Quantum states in solids are not only determined by energy bands but also by the geometry and topology of the underlying Bloch wave functions. These hidden structures govern a wide range of modern phenomena—from the quantum Hall effect and Berry-phase physics to topological insulators, quantum anomalous responses, and unconventional transport in magnets and superconductors. This course provides an introduction to the geometric and topological concepts that shape the behavior of electrons, magnons, and other quasiparticles in condensed matter systems. We develop the necessary mathematical tools (Berry curvature, quantum metric, topological invariants, ...) and explore how they manifest in experiments. The focus is on conceptual understanding through modern examples rather than heavy formalism. The lecture is aimed at Master’s and PhD students in physics with an interest in condensed matter, quantum materials, or theoretical physics. Prior knowledge of the theory of the solid state is useful.
- Lehrende/r: Alexander Mook