Ryan Bushling, University of Washington

PDL C401
The projection problem of geometric measure theory is the following: given a set A ⊆ ℝn, what is the relationship between the geometric properties of A and those of its projections onto kdimensional subspaces of ℝn? One way of answering this is to bound the dimension of the socalled exceptional set of orthogonal projections of A—the set of kplanes onto which the orthogonal projection of A has unusually low dimension compared to the dimension of A. Our purpose is to review the most important results of this sort, with an eye toward the technical tools involved in their proof, and to survey the author's own research in this area.