Barry Mazur

Barry Charles Mazur ( born December 19, 1937 in New York City ) is an American mathematician who works in the field of topology, number theory and arithmetic algebraic geometry.

Life and work

Mazur attended the Bronx High School of Science and went on to study at the Massachusetts Institute of Technology (MIT) and Princeton University, where he in 1959 received his doctorate at Ralph Fox and RH Bing ( On the embedding of spheres ), while at the same time from 1958 Research Fellow at the neighboring Institute for Advanced Study was. After that he went to Harvard, where he was a Junior Fellow at first, in 1962 assistant professor, associate professor in 1965 and from 1969 Professor of Mathematics ( from 1982 William Petschek Professor, from 1998 Professor Gerhard Gade ). He is a regular guest stays at the IHES in Paris.

Mazur initially worked in the field of geometric topology, where he proved simultaneously with Morton Brown the generalized Schoenflies presumption that states in clear terms that a two-dimensional knotted sphere in three-dimensional space ( in contrast to the case of a " thread" ) always lead to a can be unknotted normal sphere - without the use of cuts or " perforations " (with an analogous conjecture in higher dimensions ). Together with Brown, he was awarded the Oswald Veblen Prize -.

As a student of Alexander Grothendieck, who held the early 1960s regularly lectures at Harvard, he then shifted his interest in algebraic geometry, which followed the theory of numbers.

In On Modular curves and the Eisenstein ideal of 1978, he classified the possible torsion subgroups (finite subgroups ) of the group of rational points on elliptic curves. Zn is the cyclic group of order n, then the possible torsion subgroups of elliptic curves over the rational numbers are Zn with 1 ≤ n ≤ 10, and Z12; and the direct sum of Z2 with Z2, Z4, Z6 or Z8.

In Class fields of abelian extensions of Q ( Inventiones Mathematicae 1984) Mazur proved by Andrew Wiles, the main conjecture of Iwasawa theory ( one founded by Kenkichi Iwasawa branch of algebraic number theory). From Mazur stems the term of the deformation of Galois representations, the ' played an important role in Andrew Wiles proof of the Taniyama - Shimura conjecture and the great Fermat theorem.

In 1965 he received the Veblen Prize in Geometry from the American Mathematical Society ( AMS ), 1982 Cole Award, the 1994 Chauvenet Prize, and the 2000 Leroy P. Steele Prize of the AMS. In 1982 he was elected to the National Academy of Sciences, the American Philosophical Society in 2001. In 1983 he gave a plenary lecture at the ICM in Warsaw (Modular Curves and Arithmetic ) and in 1974 he was invited speaker at the ICM in Vancouver (P- adic analytic number theory of elliptic curves and abelian varieties over Q). In 2002 he was invited speaker at the International Congress of Mathematicians in Beijing with Karl Rubin (Elliptic curves and class field theory ). For 2011 him the National Medal of Science was awarded. He is a Fellow of the American Mathematical Society.

His doctoral include Noam Elkies, Glenn Stevens, Michael McQuillan, Michael Harris and Paul Vojta.

Writings

  • Barry Mazur: Imagining numbers: particularly the square root of minus fifteen. Farrar Straus Giroux, 2004, ISBN 0-374-17469-5 ( popular book ).
  • B. Mazur Arithmetic on Curves In: Bulletin of the American Mathematical Society., 1986, p.207 (especially to Faltings theorem, Online).
  • B. Mazur: Number theory as gadfly. In: American Mathematical Monthly. 98, 1991, pp. 593-610, doi: 10.2307/2324924 ( the background of Wiles proof of the Shimura - Taniyama conjecture, Mazur received the Chauvenet price).
  • Barry Mazur, Michael Artin: Etale Homotopy. Springer, 1969, ISBN 3-540-04619-4.
  • B. Mazur: Perturbations, deformation, and variations ( and "near- misses " ) in geometry, physics, and number theory. In: Bull Amer. Math Soc .. 41, No. 3, 2004, pp. 307-336 (online, accessed 9 April 2011 ).
  • B. Mazur: Deformation of Galois representations. In: Cornell, Silverman, Stevens * Barry Mazur: Modular forms and Fermat's Last Theorem. Springer 1997.
  • B. Mazur: Deforming Galois representations. In: Ihara, Ribet, Serre (eds.): Galois groups over Q. MSRI Publications Vol 16, Springer 1989.
  • B. Mazur, Peter Swinnerton - Dyer: Arithmetic of Weil curves. In: Inventiones Mathematicae. 25, No. 1, 1974, pp. 1-61, doi: 10.1007/BF01389997 (online, accessed 9 April 2011 ).
  • B. Mazur, Dorian Goldfeld: Rational isogenies of prime degree. In: Inventiones Mathematicae. 44, No. 2, 1978, pp. 129-162, doi: 10.1007/BF01390348 (online, accessed 9 April 2011 ).
  • B. Mazur, Andrew Wiles: Class fields of abelian extensions of Q. In: Inventiones Mathematicae. 76, No. 2, 1984, pp. 179-330, doi: 10.1007/BF01388599 (online, accessed 9 April 2011 ).
  • B. Mazur, John T. Tate, Jeremy Teitelbaum: On p- adic analogues of the conjectures of Birch and Swinnerton - Dyer. In: Inventiones Mathematicae. 84, No. 1, 1986, pp. 1-48, doi: 10.1007/BF01388731 (online, accessed 9 April 2011 ).
  • B. Mazur: Finding meaning in error terms. In: Bull Amer. Math Soc .. 45, No. 2, 2008, pp. 185-228 (online, accessed 9 April 2011 ).
R. H. Bing Harvard University Institut des Hautes Études Scientifiques Oswald Veblen Prize in Geometry Pierre de Fermat Cole Prize Michael McQuillan (mathematician) Michael Harris (mathematician) Digital Object Identifier Peter Swinnerton-Dyer Dorian M. Goldfeld John Tate Eric Friedlander Integrated Authority File
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