Hofstadter's Butterfly
Student Geometric Functional Analysis Seminar
Meeting Details
For more information about this meeting, contact Michael Francis.
Speaker: Alp Uzman, Penn State Mathematics Department
Abstract: Artur Avila's work on the quasi-periodic Schrodinger cocycles is towards illuminating deep connections between spectral theory and dynamics. In this talk I will focus on a specific case, namely the so-called Hofstadter's Butterfly, to give a sense of what such a connection might look like; in particular I will state the Aubry-Andre conjecture and Avila's solution of it, joint with Raphael Krikorian. Hofstadter's Butterfly is a "recursive" graph that crops up in solid state physics, which can be plotted by adjoining the spectra of a certain family of linear operators on square-integrable two-sided complex sequences, and said family of linear operators are studied extensively. If time permits I will further go into details and mention the main ingredients of Avila's and Krikorian's solution.
Room Reservation Information
Room Number: 315 McAllister
Date: 11/29/2017
Time: 1:20pm - 2:20pm