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

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)

- 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

category: people

Last revised on July 19, 2021 at 09:28:57. See the history of this page for a list of all contributions to it.