David Mumford

David Bryant Mumford ( born June 11, 1937 in Worth, Sussex ) is an English mathematician.

Life

Mumford's father was a member of the UN since its founding in 1945 and moved the family halfway around the world, the mother was U.S. citizen. Since 1940, he grew up in Long Iceland in the USA. David Mumford studied from 1953 at Harvard University, where he received his doctorate with Oscar Zariski 1961. He then worked as a lecturer at Harvard and received in 1967 a chair of mathematics. 1981 to 1984 he headed the Department of Mathematics, and between 1991 and 1994, he was Vice President of the University. In 1996 he went to the Department of Applied Mathematics at Brown University.

Services

Mumford worked about 1959-1982 in the field of algebraic geometry, where he made ​​important contributions. In particular, he was concerned with the classification of curves, surfaces and Abelian varieties and developed for this purpose, the geometric invariant theory. Technically speaking, it comes to the construction of so-called moduli spaces. He continued the work of the Italian school ( Federigo Enriques and others) - in the sense of mathematically rigorous algebraic formulation of his teacher Oscar Zariski - for the classification of algebraic surfaces continues, especially for surfaces over finite fields ( characteristic p ). As a student of Alexander Grothendieck at Harvard he used early in his reformulation of algebraic geometry and also wrote one of the major textbooks of schema theory. At the same time he was always looking for the connection to classical results such as the Italian school to connect with the new formulation.

Since 1983, his interest lies in the theory of vision, it is particularly concerned the Image Understanding (Computer Vision), the statistical treatment of image signals, as well as problems of neural image processing. The specific statistical theory in Mumford works is called by her father Ulf Grenander " pattern theory". With Shah, he constructed a simple model for image segmentation as the minimization of an energy functional ( formalized the edge and face detection and best possible correspondence with the pixel data ) and formulated the Mumford - Shah conjecture for this model.

In 2002, he co-signed a with numerous illustrations provided, more generally comprehensible book about the sometimes fractal figures, which are obtained as invariant boundary figures from the repeated application of the transformations small shear groups (discrete subgroups of Möbius transformations ).

Honors

1974 David Mumford was awarded the Fields Medal. Since 1975 he is a member of the National Academy of Sciences. 1987-1992 he was a MacArthur Fellow. From 1995 to 1999 he was president of the International Mathematical Union ( IMU). In 2006 he was honored with the Shaw Prize for mathematics. In 2007 he received the Leroy P. Steele Prize of the American Mathematical Society, whose fellow he is. In 2008 he the Wolf Prize in mathematics was awarded (jointly with Pierre Deligne and Phillip Griffiths ). In 1992 he gave a plenary lecture at the first European Congress of Mathematicians in Paris ( computer vision from a mathematical perspective ). In 2002 he gave a plenary lecture at the International Congress of Mathematicians in Beijing (Pattern theory: the mathematics of perception ), 1970 he was invited speaker at the ICM in Nice ( The structure of the moduli space of curves and abelian varieties ) and in 1962 in Stockholm ( Projective invariants of projective structures and applications ). In 2010 he received the National Medal of Science awarded in the United States.

Works

  • Geometric Invariant Theory. New York 1965 3.Aufl. , Springer 1994
  • Abelian Varieties. Oxford University Press, 1970, 2nd ed .. 1974
  • Algebraic Geometry I: Complex Projective Varieties. New York, Springer, 1976 3.Aufl. 2004
  • The red book of Varieties and Schemes, 2nd ed. , Springer 1999 ( along with " Curves and Their Jacobians " )
  • Curves and Their Jacobians, University of Michigan Press 1974
  • Tata lectures on Theta Functions, 3 vols, 1983-1991 Birkhäuser, Bd.1 in 3.Aufl. , Springer 1994
  • Lectures on curves on algebraic surface to 1966
  • With Caroline Series, David Wright Indra's Pearls -the vision of Felix Klein, Cambridge UP 2002
Machine vision MacArthur Fellows Program Mathematics Genealogy Project Jesse Douglas Laurent Schwartz Atle Selberg Kunihiko Kodaira Jean-Pierre Serre Klaus Roth Paul Cohen (mathematician) Stephen Smale Alan Baker (mathematician) Heisuke Hironaka Sergei Novikov (mathematician) Charles Fefferman Alain Connes Simon Donaldson Gerd Faltings Michael Freedman Vaughan Jones Edward Witten Jean Bourgain Pierre-Louis Lions Jean-Christophe Yoccoz Curtis T. McMullen Laurent Lafforgue Andrei Okounkov Terence Tao Wendelin Werner Elon Lindenstrauss Carl Ludwig Siegel Jean Leray Henri Cartan Hassler Whitney Mark Krein Hans Lewy Samuel Eilenberg Ennio de Giorgi Ilya Piatetski-Shapiro Lennart Carleson Mikhail Leonidovich Gromov Jacques Tits Joseph Keller Yakov Sinai Raoul Bott John Tate Luis Caffarelli Michael Artin Integrated Authority File Worth, Schleswig-Holstein
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