Mathematical Aspects of Quantum Hall Physics in Microscopic Models of Interacting Fermions - Part 1

Explore the mathematical foundations of quantum Hall physics through microscopic models of interacting fermions in this comprehensive lecture presented by Stefan Teufel at CY Advanced Studies during the Quantissima sur Oise Thematic Month 2025. Delve into the rigorous mathematical framework underlying quantum Hall phenomena, examining how interacting fermion systems exhibit the remarkable properties observed in quantum Hall states. Learn about the theoretical approaches used to analyze these complex many-body systems, including the mathematical tools and techniques essential for understanding the emergence of quantum Hall physics from first principles. Discover how microscopic interactions between fermions give rise to the macroscopic quantum Hall effects, with particular emphasis on the mathematical structures that govern these phenomena. The lecture provides a detailed examination of the theoretical underpinnings that connect microscopic quantum mechanical descriptions to the observed quantum Hall behavior, offering insights into both the mathematical elegance and physical significance of these systems.