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Barry Mazur
Barry Charles Mazur (; born December 19, 1937) is an American mathematician and the Gerhard Gade University Professor at Harvard University. His contributions to mathematics include his contributions to Wiles's proof of Fermat's Last Theorem in number theory, Mazur's torsion theorem in arithmetic geometry, the Mazur swindle in geometric topology, and the Mazur manifold in differential topology. Life Born in New York City, Mazur attended the Bronx High School of Science and MIT, although he did not graduate from the latter on account of failing a then-present ROTC requirement. He was nonetheless accepted for graduate studies at Princeton University, from where he received his PhD in mathematics in 1959 after completing a doctoral dissertation titled "On embeddings of spheres." He then became a Junior Fellow at Harvard University from 1961 to 1964. He is the Gerhard Gade University Professor and a Senior Fellow at Harvard. He is the brother of Joseph Mazur and the father of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University
Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher learning in the United States and one of the most prestigious and highly ranked universities in the world. The university is composed of ten academic faculties plus Harvard Radcliffe Institute. The Faculty of Arts and Sciences offers study in a wide range of undergraduate and graduate academic disciplines, and other faculties offer only graduate degrees, including professional degrees. Harvard has three main campuses: the Cambridge campus centered on Harvard Yard; an adjoining campus immediately across Charles River in the Allston neighborhood of Boston; and the medical campus in Boston's Longwood Medical Area. Harvard's endowment is valued at $50.9 billion, making it the wealthiest academic institution in the world. Endowment inco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diophantine Geometry
In mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it became clear for some mathematicians that methods of algebraic geometry are ideal tools to study these equations. Four theorems in Diophantine geometry which are of fundamental importance include: * Mordell–Weil Theorem * Roth's Theorem * Siegel's Theorem * Faltings's Theorem Background Serge Lang published a book ''Diophantine Geometry'' in the area in 1962, and by this book he coined the term "Diophantine Geometry". The traditional arrangement of material on Diophantine equations was by degree and number of variables, as in Mordell's ''Diophantine Equations'' (1969). Mordell's book starts with a remark on homogeneous equations ''f'' = 0 over the rational field, attributed to C. F. Gauss, that non-zero solutions in integers (even primitive lattice points) exist if non-zero rational solutions do, and notes a caveat of L. E. D ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Veblen Prize
__NOTOC__ The Oswald Veblen Prize in Geometry is an award granted by the American Mathematical Society for notable research in geometry or topology. It was founded in 1961 in memory of Oswald Veblen. The Veblen Prize is now worth US$5000, and is awarded every three years. The first seven prize winners were awarded for works in topology. James Harris Simons and William Thurston were the first ones to receive it for works in geometry (for some distinctions, see geometry and topology). As of 2020, there have been thirty-four prize recipients. List of recipients * 1964 Christos Papakyriakopoulos * 1964 Raoul Bott * 1966 Stephen Smale * 1966 Morton Brown and Barry Mazur * 1971 Robion Kirby * 1971 Dennis Sullivan * 1976 William Thurston * 1976 James Harris Simons * 1981 Mikhail Gromov for: ::''Manifolds of negative curvature.'' Journal of Differential Geometry 13 (1978), no. 2, 223–230. ::''Almost flat manifolds.'' Journal of Differential Geometry 13 (1978), no. 2, 231–241. ::''C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cole Prize
The Frank Nelson Cole Prize, or Cole Prize for short, is one of twenty-two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number theory.. The prize is named after Frank Nelson Cole, who served the Society for 25 years. The Cole Prize in algebra was funded by Cole himself, from funds given to him as a retirement gift; the prize fund was later augmented by his son, leading to the double award.. To be eligible for the Cole prize, the author must be a member of the American Mathematical Society or the paper should appear in a recognized North American journal. The first award for algebra was made in 1928 to L. E. Dickson Leonard Eugene Dickson (January 22, 1874 – January 17, 1954) was an American mathematician. He was one of the first American researchers in abstract algebra, in particular the theory of finite fields and classical groups, and is also reme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chauvenet Prize
The Chauvenet Prize is the highest award for mathematical expository writing. It consists of a prize of $1,000 and a certificate, and is awarded yearly by the Mathematical Association of America in recognition of an outstanding expository article on a mathematical topic. The prize is named in honor of William Chauvenet and was established through a gift from J. L. Coolidge in 1925. The Chauvenet Prize was the first award established by the Mathematical Association of America. A gift from MAA president Walter B. Ford in 1928 allowed the award to be given every 3 years instead of the originally planned 5 years. Winners *1925 G. A. Bliss *1929 T. H. Hildebrandt *1932 G. H. Hardy *1935 Dunham Jackson *1938 G. T. Whyburn *1941 Saunders Mac Lane *1944 R. H. Cameron *1947 Paul Halmos *1950 Mark Kac *1953 E. J. McShane *1956 Richard H. Bruck *1960 Cornelius Lanczos *1963 Philip J. Davis *1964 Leon Henkin *1965 Jack K. Hale & Joseph P. LaSalle *1967 Guido Weiss *1968 Mark ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
National Medal Of Science
