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 His lecture notes on scheme theory circulated for years in unpublished form, at a time when they were the only accessible introduction.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.
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.
- O'Connor, John J., and Edmund F. Robertson. "David Mumford". MacTutor History of Mathematics archive.
- Mumford's page at Brown University