Mathematical Methods for Condensed Matter Physics

The course provides an introduction, with an analytic perspective, to the basic mathematical tools necessary to develop a deeper understanding of the mathematical theories of topological insulators. In particular, the course will cover the following topics: direct integrals of Hilbert spaces, stability theorems for relatively bounded perturbations, Bloch-Floquet transform and its application to periodic Schrodinger operators,
introduction to the theory of vector bundles and Chern classes, and the denition of  the Bloch bundle. Moreover, the basic mathematical models (continuous and discrete) for non-interacting and also interacting fermions will be discussed.

Due to the Covid19 situation the course is organized as follows:

Parts of the lecture (2 x 60 minutes per week) are recorded in advance and will be made available on ILIAS step by step. Lecture notes and exercises are uploaded on ILIAS together with the video of the lecture.

Each week there will be also an exercise class, which is held online via Zoom every Wednesday at 10:00 a.m.. The information to access the exercise class is provided through ILIAS.