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Dolgachev
Igor V. Dolgachev (born 7 April 1944) is a Russian–American mathematician specializing in algebraic geometry. He has been a professor at the University of Michigan since 1978. He introduced Dolgachev surfaces in 1981. Dolgachev completed his Ph.D. at Moscow State University in 1970, with thesis ''On the purity of the degeneration locus of families of curves'' written under the supervision of Igor Shafarevich Igor Rostislavovich Shafarevich (; 3 June 1923 – 19 February 2017) was a Soviet and Russian mathematician who contributed to algebraic number theory and algebraic geometry. Outside mathematics, he wrote books and articles that criticised social .... References External links Dolgachev's website at University of Michigan 1944 births Living people Moscow State University alumni Soviet mathematicians Russian mathematicians 20th-century American mathematicians 21st-century American mathematicians University of Michigan faculty Algebraic geometers {{Rus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dolgachev Surface
In mathematics, Dolgachev surfaces are certain simply connected elliptic surfaces, introduced by . They can be used to give examples of an infinite family of homeomorphic simply connected compact 4-manifolds, no two of which are diffeomorphic. Properties The blowup X_0 of the projective plane in 9 points can be realized as an elliptic fibration all of whose fibers are irreducible. A Dolgachev surface X_q is given by applying logarithmic transformations of orders 2 and ''q'' to two smooth fibers for some q\ge 3. The Dolgachev surfaces are simply connected, and the bilinear form on the second cohomology group is odd of signature (1,9) (so it is the unimodular lattice I_). The geometric genus p_g is 0 and the Kodaira dimension is 1. found the first examples of simply-connected homeomorphic but not diffeomorphic 4-manifolds X_0 and X_3. More generally the surfaces X_q and X_r are always homeomorphic, but are not diffeomorphic unless q=r. showed that the Dolgachev surfac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Igor Shafarevich
Igor Rostislavovich Shafarevich (; 3 June 1923 – 19 February 2017) was a Soviet and Russian mathematician who contributed to algebraic number theory and algebraic geometry. Outside mathematics, he wrote books and articles that criticised socialism and other books which were described as anti-semitic. Mathematics From his early years, Shafarevich made fundamental contributions to several parts of mathematics including algebraic number theory, algebraic geometry and arithmetic algebraic geometry. In particular, in algebraic number theory, the Shafarevich–Weil theorem extends the commutative reciprocity map to the case of Galois groups, which are central extensions of abelian groups by finite groups. Shafarevich was the first mathematician to give a completely self-contained formula for the Hilbert pairing, thus initiating an important branch of the study of explicit formulas in number theory. Another famous (and slightly incomplete) result is Shafarevich's theorem on solvable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Michigan
The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Michigan is one of the earliest American research universities and is a founding member of the Association of American Universities. In the fall of 2023, the university employed 8,189 faculty members and enrolled 52,065 students in its programs. The university is Carnegie Classification of Institutions of Higher Education, classified among "R1: Doctoral Universities – Very high research activity". It consists of nineteen colleges and offers 250 degree programs at the undergraduate and graduate levels. The university is Higher education accreditation in the United States, accredited by the Higher Learning Commission. In 2021, it ranked third among American universities in List of countries by research and development spending, research expe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow State University
Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, and six branches. Alumni of the university include past leaders of the Soviet Union and other governments. As of 2019, 13 List of Nobel laureates, Nobel laureates, six Fields Medal winners, and one Turing Award winner were affiliated with the university. History Imperial Moscow University Ivan Shuvalov and Mikhail Lomonosov promoted the idea of a university in Moscow, and Elizabeth of Russia, Russian Empress Elizabeth decreed its establishment on . The first lectures were given on . Saint Petersburg State University and MSU each claim to be Russia's oldest university. Though Moscow State University was founded in 1755, St. Petersburg which has had a continuous existence as a "university" since 1819 sees itself as the successor of an a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects. The fundamental objects of study in algebraic geometry are algebraic variety, algebraic varieties, which are geometric manifestations of solution set, solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are line (geometry), lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscate of Bernoulli, lemniscates and Cassini ovals. These are plane algebraic curves. A point of the plane lies on an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of points of special interest like singular point of a curve, singular 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] |
1944 Births
Events Below, the events of World War II have the "WWII" prefix. January * January 2 – WWII: ** Free France, Free French General Jean de Lattre de Tassigny is appointed to command First Army (France), French Army B, part of the Sixth United States Army Group in North Africa. ** Landing at Saidor: 13,000 US and Australian troops land on Papua New Guinea in an attempt to cut off a Japanese retreat. * January 8 – WWII: Philippine Commonwealth troops enter the province of Ilocos Sur in northern Luzon and attack Japanese forces. * January 11 ** United States President Franklin D. Roosevelt proposes a Second Bill of Rights for social and economic security, in his State of the Union address. ** The Nazi German administration expands Kraków-Płaszów concentration camp into the larger standalone ''Konzentrationslager Plaszow bei Krakau'' in occupied Poland. * January 12 – WWII: Winston Churchill and Charles de Gaulle begin a 2-day conference in Marrakech. * Janua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Purpose: Because living persons may suffer personal harm from inappropriate information, we should watch their articles carefully. By adding an article to this category, it marks them with a notice about sources whenever someone tries to edit them, to remind them of WP:BLP (biographies of living persons) policy that these articles must maintain a neutral point of view, maintain factual accuracy, and be properly sourced. Recent changes to these articles are listed on Special:RecentChangesLinked/Living people. Organization: This category should not be sub-categorized. Entries are generally sorted by family name In many societies, a surname, family name, or last name is the mostly hereditary portion of one's personal name that indicates one's family. It is typically combined with a given name to form the full name of a person, although several give .... Maintenance: Individuals of advanced age (over 90), for whom there has been no new documentation in the last ten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow State University Alumni
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] |
Soviet 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] |
