nLab David Mumford

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

• website

Selected writings

On geometric invariant theory:

• David Mumford, John Fogarty, Frances Clare Kirwan, Geometric invariant theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (2) 34, Springer-Verlag (1965/1982) (ISBN:978-3-540-56963-3, pdf)

Introducing the notion of algebraic stacks and (what came to be called) Deligne-Mumford stacks, and on the example of the moduli space of curves:

• Pierre Deligne, David Mumford, The irreducibility of the space of curves of given genus, Publications Mathématiques de l’IHÉS (Paris) 36 (1969) 75-109 [doi:10.1007/BF02684599, numdam:PMIHES_1969__36__75_0]

On algebraic surfaces:

• Oscar Zariski, Shreeram S. Abhyankar, Joseph Lipman, David Mumford (eds.), Algebraic surfaces, Classics in mathematics (second supplemented ed.) (2004) [1935], Berlin, New York: Springer-Verlag, ISBN 978-3-540-58658-6, MR 0469915

category: people