Svetlana Jitomirskaya (University of California, Irvine): 

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TITLE: 

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Quantitative Aubry Duality and sharp results on absolutely continuous
spectra of 1D quasiperiodic operators. 

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ABSTRACT: 



Aubry duality (a Fourier-type transform acting on families of
quasiperiodic operators) has previously been understood only on the
qualitative level. We develop a quantitative version that, along with a
localization-type statement, allows to prove several sharp results on the
regime of absolutely continuous spectrum of 1D Schrodinger operators with
analytic quasiperiodic potentials with Diophantine frequencies: full
non-perturbative version of Eliasson theory, exact modulus of continuity
of the integrated density of states, dry Ten martini problem. It also
allowed to analyze, for the first time, individual absolutely continuous
measures in this setting. The talk is based on joint work with Artur
Avila.