Random matrix theory and analysis of quasiperiodic Schroedinger operators

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Recently, there have been new very promising developments inanalysis of gap probabilities for random matrices and quasiperiodicSchroedinger operators. This led in particular, to a proof of a 40 yearold conjecture about Hausdorff dimension of the spectrum of thealmost Mathieu operator. The project will be to utilise these newideas to study the Hausdorff properties of the spectra of thisoperator and also to compute important gap probabilities for maintypes of random matrices.