Bogolubov's celebrated 1947 theory of Bose gases was invented to
explain the superfluidity of liquid Helium. Only a few rigorous aspects of
the theory have been validated rigorously. I will discuss cases of Bose
gases in which Bogolubov's theory correctly predicts the ground state energy
in certain asymptotic limits. In particular, I will discuss a recent proof
of the famous Lee-Huang-Yang formula for the ground state energy of a dilute
Bose gas. I will also briefly mention what may be derived from Bogolubov's
method when applied to the charged Bose gas.
This is joint work with E.H. Lieb.