  A strong-coupling expansion for the phase boundary of the (incompressible)
Mott insulator is presented for the bose Hubbard model. Both the pure case and
the disordered case are examined. Extrapolations of the series expansions
provide results that are as accurate as the Monte Carlo simulations and agree
with the exact solutions. The shape difference between Kosterlitz-Thouless
critical behavior in one-dimension and power-law singularities in higher
dimensions arises naturally in this strong-coupling expansion. Bounded disorder
distributions produce a ``first-order'' kink to the Mott phase boundary in the
thermodynamic limit because of the presence of Lifshitz's rare regions.
