Work On Pathologies in Algebraic Geometry
In a sequence of four papers published in the American Journal of Mathematics between 1961 and 1975, Mumford explored pathological behavior in algebraic geometry, that is, phenomena that would not arise if the world of algebraic geometry were as well-behaved as one might expect from looking at the simplest examples. These pathologies fall into two types: (a) bad behavior in characteristic p and (b) bad behavior in moduli spaces.
Read more about this topic: David Mumford
Famous quotes containing the words work, algebraic and/or geometry:
“Juggling produces both practical and psychological benefits.... A woman’s involvement in one role can enhance her functioning in another. Being a wife can make it easier to work outside the home. Being a mother can facilitate the activities and foster the skills of the efficient wife or of the effective worker. And employment outside the home can contribute in substantial, practical ways to how one works within the home, as a spouse and as a parent.”
—Faye J. Crosby (20th century)
“I have no scheme about it,—no designs on men at all; and, if I had, my mode would be to tempt them with the fruit, and not with the manure. To what end do I lead a simple life at all, pray? That I may teach others to simplify their lives?—and so all our lives be simplified merely, like an algebraic formula? Or not, rather, that I may make use of the ground I have cleared, to live more worthily and profitably?”
—Henry David Thoreau (1817–1862)
“I am present at the sowing of the seed of the world. With a geometry of sunbeams, the soul lays the foundations of nature.”
—Ralph Waldo Emerson (1803–1882)