David Bryant Mumford

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

David Mumford, Berkeley 2010

David Mumford

Life

Mumford's father had been a member of the UN since it was founded in 1945 and moved with the family halfway around the world, the mother was American . Since 1940 he grew up in the USA in Long Island . David Mumford studied from 1953 at Harvard University , where he received his doctorate in 1961 under Oscar Zariski . He then worked as a lecturer at Harvard and was given a chair in mathematics in 1967. From 1981 to 1984 he headed the Department of Mathematics and from 1991 to 1994 he was vice president of the university. In 1996 he went to the Applied Mathematics department at Brown University .

Services

Mumford worked between 1959 and 1982 in the field of algebraic geometry , where he made important contributions. In particular, he dealt with the classification of curves , surfaces and Abelian varieties and developed the geometric invariant theory . Technically speaking, it is about the construction of so-called modular rooms . He continued the work of the Italian school ( Federigo Enriques et al.) - in the sense of the mathematically strict algebraic formulation of his teacher Oscar Zariski - on the classification of algebraic surfaces, in particular for surfaces over finite bodies (characteristic p). As a student of Alexander Grothendieck at Harvard, he used his reformulation of algebraic geometry early on and also wrote one of the most important textbooks on schema theory. At the same time, he was always looking for a connection to classic results, e.g. B. to connect the Italian school with the new formulation.

He played a key role in the development of the theory of toric varieties from 1970 onwards. He was a co-author of an early standard work in this field.

Since 1983 he has been interested in the theory of vision; he is particularly interested in image understanding (computer vision), the statistical treatment of image signals and problems of neural image processing . The special statistical theory in which Mumford works is called "pattern theory" by her father Ulf Grenander . With Shah, he set up a simple model for image segmentation as a minimization of an energy functional (which formalizes edge and surface detection and the best possible match with the pixel data) and formulated the Mumford-Shah conjectures for this model.

In 2002 he and others wrote a book with numerous illustrations, also more generally understandable, about the partly fractal figures that result as invariant boundary figures from the repeated application of the transformations of Kleinian groups (discrete subgroups of Möbius transformations ).

Honors

In 1962, Mumford became a Sloan Research Fellow . In 1964 he was elected to the American Academy of Arts and Sciences and in 1997 to the American Philosophical Society . In 1974 he was awarded the Fields Medal . He has been a member of the National Academy of Sciences since 1975 . From 1987 to 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 , of which he is a fellow. In 2008 he was awarded the Wolf Prize for Mathematics (together 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 ), in 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 was awarded the National Medal of Science in the USA and in 2012 the BBVA Foundation Frontiers of Knowledge Award .

In 2003/04 he was on the first Abel Prize Committee .

Fonts

• Geometric Invariant Theory (= results of mathematics and its border areas . New part 34). Springer, Berlin et al. 1965.
• Lectures on curves on an algebraic surface (= Annals of Mathematics Studies. 59, ISSN  0066-2313 ). With a section by GM Bergman. Princeton University Press, Princeton NJ 1966.
• Abelian Varieties (= Tata Institute of Fundamental Research Studies in Mathematics. 5, ZDB -ID 2808653-3 ). Oxford University Press, Oxford et al. 1970.
• with George Kempf , Finn Knudsen, Bernard Saint-Donat: Toroidal Embeddings 1 (= Lecture Notes in Mathematics. 339, 1). Springer, Berlin et al. 1973, ISBN 3-540-06432-X .
• Algebraic Geometry I. Complex Projective Varieties (= The basic teachings of the mathematical sciences in single representations . 221). Springer, Berlin et al. 1976, ISBN 3-540-07603-4 .
• Curves and their Jacobians. University of Michigan Press, Ann Arbor 1975, ISBN 0-472-66000-4 .
• Tata lectures on Theta. 3 volumes. Birkhäuser, Boston MA 1983-1991.
• The red book of Varieties and Schemes (= Lecture Notes in Mathematics. 1358). Springer, Berlin et al. 1988, ISBN 3-540-50497-4 .
• with Caroline Series , David Wright: Indra's Pearls. The vision of Felix Klein. Cambridge University Press, Cambridge 2002, ISBN 0-521-35253-3 .

Web links

• Autobiography of David Mumford (English)
• John J. O'Connor, Edmund F. Robertson :  David Bryant Mumford. In: MacTutor History of Mathematics archive .
• David Bryant Mumford in the Mathematics Genealogy Project (English)
• On the award of the Steele Prize 2007 (PDF file; 160 kB)
• Homepage of David Bryant Mumford, also some explanations about the "pattern theory"

References

1. ^ David A. Cox , John B. Little , Henry K. Schenck: Toric varieties (= Graduate Studies in Mathematics. 124). American Mathematical Society, Providence RI 2011, ISBN 978-0-8218-4819-7 , p. 788.
2. ^ Morel, Bourbaki Seminar 1995/96, online, pdf
3. ^ Abel Committee