Location: Zoom
https://unm.zoom.us/j/96832154356?pwd=S3BpaDd1TkNCQmN2L3lZdmVDUXdzUT09
Meeting ID: 968 3215 4356
Passcode: 31415926

 

Title: Logarithmic capacities of rational frequency approximants for discrete Schrödinger operators

 

Abstract: In their Analytic quasi-periodic Schrödinger operators and rational frequency approximants paper, Svetlana Jitomirskaya and Chris Marx proved the following result: Consider a quasi-periodic Schrödinger operator with analytic potential and irrational frequency. Given any rational approximating the irrational frequency, let S+ and S- denote the union and the intersection of the spectra taken over the phase, respectively. They showed that up to sets of zero Lebesgue measure, the spectrum and the absolutely continuous spectrum can be obtained asymptotically from S+ and S- of the periodic operators associated with the continued fraction expansion of the irrational frequency, respectively. 

 

In this talk, I will discuss these results with logarithmic capacity instead of Lebesgue measure for quasi-periodic Schrödinger operators with analytic potentials.  I will also discuss the special case of the almost Mathieu operator. This is a joint work with Svetlana Jitomirskaya.

 

Bio: Burak is a visiting professor at Michigan State University. His PhD is from Texas A&M where he worked with Alexei Poltoratski. His research interests are in spectral theory, complex analysis and approximation theory. For more information see his homepage.