Speaker: Jake Fillman (Texas State University)

Title: Almost-Periodic Schrödinger Operators with Thin Spectra

Abstract: The determination of the spectrum of a Schrödinger operator is a fundamental problem in mathematical quantum mechanics. We will discuss a series of results showing that almost-periodic Schrödinger operators can exhibit spectra that are remarkably thin in the sense of Lebesgue measure and fractal dimensions: the spectrum can be a Cantor set of zero Lebesgue measure and zero Hausdorff dimension.  [joint work with D. Damanik, A. Gorodetski, and M. Lukic]