This research is concerned with a number of closely related questions about the cohomology and representation theory of semisimple algebraic groups and finite groups of Lie type. One major focus is the cohomology of line bundles on flag varieties, where the study of module structure would illuminate the vanishing behavior. This research is in the general area of algebraic groups. The proposed research falls under two broad headings: cohomology of line bundles on flag varieties, and injective modules. Advances along these lines would both shed light on Lusztig's conjecture, as well as, point the way beyond it.
