Selected Topics in Mathematical Quantum Many-Body Systems

This course will present functional analytic methods for the study of many-body quantum systems. These systems, composed of a large number of interacting particles, play a central role in various areas of physics, from condensed matter to nuclear physics. Within this context, Bogoliubov theory provides a powerful framework for capturing quantum effects arising from particle correlations.

We will focus in particular on dilute quantum gases, which have attracted considerable attention in both the mathematical and experimental physics communities—especially in light of recent advances in the study of ultracold atomic gases. A central topic of the course will be recent applications of Bogoliubov theory to dilute Fermi gases, with the goal of developing a rigorous understanding of the role played by quantum correlations.