Mathematical Sciences: Mathematical Physics

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This is a research project in mathematical physics. The main focus is on Schroedinger operators, which are basic to the modelling of physical systems at the microscopic level. In particular, Professor Simon will investigate random Schroedinger operators, in which the potential term (normally a function of position) is a stochastic process. He and Professor Avron will also use Schroedinger operators in constructing a theory of flux through networks. Various topological problems that have arisen in mathematical physics, e.g. concerning the set of hermitian matrices with nondegenerate eigenvalues, will be attacked.