EVENT DETAILS AND ABSTRACT

Title: Deformations of standard Koszul algebras and localization in equivariant cohomology.
Speaker: Tom Braden
Speaker Info: U Mass Amherst
Brief Description:
Special Note: Note special time (3pm)
Abstract:

We show that the center of a flat graded deformation of a standard Koszul algebra behaves in many ways like the torus-equivariant cohomology ring of an algebraic variety with finite fixed-point set. In particular, the center acts by characters on the deformed standard modules, providing a "localization map." We construct a universal graded deformation, and show that the spectrum of its center is supported on a certain arrangement of hyperplanes which is orthogonal to the arrangement coming from the Koszul dual algebra. This is an algebraic generalization of a duality discovered by Goresky and MacPherson between the equivariant cohomology rings of partial flag varieties and Springer fibers.