Ergodic Theory and Spectral Theory Seminar: "Introduction to spectral analysis of ergodic Schrodinger Operators"

Title: Introduction to spectral analysis of ergodic Schrodinger Operators

Speaker: Zhenghe Zhang

Abstract: This will be the first of series of talks introducing the spectral analysis of ergodic type of Schrodinger Operators, the study of which lies across dynamical systems, spectral theory, and mathematical physics. It has been a field of very active study since the late 1970’s. In particular, it has made striking progress in the past 20 years since seminal works of Jitomirskaya, Bourgain-Goldstein, Goldstein-Schlag, and recently numerous works of Avila, whose work in this field partly led to the Fields medal he was awarded in 2014. We will get started with the physical background, i.e. the one-dimensional discrete Schrodinger equations which models the motion of quantum particles in disorder media, such as the motion of electron in alloys. Then we will introduce the spectral analysis of 1-dimensional discrete Schrodinger operators and the dynamics of the associated Schrodinger cocycles. Along the way, we will introduce necessary notions and techniques from dynamical systems and ergodic theory. The talks should be suitable for beginning graduate students.

Friday, April 6 at 2:10pm to 3:00pm

Campus Surge, 268

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