What is equivariant localization?

Speaker: Tom Braden (UMass)

Abstract: The cohomology ring is a very important invariant of topological spaces.  Elements of this ring behave in some respects like functions on the space, but unlike functions, they are not local: cohomology classes on smaller subsets do not generally glue to classes on the whole space.  But when the space has an action by a group of symmetries, one can consider the richer equivariant cohomology ring.  In nice situations, elements of equivariant cohomology do have a local nature, since they are completely determined by their restriction to the set of fixed points.  I will illustrate these ideas using various examples such as toric varieties, Grassmannians and arrangement Schubert varieties, where localization reduces questions about cohomology and equivariant cohomology to elementary manipulations of finite collections of polynomials.