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Vyacheslav Shokurov
Vyacheslav Vladimirovich Shokurov (russian: Вячеслав Владимирович Шокуров; born 18 May 1950) is a Russian mathematician best known for his research in algebraic geometry. The proof of the Noether–Enriques–Petri theorem, the cone theorem, the existence of a line on smooth Fano varieties and, finally, the existence of log flips—these are several of Shokurov's contributions to the subject. Early years In 1968 Shokurov became a student at the Faculty of Mechanics and Mathematics of Moscow State University. Already as an undergraduate, Shokurov showed himself to be a mathematician of outstanding talent. In 1970, he proved the scheme analog of the Noether–Enriques–Petri theorem, which later allowed him to solve a Schottky-type problem for the polarized Prym varieties, and to prove the existence of a line on smooth Fano varieties. Upon his graduation Shokurov entered the Ph.D. program in Moscow State University under the supervision of Yuri Man ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cone Of Curves
In mathematics, the cone of curves (sometimes the Kleiman-Mori cone) of an algebraic variety X is a combinatorial invariant of importance to the birational geometry of X. Definition Let X be a proper variety. By definition, a (real) ''1-cycle'' on X is a formal linear combination C=\sum a_iC_i of irreducible, reduced and proper curves C_i, with coefficients a_i \in \mathbb. ''Numerical equivalence'' of 1-cycles is defined by intersections: two 1-cycles C and C' are numerically equivalent if C \cdot D = C' \cdot D for every Cartier divisor D on X. Denote the real vector space of 1-cycles modulo numerical equivalence by N_1(X). We define the ''cone of curves'' of X to be : NE(X) = \left\ where the C_i are irreducible, reduced, proper curves on X, and _i/math> their classes in N_1(X). It is not difficult to see that NE(X) is indeed a convex cone in the sense of convex geometry. Applications One useful application of the notion of the cone of curves is the Kleiman conditi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cone Theorem
In mathematics, the cone of curves (sometimes the Kleiman-Mori cone) of an algebraic variety X is a combinatorial invariant of importance to the birational geometry of X. Definition Let X be a proper variety. By definition, a (real) ''1-cycle'' on X is a formal linear combination C=\sum a_iC_i of irreducible, reduced and proper curves C_i, with coefficients a_i \in \mathbb. ''Numerical equivalence'' of 1-cycles is defined by intersections: two 1-cycles C and C' are numerically equivalent if C \cdot D = C' \cdot D for every Cartier divisor D on X. Denote the real vector space of 1-cycles modulo numerical equivalence by N_1(X). We define the ''cone of curves'' of X to be : NE(X) = \left\ where the C_i are irreducible, reduced, proper curves on X, and _i/math> their classes in N_1(X). It is not difficult to see that NE(X) is indeed a convex cone in the sense of convex geometry. Applications One useful application of the notion of the cone of curves is the Kleiman condition, w ... [...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] |
Vasily Iskovskikh
Vasili, Vasily, Vasilii or Vasiliy (Russian: Василий) is a Russian masculine given name of Greek origin and corresponds to ''Basil''. It may refer to: *Vasili I of Moscow Grand Prince from 1389–1425 *Vasili II of Moscow Grand Prince from 1425–1462 *Vasili III of Russia Tsar from 1505–1533 *Vasili IV of Russia Tsar from 1606–1610 *Basil Fool for Christ (1469–1557), also known as Saint Basil, or Vasily Blazhenny *Vasily Alekseyev (1942–2011), Soviet weightlifter *Vasily Arkhipov (1926–1998), Soviet Naval officer in the Cuban Missile Crisis *Vasily Boldyrev (1875–1933), Russian general *Vasily Chapayev (1887–1919), Russian Army commander *Vasily Chuikov (1900–1982), Soviet marschal *Vasily Degtyaryov (1880–1949), Russian weapons designer and Major General *Vasily Dzhugashvili (1921–1962), Stalin's son *Vasili Golovachov (born 1948), Russian science fiction author *Vasily Grossman (1905–1964), Soviet writer and journalist *Vasily Ignatenko (1961–1986 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematicians From Moscow
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 Hypatia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics () is an area of knowledge that includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures ( algebra), shapes and spaces in which they are contained ( geometry), and quantities and their changes ( calculus and analysis). There is no general consensus about its exact scope or epistemological status. Most of mathematical activity consists of discovering and proving (by pure reasoning) properties of abstract objects. These objects are either abstractions from nature (such as natural numbers or lines), or (in modern mathematics) abstract entities of which certain properties, called axioms, are stipulated. A proof consists of a succession of applications of some deductive rules to already known results, including previously proved theorems, axioms and (in case of abstraction from nature) some basic properties that are considered as true starting points of the theory under consideration. The result of a proof i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russian Mathematical Surveys
