Abstract: In this talk, I am going to describe recent progress in the mathematical analysis of dilute Bose gases. In particular, I am going to discuss a rigorous version of Bogoliubov theory and I am going to show how it can be used to derive precise estimates on the low-energy spectrum of Bose gases in the so-called Gross-Pitaevskii regime and to prove bounds on the ground state energy per unit volume in the thermodynamic limit.
