Aperiodic systems from a spectral point of view

06.02.2019, 14:00  –  Haus 9, Raum 2.22
Institutskolloquium

Jean Bellissard (Georgia Institute of Technology Atlanta and WWU Münster), Hans Daniel Lenz (Universität Friedrich Schiller Jena)

14:00 Jean V. Bellissard: Self-adjoint Operators on aperiodic media

15:00 Tea and Coffee break

15:30 Hans Daniel Lenz: Discrete spectrum for topological dynamical systems

Jean V. Bellissard (WWU, Münster and Georgia Institute of Technology, Atlanta, Georgia): Self-adjoint Operators on aperiodic media
Various aperiodic media have been studied by physicists since the early fifties. The problem of computing the energy spectrum of various degrees of freedom, like electrons, phonons or spin waves on such media is still largely open and considered as a hard problem. We will present the main methods used to compute the energy spectrum, which consist in several approximations. In this talk we will focus on mathematical results recently obtained to justify these approximations. (Joint work with Siegfried Beckus and Giuseppe De Nittis)

Hans Daniel Lenz (Universität Friedrich Schiller, Jena): Discrete spectrum for topological dynamical systems
Discrete spectrum is a most basic feature that a dynamical system may have.  In the context of aperiodic order dynamical systems with discrete spectrum have received particular interest in recent years. We give an introduction into the topic and discuss characterizations for discrete spectrum via almost periodicity.