Unitary Fermi gas and beyond

A Fermi gas at infinite scattering length (a unitary Fermi gas) has been realized in ultracold atom experiments and attracted considerable interest across many subfields because of its strong interaction, scale invariance, and universality. I will start with introducing an epsilon expansion technique, which proovides reasonable estimates of key quantities of the unitary Fermi gas. The epsilon expansion also reveals the fact that the unitary Fermi gas (and the Efimov effect for bosons) exists only in 3D and becomes trivial in other dimensions. However, I show that analogs of the unitary Fermi gas (and associated BCS-BEC crossover physics) exist in "mixed dimensions" and 4-body interaction in 1D, where I discuss the appearance of rich many-body physics. This study considerably extends our perspectives on the universal few-body and many-body physics and hopefully opens up very rich new research areas.