''Uspekhi Matematicheskikh Nauk'' (russian: Успехи математических наук) is a Russian mathematical journal, published by the Russian Academy of Sciences and Moscow Mathematical Society and translated into English as ''Russian Mathematical Surveys''. ''Uspekhi Matematicheskikh Nauk'' was founded in 1936, with Lazar Lyusternik as its editor-in-chief. Initially, it appeared irregularly, with issues devoted to specific topics within mathematics together with non-research articles about the work of different mathematical institutes in Russia and abroad. Its third issue, in 1937, was devoted to attacks on Nikolai Luzin, but in an anniversary issue 24 years later this politicization of the journal was downplayed. After a hiatus for World War II, the journal began publishing on a regular schedule in 1946. Its translation, ''Russian Mathematical Surveys'', began in 1960 and since 1997 has been published jointly by the London Mathematical Society, Turpion Ltd, and the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fields Medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award honours the Canadian mathematician John Charles Fields. The Fields Medal is regarded as one of the highest honors a mathematician can receive, and has been described as the Nobel Prize of Mathematics, although there are several major differences, including frequency of award, number of awards, age limits, monetary value, and award criteria. According to the annual Academic Excellence Survey by ARWU, the Fields Medal is consistently regarded as the top award in the field of mathematics worldwide, and in another reputation survey conducted by IREG in 2013–14, the Fields Medal came closely after the Abel Prize as the second most prestigious international award in mathematics. The prize includes a monetary award which, since 2006, has bee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baltimore
Baltimore ( , locally: or ) is the most populous city in the U.S. state of Maryland, fourth most populous city in the Mid-Atlantic, and the 30th most populous city in the United States with a population of 585,708 in 2020. Baltimore was designated an independent city by the Constitution of Maryland in 1851, and today is the most populous independent city in the United States. As of 2021, the population of the Baltimore metropolitan area was estimated to be 2,838,327, making it the 20th largest metropolitan area in the country. Baltimore is located about north northeast of Washington, D.C., making it a principal city in the Washington–Baltimore combined statistical area (CSA), the third-largest CSA in the nation, with a 2021 estimated population of 9,946,526. Prior to European colonization, the Baltimore region was used as hunting grounds by the Susquehannock Native Americans, who were primarily settled further northwest than where the city was later built. Colonist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James McKernan
James McKernan (born 1964) is a mathematician, and a professor of mathematics at the University of California, San Diego. He was a professor at MIT from 2007 until 2013. Education McKernan was educated at the Campion School, Hornchurch, and Trinity College, Cambridge, before going on to earn his Ph.D. from Harvard University in 1991. His dissertation, ''On the Hyperplane Sections of a Variety in Projective Space'', was supervised by Joe Harris. Recognition McKernan was the joint winner of the Cole Prize in 2009, and joint recipient of the Clay Research Award in 2007. Both honors were received jointly with his colleague Christopher Hacon. He gave an invited talk at the International Congress of Mathematicians in 2010, on the topic of "Algebraic Geometry". He was the joint winner (with Christopher Hacon) of the 2018 Breakthrough Prize in Mathematics. He was elected as a Fellow of the American Mathematical Society The American Mathematical Society (AMS) is an association ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christopher Hacon
Christopher Derek Hacon (born 14 February 1970) is a mathematician with British, Italian and US nationalities. He is currently distinguished professor of mathematics at the University of Utah where he holds a Presidential Endowed Chair. His research interests include algebraic geometry. Hacon was born in Manchester, but grew up in Italy where he studied at the Scuola Normale Superiore and received a degree in mathematics at the University of Pisa in 1992. He received his doctorate from the University of California, Los Angeles in 1998, under supervision of Robert Lazarsfeld. Awards and honors In 2007, he was awarded a Clay Research Award for his work, joint with James McKernan, on "the birational geometry of algebraic varieties in dimension greater than three, in particular, for ninductive proof of the existence of flips." In 2009, he was awarded the Cole Prize for outstanding contribution to algebra, along with McKernan. He was an invited speaker at the Internationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shigefumi Mori
is a Japanese mathematician, known for his work in algebraic geometry, particularly in relation to the classification of three-folds. Career Mori completed his Ph.D. titled "The Endomorphism Rings of Some Abelian Varieties" under Masayoshi Nagata at Kyoto University in 1978. He was visiting professor at Harvard University during 1977–1980, the Institute for Advanced Study in 1981–82, Columbia University 1985–87 and the University of Utah for periods during 1987–89 and again during 1991–92. He has been a professor at Kyoto University since 1990. Work He generalized the classical approach to the classification of algebraic surfaces to the classification of algebraic three-folds. The classical approach used the concept of minimal model (birational geometry), minimal models of algebraic surfaces. He found that the concept of minimal model (birational geometry), minimal models can be applied to three-folds as well if we allow some Singularity (mathematics), singularities on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