The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral and social sciences, biology, chemistry, engineering, mathematics and physics. The twelve member presidential Committee on the National Medal of Science is responsible for selecting award recipients and is administered by the National Science Foundation (NSF). History The National Medal of Science was established on August 25, 1959, by an act of the Congress of the United States under . The medal was originally to honor scientists in the fields of the "physical, biological, mathematical, or engineering sciences". The Committee on the National Medal of Science was established on August 23, 1961, by executive order 10961 of President John F. Kennedy. On January 7, 1979, the American Association for the Advancement of Science (AAAS) passed a resolution propo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chern Medal
The Chern Medal is an international award recognizing outstanding lifelong achievement of the highest level in the field of mathematics. The prize is given at the International Congress of Mathematicians (ICM), which is held every four years. Introduction It is named in honor of the late Chinese mathematician Shiing-Shen Chern. The award is a joint effort of the International Mathematical Union (IMU) and the Chern Medal Foundation (CMF) to be bestowed in the same fashion as the IMU's other three awards (the Fields Medal, the Abacus Medal, and the Gauss Prize), i.e. at the opening ceremony of the International Congress of Mathematicians (ICM), which is held every four years. The first such occasion was at the 2010 ICM in Hyderabad, India. Each recipient receives a medal decorated with Chern's likeness, a cash prize of $250,000 (USD), and the opportunity to direct $250,000 of charitable donations to one or more organizations for the purpose of supporting research, education, or ou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mazur's Torsion Theorem
In algebraic geometry and number theory, the torsion conjecture or uniform boundedness conjecture for torsion points for abelian varieties states that the order of the torsion group of an abelian variety over a number field can be bounded in terms of the dimension of the variety and the number field. A stronger version of the conjecture is that the torsion is bounded in terms of the dimension of the variety and the degree of the number field. The torsion conjecture has been completely resolved in the case of elliptic curves. Elliptic curves From 1906 to 1911, Beppo Levi published a series of papers investigating the possible finite orders of points on elliptic curves over the rationals. He showed that there are infinitely many elliptic curves over the rationals with the following torsion groups: * ''C''''n'' with 1 ≤ ''n'' ≤ 10, where ''C''''n'' denotes the cyclic group of order ''n''; * ''C''12; * ''C''2n × ''C''2 with 1 ≤ ''n'' ≤ 4, where × denotes the direct sum. At ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mazur's Control Theorem
In number theory, Mazur's control theorem, introduced by , describes the behavior in Z''p'' extensions of the Selmer group of an abelian variety over a number field In mathematics, an algebraic number field (or simply number field) is an extension field K of the field of rational numbers such that the field extension K / \mathbb has finite degree (and hence is an algebraic field extension). Thus K is a f .... References * Theorems in algebraic number theory {{numtheory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mazur's Conjecture B
In arithmetic geometry, the uniform boundedness conjecture for rational points asserts that for a given number field K and a positive integer g \geq 2 that there exists a number N(K,g) depending only on K and g such that for any algebraic curve C defined over K having genus equal to g has at most N(K,g) K-rational points. This is a refinement of Faltings's theorem, which asserts that the set of K-rational points C(K) is necessarily finite. Progress The first significant progress towards the conjecture was due to Caporaso, Harris, and Mazur. They proved that the conjecture holds if one assumes the Bombieri–Lang conjecture. Mazur's Conjecture B A variant of the conjecture, due to Mazur, asserts that there should be a number N(K,g,r) such that for any algebraic curve C defined over K having genus g and whose Jacobian variety J_C has Mordell–Weil rank over K equal to r, the number of K-rational points of C is at most N(K,g,r). This variant of the conjecture is known as Mazur's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mazur Manifold
In differential topology, a branch of mathematics, a Mazur manifold is a contractible, compact, smooth four-dimensional manifold (with boundary) which is not diffeomorphic to the standard 4-ball. The boundary of a Mazur manifold is necessarily a homology 3-sphere. Frequently the term ''Mazur manifold'' is restricted to a special class of the above definition: 4-manifolds that have a handle decomposition containing exactly three handles: a single 0-handle, a single 1-handle and single 2-handle. This is equivalent to saying the manifold must be of the form S^1 \times D^3 union a 2-handle. An observation of Mazur's shows that the double of such manifolds is diffeomorphic to S^4 with the standard smooth structure. History Barry Mazur and Valentin Poenaru discovered these manifolds simultaneously. Akbulut and Kirby showed that the Brieskorn homology spheres \Sigma(2,5,7) , \Sigma(3,4,5) and \Sigma(2,3,13) are boundaries of Mazur manifolds. These results were later generalized ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fontaine–Mazur Conjecture
In mathematics, the Fontaine–Mazur conjectures are some conjectures introduced by about when ''p''-adic representations of Galois groups of number fields can be constructed from representations on étale cohomology In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil conjecture ... groups of a varieties. Some cases of this conjecture in dimension 2 were already proved by . References * * External links Galois theory Number theory Conjectures {{abstract-algebra-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
