Title: Localization for the Anderson model
Abstract: Anderson localization is a physical phenomenon in which electron transport in amorphous solid materials is inhibited by the presence of disorder. The Anderson model for this phenomenon consists of the Laplacian on a lattice perturbed by a random potential. After briefly discussing the mathematical theory of the Anderson model, I will explain my recent joint work with Jian Ding. We prove that, in the case of a Bernoulli potential and a two dimensional lattice, the eigenfunctions near the edge of the spectrum are exponentially localized. A key ingredient is a new unique continuation result for eigenfunctions of random Hamiltonians in dimension two.