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Penn Mathematics Colloquium

Wednesday, April 24, 2019 - 3:30pm

Charles Smart

Univ. Chicago


University of Pennsylvania


Tea at 3:00 in DRL 4E17

Anderson localization is a physical phenomenon in which electron transport in solid materials is inhibited by disorder. The Anderson model for this phenomenon consists of the Laplacian on a lattice perturbed by a random potential.

After briefly reviewing 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.