular there is a wealth of rigidity results in this setting, and a celebrated theorem of Grigory Margulis states that in most cases all lattices are obtained as arithmetic groups. Lattices are also well-studied in some other classes of groups, in particular groups associated to Kac–Moody algebras and automorphisms groups of regular trees (the latter are known as ''tree lattices''). Lattices are of inter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russian-American
Russian Americans ( rus, русские американцы, r=russkiye amerikantsy, p= ˈruskʲɪje ɐmʲɪrʲɪˈkant͡sɨ) are Americans of full or partial Russians, Russian ancestry. The term can apply to recent Russian diaspora, Russian immigrants to the United States, as well as to those who settled in the 19th-century Russian America, Russian possessions in northwestern America. Russian Americans comprise the largest Eastern European and East Slavs, East Slavic population in the U.S., the second-largest Slavic Americans, Slavic population generally, the nineteenth-largest ancestry group overall, and the eleventh-largest from Europe. In the mid-19th century, waves of Russian immigrants fleeing religious persecution settled in the U.S., including Russian Jews and Spiritual Christians. These groups mainly settled in coastal cities, including Alaska, Brooklyn (New York City) on the Northeastern United States, East Coast, and Los Angeles, San Francisco, and Portland, Oregon, on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abel Prize
The Abel Prize ( ; no, Abelprisen ) is awarded annually by the King of Norway to one or more outstanding mathematicians. It is named after the Norwegian mathematician Niels Henrik Abel (1802–1829) and directly modeled after the Nobel Prizes. It comes with a monetary award of 7.5 million Norwegian kroner (NOK; increased from 6 million NOK in 2019). The Abel Prize's history dates back to 1899, when its establishment was proposed by the Norwegian mathematician Sophus Lie when he learned that Alfred Nobel's plans for annual prizes would not include a prize in mathematics. In 1902, King Oscar II of Sweden and Norway indicated his willingness to finance the creation of a mathematics prize to complement the Nobel Prizes, but the establishment of the prize was prevented by the dissolution of the union between Norway and Sweden in 1905. It took almost a century before the prize was finally established by the Government of Norway in 2001, and it was specifically intended "to give t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
