Advanced topics chosen by the instructor. The content of this course changes, as in the case of seminars.

Description: Ergodic Schrodinger operators include, as particular cases, several popular models in solid-state physics, most notably, random and quasiperiodic operators. Mathematically, this theory lies at the intersection of functional analysis, harmonic analysis, probability, and ergodic theory, using methods and ideas from and providing a wealth of interesting open problems to all four. Topics include: Singular-continuous spectra (Wonderland theorem), the basics of (ergodic) Schrodinger operators: Schrödinger operators and quantum dynamics, corollaries of ergodicity, integrated density of states and Bourgain-Klein continuity theorem; Anderson localization for the Anderson model, basic properties of cocycles, multiplicative ergodic theorem, Lyapunov exponents, Kotani theory, one-dimensional quasiperiodic localization, and, time permitting, Avila's global theory of one-dimensional analytic quasiperiodic operators. Various open problems will be discussed. Prerequisite: spectral theory of bounded self-adjoint/normal operators (as in 206 or 224A in the Fall 2023) and the basics of ergodic theory

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