The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime

We consider a gas of interacting bosons trapped in a box of side length one in the Gross-Pitaevskii limit. We review the proof of the validity of Bogoliubov's prediction for the ground state energy and the low-energy excitation spectrum. This note is based on joint work with C. Brennecke, S. Cenatiempo and B. Schlein.