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Phase transitions for the almost Mathieu operator

Tuesday 7th April 2015 - 13:30 to 14:30
INI Seminar Room 1
Co-authors: Artur Avila (IMPA & Paris 7), Jiangong You (Nanjing University)

For the almost Mathieu operator with any fixed frequency, we locate the point where phase transition from singular continuous spectrum to pure point spectrum takes place, which settles Aubry-Andr\'e conjecture for all irrational frequencies, and also solves Avila and Jitomirskaya's conjectures. Together with former paper of Avila, we give a complete description of phase transitions for the almost Mathieu operator.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons