  After a brief historical overview of superfluidity in connection with neutron
matter and cold fermionic atoms, we discuss the commonalities between these two
systems as well as their relevance to the physics of neutron star crusts. We
then present the methodological tools we use to attack the many-body problem,
comparing Quantum Monte Carlo to mean-field theory and to the analytic
expectations at weak coupling. We review recent results on the equation of
state and the pairing gap of cold atoms and neutron matter and contrast them
with a variety of calculations by other groups. We conclude by giving a few
directions of possible future inquiry.
