I will report on studies of repulsive and attractive branches of a two-component normal Fermi gas in the BCS-BEC crossover by means of quantum Monte Carlo simulations. The results for the repulsive branch are relevant to the question of the emergence of itinerant ferromagnetism in the gas. I will discuss the zero-temperature equation of state of both balanced and unbalanced mixtures resulting in the phase diagram in the interaction-polarization plane. The critical density for the onset of ferromagnetic behavior and the stability of the fully ferromagnetic state will also be addressed.
I will also report on recent calculations of the attractive normal branch for a balanced gas close to the unitary limit. This branch is unstable due to pairing, but it can be stabilized by temperature or polarization. We obtain good agreement with recent experiments carried out at ENS extrapolated to zero unbalance and we also find that the gas is well described by Landau theory of Fermi liquids. This latter result can shed some light on the possible existence of the pseudo-gap phase above the superfluid transition temperature.