Piotr Pragacz: Diagonal subschemes and vector bundles.

Abstract: This is a joint work with V. Pati and V. Srinivas.
We shall discuss the following problem: when the diagonal of a scheme
X is the zero scheme of a section of a vector bundle of rank dimX
on X x X  ? This problem arose in computations of fundamental classes
of degeneracy loci. We will give a pretty complete answer in the surface
case, and discuss some higher dimensional varieties.