Spectral theory and Avila's global theory for one-frequency quasi-periodic analytic Schrödinger cocycles

Mini-Curso - Sistemas Dinâmicos - Spectral theory and Avila's global theory for one-frequency quasi-periodic analytic Schrödinger cocycles
Expositor: Xiao-Chuan Liu
Instituição: USP-São Paulo
Data e Horário: 18/09/2019 e 19/09/2019 | 17h:15min

RESUMO: The purpose of this series of talks is to try covering the following topics, with emphasis on comparing results instead of introducing the proofs. 1. Basics on Spectral Theory of Schrödinger Operators, with an emphasis on Almost Mathieu operators. 2. Avila's Global Theory on quasi-periodic one-frequency analytic Schrödinger operators. 3. Reducibility Theory of SL(2,R) cocycles. This is meant as a working seminar, (given by and) addressed to non experts in the field, in the hope of creating possible collaborations in the future. Main References. 1. Avila, Artur. "Global theory of one-frequency Schrödinger operators." Acta Mathematica 215.1 (2015): 1-54. 2. Avila, Artur, and Svetlana Jitomirskaya. "Almost localization and almost reducibility." Journal of the European Mathematical Society 12(2010),93–131. 3. You, Jiangong. "Quantitative almost reducibility and its applications." International Congress of Mathematicians, Rio de Janeiro. 2018. 4. Avila, Artur. Video: Talk at the Conference In Memory of Jean-Christophe Yoccoz. 2017/05/31. Available at the following address. https://www.youtube.com/watch?time_continue=2&v=TTuM8EdXxhI

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