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Hausdorff dimension of the spectrum of the almost Mathieu operator

Presented by: 
Igor Krasovsky Imperial College London
Date: 
Thursday 31st October 2019 - 10:00 to 11:00
Venue: 
INI Seminar Room 1
Abstract: 
We will discuss the well-known quasiperiodic operator: the almost Mathieu operator in the critical case. We give a new and elementary proof (the first proof was completed in 2006 by Avila and Krikorian by a different method) of the fact that its spectrum is a zero measure Cantor set. We furthermore prove a conjecture going back to the work of David Thouless in 1980s, that the Hausdorff dimension of the spectrum is not larger than 1/2. This is a joint work with Svetlana Jitomirskaya.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons