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 on, work, algebraic and/or geometry:
“Most of our platitudes notwithstanding, self-deception remains the most difficult deception. The tricks that work on others count for nothing in that very well-lit back alley where one keeps assignations with oneself: no winning smiles will do here, no prettily drawn lists of good intentions.”
—Joan Didion (b. 1934)
“... work is only part of a man’s life; play, family, church, individual and group contacts, educational opportunities, the intelligent exercise of citizenship, all play a part in a well-rounded life. Workers are men and women with potentialities for mental and spiritual development as well as for physical health. We are paying the price today of having too long sidestepped all that this means to the mental, moral, and spiritual health of our nation.”
—Mary Barnett Gilson (1877–?)
“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)
“The geometry of landscape and situation seems to create its own systems of time, the sense of a dynamic element which is cinematising the events of the canvas, translating a posture or ceremony into dynamic terms. The greatest movie of the 20th century is the Mona Lisa, just as the greatest novel is Gray’s Anatomy.”
—J.G. (James Graham)