Presented by:
Igor Krasovsky
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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