Mathematical Aspects of Quantum Hall Physics in Microscopic Models of Interacting Fermions - Part 3

Explore the mathematical foundations of quantum Hall physics through microscopic models of interacting fermions in this advanced lecture presented by Stefan Teufel at CY Advanced Studies during the Quantissima sur Oise Thematic Month 2025. Delve into the third part of this comprehensive series examining the rigorous mathematical treatment of quantum Hall systems, focusing on the theoretical framework that describes the behavior of interacting fermionic particles in strong magnetic fields. Investigate the mathematical tools and techniques used to analyze these complex many-body quantum systems, including the role of Landau levels, incompressible quantum fluids, and the emergence of fractional quantum Hall states. Examine how mathematical physics approaches provide insights into the topological properties and collective excitations that characterize these remarkable quantum phases of matter. Build upon concepts from previous parts of the series to understand advanced topics in the mathematical description of strongly correlated electron systems in two-dimensional geometries subject to perpendicular magnetic fields.