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Gregory Margulis
Grigory Aleksandrovich Margulis (, 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 (with Hillel Furstenberg), 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 David Kazhdan produced the Kazhdan–Margulis theorem, a ... [...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] |
Oppenheim Conjecture
In Diophantine approximation, a subfield of number theory, 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 Margulis, settling the conjecture in the affirmative, used methods arising from ergodic theory and the study of discrete subgroups of semisimple Lie groups. Overview 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 ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russians
Russians ( ) are an East Slavs, East Slavic ethnic group native to Eastern Europe. Their mother tongue is Russian language, Russian, the most spoken Slavic languages, Slavic language. The majority of Russians adhere to Eastern Orthodox Church, Orthodox Christianity, ever since the Middle Ages. By total numbers, they compose the largest Slavs, Slavic and Ethnic groups in Europe, European nation. Genetic studies show that Russians are closely related to Polish people, Poles, Belarusians, Ukrainians, as well as Estonians, Latvians, Lithuanians, and Finns. They were formed from East Slavic tribes, and their cultural ancestry is based in Kievan Rus'. The Russian word for the Russians is derived from the Names of Rus', Russia and Ruthenia, people of Rus' and the territory of Rus'. Russians share many historical and cultural traits with other European peoples, and especially with other East Slavic ethnic groups, specifically Belarusians and Ukrainians. The vast majority of Russians ... [...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 (1803–18 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The New York Times
''The New York Times'' (''NYT'') is an American daily newspaper based in New York City. ''The New York Times'' covers domestic, national, and international news, and publishes opinion pieces, investigative reports, and reviews. As one of the longest-running newspapers in the United States, the ''Times'' serves as one of the country's Newspaper of record, newspapers of record. , ''The New York Times'' had 9.13 million total and 8.83 million online subscribers, both by significant margins the List of newspapers in the United States, highest numbers for any newspaper in the United States; the total also included 296,330 print subscribers, making the ''Times'' the second-largest newspaper by print circulation in the United States, following ''The Wall Street Journal'', also based in New York City. ''The New York Times'' is published by the New York Times Company; since 1896, the company has been chaired by the Ochs-Sulzberger family, whose current chairman and the paper's publ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hillel Furstenberg
Hillel "Harry" Furstenberg (; born September 29, 1935) is a German-born American-Israeli mathematician and professor emeritus at the Hebrew University of Jerusalem. He is a member of the Israel Academy of Sciences and Humanities and U.S. National Academy of Sciences and a laureate of the Abel Prize and the Wolf Prize in Mathematics. He is known for his application of probability theory and ergodic theory methods to other areas of mathematics, including number theory and Lie groups. Biography Furstenberg was born to German Jews in Nazi Germany, in 1935 (originally named "Fürstenberg"). In 1939, shortly after Kristallnacht, his family escaped to the United States and settled in the Washington Heights neighborhood of New York City, escaping the Holocaust. He attended Marsha Stern Talmudical Academy and then Yeshiva University, where he concluded his BA and MSc studies at the age of 20 in 1955. Furstenberg published several papers as an undergraduate, including "''Note on one ... [...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 ''p''/''q'' is a "good" approximation of a real number ''α'' if the absolute value of the difference between ''p''/''q'' and ''α'' may not decrease if ''p''/''q'' is replaced by another rational number with a smaller denominator. This problem was solved during the 18th century by means of simple 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 i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ergodic Theory
Ergodic theory is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, "statistical properties" refers to 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 phase space eventua ... [...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 a ... [...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, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); 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's theorem. The number of known mathematicians grew when Pythagoras of Samos () 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 math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russian-American
Russian Americans are Americans of full or partial Russian ancestry. The term can apply to recent Russian immigrants to the United States, as well as to those that settled in the 19th-century Russian possessions in what is now Alaska. Russian Americans comprise the largest Eastern European and East Slavic population in the United States, the second-largest Slavic population after Polish Americans, 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 US, including Russian Jews and Spiritual Christians. From 1880 to 1917, within the wave of European immigration to the US that occurred during that period, a large number of Russians immigrated primarily for economic opportunities. These groups mainly settled in coastal cities, including Brooklyn (New York City) on the Northeastern United States, East Coast, and Los Angeles, San Francisco, Portland, Or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
