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Kolyvagin
Victor Alexandrovich Kolyvagin (, born 11 March, 1955) is a Russian mathematician who wrote a series of papers on Euler systems, leading to breakthroughs on the Birch and Swinnerton-Dyer conjecture, and Iwasawa's conjecture for cyclotomic fields. His work also influenced Andrew Wiles's work on Fermat's Last Theorem. Career Kolyvagin received his Ph.D. in Mathematics in 1981 from Moscow State University, where his advisor was Yuri I. Manin. He then worked at Steklov Institute of Mathematics in Moscow until 1994. Since 1994 he has been a professor of mathematics in the United States. He was a professor at Johns Hopkins University until 2002 when he became the first person to hold the Mina Rees Chair in mathematics at the Graduate Center of the City University of New York. Awards In 1990 he received the of the USSR Academy of Sciences The Academy of Sciences of the Soviet Union was the highest scientific institution of the Soviet Union from 1925 to 1991. It united the count ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler System
In mathematics, particularly number theory, an Euler system is a collection of compatible elements of Galois cohomology groups indexed by fields. They were introduced by in his work on Heegner points on modular elliptic curves, which was motivated by his earlier paper and the work of . Euler systems are named after Leonhard Euler because the factors relating different elements of an Euler system resemble the Euler factors of an Euler product. Euler systems can be used to construct annihilators of ideal class groups or Selmer groups, thus giving bounds on their orders, which in turn has led to deep theorems such as the finiteness of some Tate-Shafarevich groups. This led to Karl Rubin's new proof of the main conjecture of Iwasawa theory, considered simpler than the original proof due to Barry Mazur and Andrew Wiles. Definition Although there are several definitions of special sorts of Euler system, there seems to be no published definition of an Euler system that covers al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive number, positive integers , , and satisfy the equation for any integer value of greater than . The cases and have been known since antiquity to have infinitely many solutions.Singh, pp. 18–20 The proposition was first stated as a theorem by Pierre de Fermat around 1637 in the margin of a copy of ''Arithmetica''. Fermat added that he had a proof that was too large to fit in the margin. Although other statements claimed by Fermat without proof were subsequently proven by others and credited as theorems of Fermat (for example, Fermat's theorem on sums of two squares), Fermat's Last Theorem resisted proof, leading to doubt that Fermat ever had a correct proof. Consequently, the proposition became known as a conjecture rather than a theorem. After 358 years of effort by mathematicians, Wiles's proof of Fermat's Last Theorem, the first success ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Birch And Swinnerton-Dyer Conjecture
In mathematics, the Birch and Swinnerton-Dyer conjecture (often called the Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory and is widely recognized as one of the most challenging mathematical problems. It is named after mathematicians Bryan John Birch and Peter Swinnerton-Dyer, who developed the conjecture during the first half of the 1960s with the help of machine computation. Only special cases of the conjecture have been proven. The modern formulation of the conjecture relates to arithmetic data associated with an elliptic curve ''E'' over a number field ''K'' to the behaviour of the Hasse–Weil ''L''-function ''L''(''E'', ''s'') of ''E'' at ''s'' = 1. More specifically, it is conjectured that the rank of the abelian group ''E''(''K'') of points of ''E'' is the order of the zero of ''L''(''E'', ''s'') at ''s'' = 1. The first non-ze ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yuri Manin
Yuri Ivanovich Manin (; 16 February 1937 – 7 January 2023) was a Russian mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics. Life and career Manin was born on 16 February 1937 in Simferopol, Crimean ASSR, Soviet Union. He received a doctorate in 1960 at the Steklov Mathematics Institute as a student of Igor Shafarevich. He became a professor at the Max-Planck-Institut für Mathematik in Bonn, where he was director from 1992 to 2005 and then director emeritus. He was also a Trustee Chair Professor at Northwestern University from 2002 to 2011. He had over the years more than 40 doctoral students, including Vladimir Berkovich, Mariusz Wodzicki, Alexander Beilinson, Ivan Cherednik, Alexei Skorobogatov, Vladimir Drinfeld, Mikhail Kapranov, Vyacheslav Shokurov, Ralph Kaufmann, Victor Kolyvagin, Alexander A. Voronov, and Hà Huy Khoái. Manin died on 7 January 2023. Res ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iwasawa Theory
