Asymmetric matter at infinite scattering length -- from many particles to few particles

Recently there has been considerable interest in studying systems with short-ranged, infinite scattering length interactions (i.e. the scale-invariant universal limit). In the first half of this talk I present ongoing work on such universal systems assuming an asymmetricnumber of spin-up and spin-down fermion species. Assuming a mixed-phase solution, I show density profiles of such systems that are confined in an harmonic oscillator (HO) trap. I elaborate on the various approximations that go into these calculations. The second half of the talk concentrates on the few-body systems that interact in the universal limit within an HO trap. Such situations might be realized in the near future using optical lattices. I give preliminary results on ground- and excited-state spectra for two- and three-body fermionic systems. I comment on how the spectra are altered from the free-case due to the confining external HO potential.