David Mumford is an algebraic geometer, who sharply switched at some point in his career to study pattern recognition. His contributions include the creation of modern geometric invariant theory (as a method of building moduli spaces), the introduction of Deligne-Mumford stacks and especially of the Deligne-Mumford compactification of the moduli space of curves, the Mumford-Tate curve, Mumford cohomological classes on the moduli space of curves, Mumford conjecture (recently proved by Madsen and Weiss), the classification of algebraic surfaces in positive characteristics and solutions to a number of difficult problems in mainstream algebraic geometry. He is also well known for clear exposition, and wrote several books on algebraic geometry (Tata lectures on theta, Geometric invariant theory, “Red book”…).
Scans of most, if not all, his papers are available at his
Pierre Deligne, David Mumford, The irreducibility of the space of curves of given genus . Publications Mathématiques de l’IHÉS (Paris) 36: 75–109 (1969) numdam
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