  We report results from a systematic analytic strong-coupling expansion of the
Bose-Hubbard model in one and two spatial dimensions. We obtain numerically
exact results for the dispersion of single particle and single hole excitations
in the Mott insulator. The boundary of the Mott phase can be determined with
previously unattainable accuracy in one and two dimensions. In one dimension we
observe the occurrence of reentrant behavior from the compressible to the
insulating phase in a region close to the critical point which was conjectured
in earlier work. Our calculation can be used as a benchmark for the development
of new numerical techniques for strongly correlated systems.
