  We apply perturbative renormalization group theory to the symmetric phase of
a dilute interacting Bose gas which is trapped in a three-dimensional harmonic
potential. Using Wilsonian energy-shell renormalization and the
epsilon-expansion, we derive the flow equations for the system. We relate these
equations to the flow for the homogeneous Bose gas. In the thermodynamic limit,
we apply our results to study the transition temperature as a function of the
scattering length. Our results compare well to previous studies of the problem.
