Speaker: Dr. Zhenghe Zhang (UCR)
Title: Uniform Hyperbolicity and its applications to 1D discrete Schroedinger Operators
Abstract: In this talk, I will first introduce the notion of uniformly hyperbolic SL(2,R) cocycles. Various equivalent conditions of the uniform hyperbolicity will be discussed. Then I will sketch my recent proof of the correspondence between uniform hyperbolicity and the resolvent set of the one-dimensional discrete Schroedinger operators. This correspondence is known as Johnson's Theorem and is one of the basic relations between dynamics of cocycles and spectral analysis of the ergodic Schroedinger operators. It was first discovered by Russell Johnson in 1980s.
Friday, October 12, 2018 at 2:10pm to 3:00pm
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