Let G be a simple algebraic group with flag variety G/B. The Springer resolution is the moment map from the cotangent bundle of G/B to the (dual of the) Lie algebra g of G. The cohomology of the fibers of this map play an important role in the representation theory of G over various fields. Identify the cotangent bundle with the vector bundle G×B n, where n is the nilradical of the Lie algebra of B. There are subbundles G×B I for each subspace I⊂n that is B-stable, and maps pI:G×B I→g. The fibers of pI are also interesting and their cohomology relates to an intersection cohomology complex on the image of pI, a nilpotent variety. In this talk we discuss two topics: (1) methods for computing the cohomology of the fibers of pI; (2) a vanishing theorem/conjecture for the cohomology of the structure sheaf on these subbundles.