In this application, we propose to study the physics of the polaronic gas. In a spin imbalanced Fermi gas, that is with a larger number of spin up particles than with spin down, the usual Cooper pairing scenario no longer applies, and this raises the question of the possible phases of the system. It was recently proposed by C. Lobo et. al. [PRL 97, 200403 (2006)], that in the strong imbalanced regime the minority atoms dressed by the Fermi sea of the majority atoms form a weakly interacting gas of quasi-particles called polarons.Whereas the basic one-body properties of these polarons seem to be quite well understood the interaction between polarons is still a debated issue, but crucial in order to understand the many-body properties of the polaronic gas. We therefore propose to study the polaronic interaction problem in homogeneous polarized Fermi gases, and its extension to optical lattices.We will tackle the problem in two different ways: (i) directly addresses the scattering problem of two finite momentum polarons with a variational approach, or with a Green’s function approach, (ii) addresses the many-body properties of the polaronic gas assuming that the p-wave scattering volume of two polarons is obtained from the first step..Allowing the applicant to be hosted at the ENS (Paris), would give him the possibility to work in a different geographical and working environment from the one in which he has already worked before. The excellence of the host institution, which has been playing at international level a leader in the experiments on strongly interacting fermions, and in the theory of polarons, together with the vanguard of the project, provide the fellow with a good training, and open the way to a position of professional maturity.