One of the fundamental findings of physics in the past century is that disorder can suppress the transport properties of waves. For instance, an electromagnetic signal might not be transmitted in the presence of random impurities in the medium. The same goes for an electron in a disordered medium or crystal. The most prominent practical application of this finding is the semiconductor, whose discovery has revolutionized technical progress up until today.

At the heart of this phenomenon is a deep mathematical theory that combines ideas from analysis and probability. The propagation of an electron in a medium can be described, in its simplest form, by a linear Schrodinger equation with a potential that represents the impurities in the medium. The transport properties (or lack thereof) of the solutions, which determine whether the medium is conducting or insulating, are reflected by the properties of the spectrum of this linear Schrodinger operator. Anderson localization refers to a broad set of results that state that under certain condition, and if the potential is sufficiently random, the spectrum is discrete and as a result solutions (wave functions) are localized in space for all times.

The purpose of this working group is to present and go through the rigorous proof of this property of random Schrodinger operators. The first meeting will be to set logistics and a plan for the group.