Dr. Sergey Morozov Mathematisches Institut der Universität München Theresienstr. 39 D-80333 München Email: morozov@math.lmu.de Tel:   +49 (0)89   2180 4613 Büro: Block B, 4. Stock, 403 Arbeitsgruppe Analysis

Spectraltheorie periodischer Operatoren

Lectures: Mo 14-16, Online via Zoom
Exercises: Mo 16-18, Online via Zoom

The course is devoted to the study of spectral properties of self-adjoint operators commuting with translations in one or several dimensions. We will start from the Floquet-Bloch theory which allows to decompose such operators into direct integrals and deduce the band structure of their spectra. Then we will study the behaviour of the band functions for particular classes of models and discuss the questions of absolute continuity of their spectra, location and absence of spectral gaps, overlapping of the band functions and the behavior of the density of states.

If you would like to attend the course, please register here and send an extra email to the lecturer. A link to the zoom meeting will be sent to the registered participants via email.

On 2 November 2020, we start with an overview of the course and the organisational matters. The time slots for the lectures and exercises can be moved upon a joint decision of the participants, so please let me know if you cannot participate due to some collision in your schedule! The exercises will begin on November 9.