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Encyclopedia > David Mumford

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 professor in the Division of Applied Mathematics at Brown University, having previously had a long academic career at Harvard University. He was born in Worth, in Sussex in England, of an English father and American mother.


At Harvard, Mumford became a student of Oscar Zariski, and 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 His lecture notes on scheme theory circulated for years in unpublished form, at a time when they were the only accessible introduction. They are now available as The Red Book of Varieties and Schemes.


Other work that was less thoroughly written up were lectures on varieties defined by quadrics, and a study of 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. 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


He was awarded a Fields Medal in 1974. During the 1980s he left algebraic geometry, in order to study brain structure. He was a MacArthur Fellow from 1987 to 1992.


He has recently published a joint book on the visual geometry of limit sets.


See also

External link

  • Mumford's page at Brown University (http://www.dam.brown.edu/people/mumford/)

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Mumford biography (679 words)
Mumford's father worked for the United Nations from its foundations in 1945 and this was his job while Mumford was growing up.
Mumford's mother was American and the family lived on Long Island Sound in the United States, a semi-enclosed arm of the North Atlantic Ocean with the New York- Connecticut shore on the north and Long Island to the south.
Mumford's major work has been a tremendously successful multi-pronged attack on problems of the existence and structure of varieties of moduli, that is, varieties whose points parameterise isomorphism classes of some type of geometric object.
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David, the youngest of the sons of Jesse, brought food each day to his brothers who were with Saul, and heard the Philistine champion, the giant Goliath, challenge the Israelites to send out their own champion to decide the outcome in single combat.
Daniel was the progeny of David and Abigail
In Judaism, David's reign represents the formation of a coherent Jewish kingdom with its political and religious capital in Jerusalem and the institution of a royal lineage that culminates in the Messianic Age.
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