Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## The Structure of the Spectrum of a Dynamically Defined Schrödinger Operator

Talk by Prof. Dr. David Damanik

Speaker invited by: Prof. Dr. Artur Avila

**Date:** 28.03.22 **Time:** 14.05 - 15.05 **Room:** ETH HG G 43

We consider Schrödinger operators whose potentials are defined by sampling the orbits of a homeomorphism of a compact metric space with a continuous function. Motivated by the phenomenon of spectral pseudo-randomness we discuss mechanisms that allow one to show that the gap structure of such a spectrum is very simple under suitable assumptions. Specific instances include applications of Johnson's approach to the gap labelling theorem and the effects of small random perturbations of a given background.