Back to main Back to page

Open PDE & Analysis Seminar

Prof Svetlana Jitomirskaya (University of California, Irvine)

On the critical almost Mathieu operator

Friday 26th June 2020, 4pm (Paris time)

Abstract : Harper's operator - the 2D discrete magnetic Laplacian - is the model behind the Hofstadter's butterfly and Thouless theory of the Quantum Hall Effect. It reduces to the critical almost Mathieu family, indexed by phase. We will present a complete proof of singular continuous spectrum for this family, for all phases, finishing a program with a long history, and based on a simple Fourier analysis and a new duality-type transform. We also present a result (with I. Krasovsky) that proves one half of the Thouless' one half conjecture from the early 80s: that Hausdorff dimension of the spectrum of Harper's operator is bounded by 1/2 for all irrational fluxes. If time permits, we will also discuss recent progress towards the Thouless Catalan conjecture (joint with I. Krasovsky and L. Konstantinov).

BBB link

This is the link to the talks: link or the url


Thomas Alazard (ENS Paris-Saclay)         Nicolas Burq (Orsay)         Iván Moyano (Nice)