Applied Math Seminar
Winter Quarter 2009
3:15 p.m.
Sloan Mathematics Corner
Building 380, Room 380-C

Friday, January 30, 2009

Svetlana Jitomirskaya
Mathematics
University of California at Irvine

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


Abstract:

The talk will be about making a rigorous sense of the intuitively clear statement that, in the context of quasiperiodic operators, localization in the momentum space means delocalization (absolutely continuos spectrum) in the original space - the so-called Aubry duality. It 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 and Diophantine frequencies: full non-perturbative version of Eliasson theory, exact modulus of continuity of the integrated density of states and individual spectral measures, dry Ten martini problem. The talk is based on joint work with Artur Avila.