Random matrix theory and analysis of quasiperiodic Schroedinger operators

Recently, there have been new very promising developments in
analysis of gap probabilities for random matrices and quasiperiodic
Schroedinger operators. This led in particular, to a proof of a 40 year
old conjecture about Hausdorff dimension of the spectrum of the
almost Mathieu operator. The project will be to utilise these new
ideas to study the Hausdorff properties of the spectra of this
operator and also to compute important gap probabilities for main
types of random matrices.