In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite Tower of fields, towers of number fields. It began as a Galois module theory of ideal class groups, initiated by (), as part of the theory of cyclotomic fields. In the early 1970s, Barry Mazur considered generalizations of Iwasawa theory to abelian variety, abelian varieties. More recently (early 1990s), Ralph Greenberg has proposed an Iwasawa theory for motive (algebraic geometry), motives. Formulation Iwasawa worked with so-called \Z_p-extensions: infinite extensions of a number field F with Galois group \Gamma isomorphic to the additive group of p-adic integers for some prime ''p''. (These were called \Gamma-extensions in early papers.) Every closed subgroup of \Gamma is of the form \Gamma^, so by Galois theory, a \Z_p-extension F_\infty/F is the same thing as a tower of fields :F=F_0 \subset F_1 \subset F_2 \subset \cdots \subset F_\infty such that \operatorname(F_n/F)\cong \Z/p^n\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CUNY Graduate Center
The Graduate School and University Center of the City University of New York (CUNY Graduate Center) is a public research institution and postgraduate university in New York City. Formed in 1961 as Division of Graduate Studies at City University of New York, it was renamed to Graduate School and University Center in 1969. Serving as the principal doctorate-granting institution of the City University of New York (CUNY) system, CUNY Graduate Center is classified among " R1: Doctoral Universities – Very High Research Activity". CUNY Graduate Center is located at the B. Altman and Company Building at 365 Fifth Avenue in Midtown Manhattan. It offers 32 doctoral programs, 18 master's programs, and operates over 30 research centers and institutes. The Graduate Center employs a core faculty of approximately 130, in addition to over 1,700 faculty members appointed from other CUNY campuses throughout New York City. As of fall 2025, the Graduate Center enrolls over 3,100 students, of whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrew Wiles
Sir Andrew John Wiles (born 11 April 1953) is an English mathematician and a Royal Society Research Professor at the University of Oxford, specialising in number theory. He is best known for Wiles's proof of Fermat's Last Theorem, proving Fermat's Last Theorem, for which he was awarded the 2016 Abel Prize and the 2017 Copley Medal and for which he was appointed a Order of the British Empire, Knight Commander of the Order of the British Empire in 2000. In 2018, Wiles was appointed the first Regius Professor of Mathematics at Oxford. Wiles is also a MacArthur Fellows Program, 1997 MacArthur Fellow. Wiles was born in Cambridge to theologian Maurice Frank Wiles and Patricia Wiles. While spending much of his childhood in Nigeria, Wiles developed an interest in mathematics and in Fermat's Last Theorem in particular. After moving to Oxford and graduating from there in 1974, he worked on unifying Galois representations, elliptic curves and modular forms, starting with Barry Mazur's gene ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johns Hopkins University
The Johns Hopkins University (often abbreviated as Johns Hopkins, Hopkins, or JHU) is a private university, private research university in Baltimore, Maryland, United States. Founded in 1876 based on the European research institution model, Johns Hopkins is considered to be the first research university in the U.S. The university was named for its first benefactor, the American entrepreneur and Quakers, Quaker philanthropist Johns Hopkins. Hopkins's $7 million bequest (equivalent to $ in ) to establish the university was the largest Philanthropy, philanthropic gift in U.S. history up to that time. Daniel Coit Gilman, who was inaugurated as :Presidents of Johns Hopkins University, Johns Hopkins's first president on February 22, 1876, led the university to revolutionize higher education in the U.S. by integrating teaching and research. In 1900, Johns Hopkins became a founding member of the Association of American Universities. The university has led all Higher education in the U ... [...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] |
Number Theorists
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations ( Diophantine geometry). Questions in number theory can often be understood through the study of analytical objects, such as the Riemann zeta function, that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, as for instance how irrational numbers can be approximated by fractions (Diophantine approximation). Number theory is one of the oldest branches of mathematics alongside geometry. One quirk of number theory is that it deals wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russian Emigrants To The United States
Russian(s) may refer to: *Russians (), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries *A citizen of Russia *Russian language, the most widely spoken of the Slavic languages *''The Russians'', a book by Hedrick Smith *Russian (comics), fictional Marvel Comics supervillain from ''The Punisher'' series *Russian (solitaire), a card game * "Russians" (song), from the album ''The Dream of the Blue Turtles'' by Sting *"Russian", from the album ''Tubular Bells 2003'' by Mike Oldfield *"Russian", from the album '' '' by Caravan Palace *Nik Russian, the perpetrator of a con committed in 2002 See also * *Russia (other) *Rus (other) Rus or RUS may refer to: People * East Slavic historical peoples (). See Names of Rus', Russia and Ruthenia ** Rus' people, the people of Rus' ** Rus, a legendary eponymous ancestor, see Lech, Czech and Rus * Rus (surname), a surname found in ... * Rossiysky (other) * Russian Rive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
