Professor William Fulton
Distinguished Oscar Zariski University Professor
University of Michigan
Wednesday, April 27, 2011
3:30pm - 4:30pm
Miller Learning Center, Room 102
Thursday, April 28, 2011
3:30pm - 4:30pm
Boyd Graduate Studies Building, Room 328
Friday, April 29, 2011
3:30pm -4:30pm
Boyd Graduate Studies Building, Room 328
The aim of this series of lectures is to sketch how the enumerative geometry of the 19th century has grown into a thriving field of equivariant cohomology in the 20th and 21st centuries.
From Schubert calculus to equivariant cohomology
We will begin by sketching the history, starting from the Steiner question (in 1848): How many conics are tangent to 5 given plane conics? Answering such questions became a thriving business in the next half century, with a powerful but unjustified method devised primarily by Schubert. Hilbert's 15th problem asked for a justification. We will discuss how the development of algebraic topology can be used to solve such problems: Schubert's calculus takes place in the cohomology rings of appropriate moduli spaces.
Equivariant cohomology grew out of a seminar led by Borel in 1958-59. When a group acts on a space, there is a richer cohomology theory, now called equivariant cohomology, that takes this action into account. Most of the moduli spaces involved in classical enumerative geometry problems do have such group actions. With luck, equivariant cohomology can be calculated by localizing around fixed points.
We will describe some of what is known (and not known) about equivariant cohomology of algebraic varieties, mostly by example. In particular, we will look at Grassmannians, flag varieties, and toric varieties.
*Refreshments will be served at 3:00pm preceding each lecture.
A banquet honoring Professor Fulton will be held on Wednesday, April 27, 2011 from 6-8pm at the Five & Ten Restaurant. To register for the banquet please fill out this form and return it with payment to Julie McEver no later than Friday, April 22, 2011.
For
additional information about the 2011 Cantrell lecture series
please contact any of the following:
Joseph H. G. Fu, fu at math dot uga dot edu
Angela Gibney, agibney at math dot uga dot edu
Daniel Krashen, krashen at math dot uga dot edu
Julie McEver, julie at math dot uga dot edu
