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”…).
On geometric invariant theory:
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:
On theta functions:
David Mumford: Tata Lectures on Theta I, Modern Birkhäuser Classics, Birkhäuser (1983) Springer (2007) [doi:10.1007/978-0-8176-4577-9]
David Mumford: Tata Lectures on Theta II — Jacobian theta functions and differential equations, Modern Birkhäuser Classics, Birkhäuser (1983), Springer (2007) [doi:10.1007/978-0-8176-4578-6]
Last revised on January 29, 2026 at 16:55:24. See the history of this page for a list of all contributions to it.