Mathematical Aspects of Quantum Hall Physics in Microscopic Models of Interacting Fermions - Part 2

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 second part of this comprehensive examination of quantum Hall systems, focusing on the rigorous mathematical treatment of many-body quantum systems where electrons interact in strong magnetic fields. Examine the theoretical frameworks used to understand the emergence of fractional quantum Hall states, the role of electron-electron interactions in creating correlated quantum phases, and the mathematical tools necessary to analyze these complex many-body phenomena. Investigate the connection between microscopic Hamiltonians and the macroscopic properties observed in quantum Hall experiments, including the formation of incompressible quantum fluids and the topological nature of quantum Hall states. Study the mathematical techniques employed to handle the interplay between kinetic energy, Coulomb interactions, and magnetic field effects in two-dimensional electron systems, providing essential insights for researchers working in condensed matter theory, mathematical physics, and quantum many-body systems.