There has been considerable effort to understand properties of dilute, strongly interacting cold fermion systems realized, for example, in the experiments on trapped cold atomic gases. An example of such a system is a dilute Fermi gas with two-body interactions, characterized by infinite scattering length and zero effective range, which has been named Unitary Fermi Gas. Its theoretical description is difficult due to absence of an apparent small dimensionless parameter, which could be used in a perturbative expansion. However, recently an analytical technique, similar to the Epsilon expansion in the theory of critical phenomena (where the dimensionality of space serves as an expansion parameter), has been proposed for the Unitary Fermi Gas [Nishida and Son, Phys. Rev. Lett. 97, 050403 (2006)]. After an introduction, I will describe some recent results:
1. Landau-Ginzburg-like functional for Unitary Fermi Gas, which allows one to study inhomogeneous phenomena such as superfluid vortex structure, the normal/superfluid phase interface in the polarized (imbalanced) gas;
2. Low energy density-density correlation function and the dynamic structure factor, an experimentally measured quantity.