"Behavior of Solutions of the Parabolic Anderson Model." Michael Cranston, University of California, Irvine The parabolic Anderson model on the integer lattice is the ordinary heat equation (with the discrete Laplacian) perturbed by a random potential. This model is relevant in modeling population growth, movements of electrons in crystals and polymers to name just a few applications. We will discuss primarily the case where the potential is the Stratonovich differential of a one-dimensional Brownian motion, with independent Brownian motions at each site of the lattice. Results to be discussed will be a.s. behavior of solutions, behavior of sums over boxes in the lattice of the solutions and the relation between quenched asymptotics, annealed asymptotics and intermittency. Variations of the model to Levy noise (instead of Brownian noise) and to continuous space will be included (time permitting.)