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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Hausdorff dimension of the spectrum of the almost Mathieu operator

## Hausdorff dimension of the spectrum of the almost Mathieu operatorAdd to your list(s) Download to your calendar using vCal - Igor Krasovsky (Imperial College London)
- Thursday 31 October 2019, 10:00-11:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact info@newton.ac.uk. CATW02 - Complex analysis in mathematical physics and applications 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. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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