Dear all, Tomorrow in the lecture we will finish our discussion about the Mott insulator with a comment about the appearance of spatial structures in the presence of an overall harmonic confinement. We will then move to a two-component Fermi gas in an optical lattice, a system which has attracted a lot of interest in recent years. We will discuss a little bit why. In particular we will see that in this system there is also a Mott insulator, and that the Mott phase is characterized by an antiferromagnetic spin coupling due to the so-called super-exchange processes. I will discuss on the observation of super-exchange in experiments. If we have time I will start with the discussion of other lattice systems with cold gases in the so-called hard-core regime. See you tomorrow! Luis