Title: L^p bounds for Schrödinger eigenfunctions

Abstract: We consider upper bounds on the growth of L^p norms of high frequency eigenfunctions of Schrödinger operators on a compact Riemannian manifold.  Our treatment will begin with a review of the classical theory for Laplace operators without a potential, including the bounds of C. Sogge.  We will then turn to a case of recent interest, nontrivial potentials which are nonsmooth and satisfy critical behavior with respect to scaling.  The Kato class potentials will also be seen to play a crucial role in establishing the existence and regularity of these eigenfunctions.  This is based on joint works with X. Huang, Y. Sire, and C. Sogge.