  In this work we study ultracold Fermions confined in a two-dimensional
optical lattice and we explore the Mott-insulator transition with the
Fermi-Hubbard model. On the basis of a mean-field approach, we study the phase
diagrams in the presence of a harmonic trapping potential. Local Mott-insulator
phases are shown to be generally situated in the center of the trap and
correspond to a vanishing variance of the local density. We then study the
effects induced by rotation on the Mott-insulator phase transition. In
particular, we show that the phase boundary reproduces the edge of the
Hofstadter butterfly.
