Starting from Bloch theorem and basis expansions for crystal wavefunctions, we will introduce geometric phases and crystal symmetries, leading to a first description of topological band theory. We will then outline the Green's function formalism and apply it to the study of interacting many-body systems, such as the Anderson Impurity Model and interacting many-electron lattice Hamiltonians. Approximate solution techniques will be discussed, especially the Dynamical Mean-Field / Iterated Perturbation Theory.

The second part of the course will regard Density Functional Theory, outlined both theoretically and through familiarization with various established DFT toolkits (VASP, Quantum ESPRESSO, ...).

The lectures will be held in english. Weelky exercise sessions will take place in the CIP pool. In the exercises, the basic ideas of various algorithms will be implemented either with the help of template programs or by means of completely self-written codes.

Electronic submission of all exercises (not mandatory) and ~30 min oral exam starting with a short presentation of results obtained by the students followed by general questions on all the topics of the course.