  We use the Kotliar-Ruckenstein slave boson technique to treat the strong
correlation of the Hubbard model. In a first part we discuss the metal to
insulator transition that is occurring on the honeycomb lattice at half
filling. We find the critical value for the interaction strength to be U/t=3.1.
Above it a gap opens in the spectrum which behaves like (U-U_c) in the vicinity
of the transition, and like U for strong coupling. In a second part we
calculate the phase diagram of the Hubbard model on the square lattice at
finite temperature. The Mermin-Wagner theorem is fulfilled in the largest part
of the phase diagram. In the strong coupling regime, the uniform magnetic
susceptibility shows a maximum in its doping dependence in agreement with
numerical simulations.
