  We analyze the collective modes of a harmonically trapped, strongly
interacting Bose gas in an optical lattice in the vicinity of the Mott
insulator transition. For that aim we employ the dynamical Gutzwiller
equations, by performing real-time evolution and by solving the equations in
linear response. We find a strong dependence on the spatial dimension of the
system: while in one dimension the frequency of the dipole mode vanishes at the
Mott transition, in higher dimensions the dominant dipole mode is featureless
and we find a signature only in the breathing mode. We discuss implications for
experiments with bosonic and fermionic atoms.
