  We present the first proof-of-principle Cauchy evolutions of asymptotically
global AdS spacetimes with no imposed symmetries, employing a numerical scheme
based on the generalized harmonic form of the Einstein equations. In this
scheme, the main difficulty in removing all symmetry assumptions can be phrased
in terms of finding a set of generalized harmonic source functions that are
consistent with AdS boundary conditions. In four spacetime dimensions, we
detail an explicit set of source functions that achieves evolution in full
generality. A similar prescription should also lead to stable evolution in
higher spacetime dimensions, various couplings with matter fields, and on the
Poincare patch. We apply this scheme to obtain the first long-time stable 3+1
simulations of four dimensional spacetimes with a negative cosmological
constant, using initial data sourced by a massless scalar field. We present
preliminary results of gravitational collapse with no symmetry assumptions, and
the subsequent quasi-normal mode ringdown to a static black hole in the bulk,
which corresponds to evolution towards a homogeneous state on the boundary.
