Equation of State and Phases of Dilute Fermi Gases

I will discuss the recent progress in understanding the the zero temperature phase diagram of the spin assymetric dilute Fermi gas as function of the coupling constant. I will show the recent ab initio calculations of the equation of state at the unitary limit. The knowledge of the equation of state establishes the values of the chemical potentials at the phase transition points. They are directly related to the density profiles of the trapped gas through LDA (Local Density Approximation). Comparisons with the recent experiments are also discussed.