22 september 2008, kl 11.15-12.15, KTH, sal 3721.

Svetlana Jitomirskaya (University of California, Irvine): Quantitative Aubry duality, non-perturbative Eliasson theory and sharp properties of absolutely continuous spectral measures of 1D quasiperiodic operators

Abstract. We develop a quantitative version of Aubry duality (a Fourier-type transform acting on families of quasiperiodic operators) that, along with a localization-type statement, allows to obtain a full non-perturbative version of the Eliasson theory, valid in a non-vanishing strip. This leads to several sharp results such as exact modulus of continuity of the integrated density of states and dry Ten martini problem for Diophantine frequencies. The method also allows to analyze, for the first time, individual absolutely continuous measures in this setting. The talk is based on joint work with Artur Avila.