A two-component Fermi gas with s-wave resonant interaction is an interesting strongly-correlated quantum many-body system. In the first part of the talk, I present some exact theorems for this system, along with a new method which facilitates their easier derivation. This method may shed a new light at the general issue of ultraviolet divergences.

In the second part, we consider the ground state of the above system in the strong-interaction limit, where it becomes a Bose-Einstein condensate of two-fermion molecules, for which most quantum many-body methods are problematic. To overcome the problems, I present a new perturbation scheme; predictions of this theory are discussed.

The ideas contained in the above methods may also have implications for other physical systems.