David Mumford

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David Bryant Mumford (born 11 June 1937) is an American mathematician known for distinguished work in algebraic geometry, and then for research into vision and pattern theory. He is currently a University Professor in the Division of Applied Mathematics at Brown University, having previously had a long academic career at Harvard University.

Contents 1 Work in algebraic geometry 2 Awards and honors 3 Current activity 4 Family 5 See also 6 Bibliography 7 External links

[edit] Work in algebraic geometry

After attending the Exeter School, Mumford went to Harvard, where he became a student of Oscar Zariski. He completed his Ph.D. in 1961, with a thesis entitled Existence of the moduli scheme for curves of any genus. His work in geometry always combined the traditional geometric insights with the latest algebraic techniques. He published on moduli spaces, with a theory summed up in his book Geometric Invariant Theory, on the equations defining an abelian variety, and on algebraic surfaces.

His books Abelian Varieties (with C. P. Ramanujam) and Curves on an Algebraic Surface combined the old and new theories (to the disadvantage of the former, it has been claimed by Shreeram Abhyankar). His lecture notes on scheme theory circulated for years in unpublished form, at a time when they were, beside the treatise Éléments de géométrie algébrique, the only accessible introduction. They are now available as The Red Book of Varieties and Schemes (ISBN 3-540-63293-X).

Other work that was less thoroughly written up were lectures on varieties defined by quadrics, and a study of Goro Shimura's many papers from the 1960s.

Mumford’s research did much to revive the classical theory of theta functions, by showing that its algebraic content was large, and enough to support the main parts of the theory by reference to finite analogues of the Heisenberg group. This work on the equations defining abelian varieties appeared in 1966-7. He published some further books of lectures on the theory.

He also was one of the founders of the toroidal embedding theory; and sought to apply the theory to Gröbner basis techniques, through students who worked in algebraic computation.

[edit] Awards and honors

He was awarded a Fields Medal in 1974. He was a MacArthur Fellow from 1987 to 1992. He won the Shaw Prize in 2006. In 2007 he was awarded the AMS Steele Prize for Mathematical Exposition

There is a long list of awards and honors besides the above, including

• Westinghouse Science Talent Search finalist, 1953;
• Junior Fellow at Harvard from 1958 to 1961;
• elected to the National Academy of Sciences in 1975; *Honorary Fellow from Tata Institute of Fundamental Research in 1978;
• Honorary D. Sc. from University of Warwick in 1983;
• Foreign Member of Accademia Nazionale de Leicei, Rome, in 1991;
• Honorary Member of London Mathematical Society in 1995;
• elected to the American Philosophical Society in 1997;
• Honorary D. Sc. from Norwegian University of Science and Technology in 2000;
• Honorary D. Sc. from Rockefeller University in 2001.

He was elected President of the International Mathematical Union in 1995 and served from 1995 to 1999.

[edit] Current activity

In 2002, he wrote a book with Caroline Series and David Wright on the visual geometry of limit sets: Indra's Pearls: The Vision of Felix Klein (ISBN 0-521-35253-3).

His current area of work is pattern theory.

[edit] Family

He was born in Worth, West Sussex in England, of an English father and American mother. His father William started an experimental school in Tanzania and worked for the then newly created United Nations during his childhood.

He met his wife Erika Jentsh at Radcliff. She was an awards-winning poet, and had a doctorate in Celtic Languages and Literature from Harvard. They had four children, Steve, Peter, Jeremy and Suchitra. After Erika passed away, he married his second wife, Jenifer Gordon.

One of his children, Steve Mumford, is a published artist residing in New York City.

He is color blind.

[edit] See also

• Mumford conjecture
• Theta representation
• Manin-Mumford conjecture
• Horrocks-Mumford bundle
• Deligne-Mumford moduli space of stable curves
• algebraic stacks, Deligne-Mumford stacks
• moduli scheme
• Prym varieties
• stable maps

[edit] Bibliography

• Lectures on Curves on Algebraic Surfaces (with George Bergman, Princeton University Press, 1964)
• Geometric Invariant Theory (Springer-Verlag, 1965 - 2nd edition, with J. Fogarty, 1982; 3rd enlarged edition, with F. Kirwan and J. Fogarty, 1994)
• The Red Book of Varieties and Schemes (mimeographed notes from Harvard Mathematics Department 1967, reprinted in Lecture Notes in Mathematics 1348, Springer-Verlag 1988)
• Abelian Varieties (Oxford University Press, 1st edition 1970; 2nd edition 1974)
• Six Appendices to Algebraic Surfaces by Oscar Zariski (2nd edition (Springer-Verlag, 1971)
• Toroidal Embeddings I (with G. Kempf, F. Knudsen and B. Saint-Donat, Lecture Notes in Mathematics #339, Springer-Verlag 1973)
• Curves and their Jacobians (University of Michigan Press, 1975)
• Smooth Compactification of Locally Symmetric Varieties (with A. Ash, M. Rapoport and Y. Tai, Math. Sci. Press, 1975)
• Algebraic Geometry I: Complex Projective Varieties (Springer-Verlag New York, 1975)
• Tata Lectures on Theta (with C. Musili, M. Nori, P. Norman, E. Previato and M. Stillman, Birkhauser-Boston, Part I 1982, Part II 1983, Part III 1991)
• Filtering, Segmentation and Depth (with M. Nitzberg and T. Shiota, Lecture Notes in Computer Science #662, 1993)
• Two and Three Dimensional Pattern of the Face (with P. Giblin, G. Gordon, P. Hallinan and A. Yuille, AKPeters, 1999)
• Indra's Pearls: The Vision of Felix Klein (with C. Series and D. Wright, Cambridge University Press, 2002)
• Selected Papers on the Classification of Varieties and Moduli Spaces, Springer-Verlag, 2004)
• Pattern Theory through Examples (with A. Desolneux, in preparation)

[edit] External links

• O'Connor, John J., and Edmund F. Robertson. "David Mumford". MacTutor History of Mathematics archive.
• David Mumford at the Mathematics Genealogy Project
• Mumford's page at Brown University
• Critical Review evaluations of Professor Mumford

Fields Medalists

1936: Ahlfors • Douglas | 1950: Schwartz • Selberg | 1954: Kodaira • Serre | 1958: Roth • Thom | 1962: Hörmander • Milnor | 1966: Atiyah • Cohen • Grothendieck • Smale | 1970: Baker • Hironaka • Novikov • Thompson | 1974: Bombieri • Mumford | 1978: Deligne • Fefferman • Margulis • Quillen | 1982: Connes • Thurston • Yau | 1986: Donaldson • Faltings • Freedman | 1990: Drinfeld • Jones • Mori • Witten | 1994: Zelmanov • Lions • Bourgain • Yoccoz | 1998: Borcherds • Gowers • Kontsevich • McMullen | 2002: Lafforgue • Voevodsky | 2006: Okounkov • Perelman • Tao • Werner edit