Berry phases in condensed matter physics

This lecture covers the conceptual aspects of the theory of electric polarization and orbital magnetization in condensed matter physics, focusing on the historical introduction, quantum mechanical theory of insulators, and the theory of orbital magnetization. The instructor discusses the challenges in defining polarization and the physics of point charges, emphasizing the quantum nature of adiabatic charge transport. The lecture explores the theory of polarization for quantum matter, highlighting the need for a different approach. It delves into the theory of P for quantum matter, emphasizing the non-trivial nature of the problem. The lecture concludes with a discussion on the robustness of the quantum anomalous Hall state and its implications for topological insulators.