Hausdorff dimension of the spectrum of the almost Mathieu operator – Igor Krasovsky

Igor Krasovsky
Imperial College of London

Date(s) : 15/02/2019   iCal
9 h 30 min - 10 h 30 min

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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