Cold quantum gases: coherent quantum phenomena from Bose-Einstein condensation to BCS pairing of fermions

Studies of trapped quantum gases of bosons and of fermions have opened up a new range of many-body problems, having a strong overlap with nuclear and neutron star physics. Topics discussed here include: the Bose yrast problem -- how many-particle Bose systems carry extreme amounts of angular momentum; the infrared divergent structure of the transition to Bose condensation in a weakly interacting system; and the physics of extremely strongly interacting Bose and Fermi systems, in the scale-free regime where the two body s-wave scattering lengths are large compared with the interparticle spacing. Such a regime is realized experimentally through use of atomic Feshbach resonances. Finally we discuss creation of BCS-paired states in trapped Fermi gases.