The equation of state and pairing gap of neutron matter at low densities are important to the structure and cooling of neutron stars, and potentially to the surface properties of neutron-rich nuclei. Cold fermionic gases provide another setting with quite similar physics. Both these systems are very strongly paired, i.e. the pairing gap is of the order of the Fermi energy. Several many-body schemes have been devised in an attempt to accurately describe the strong coupling regime. In this talk, I will discuss recent results on the equation of state, the pairing gap, and other observables that we have calculated using a microscopic ab initio method. I will also mention some even more recent results on Fermi-Fermi mixtures.
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