This summer school introduces the basic spectral theory of Schrödinger operators. The focus is on one-dimensional operators that are defined by some underlying dynamical system. The aim is to extract various spectral properties such as spectral types, behavior of generalized eigenfunctions, gap labels and the structure of the spectrum as a set. This allows to study different models such as the Fibonacci Hamiltonian.
The summer school is partially based on the recent book "One Dimensional Schrödinger Operators I. General Theory" and its application to specific models.
The summer school is aimed at young researchers such as graduate students and postdocs who are interested in these topics.
The school covers one week with three main lecturers:
- David Damanik (Rice University, Houston)
- Jake Fillman (Texas State University)
- Anton Gorodetski (University of California, Irvine)
These are complemented by problem-solving sessions.
Participants need to be comfortable with the foundational topics of the usual undergraduate math curriculum. Additionally, some knowledge about functional analysis, basic spectral theory, ergodic theory and terminologies in dynamical systems will be helpfull. Therefore, we provide an online crash course before the summer school.
The summer school is
- supported by the SPP 2026 Geometry at Infinity
- co-organized by the European Cooperation in Science and Technology within the Action Mathematical models for interacting dynamics on networks
- supported by the Hans Böckler Stiftung