In a joint work with Piotr Bizon, we study the nonlinear
evolution of a weakly perturbed anti-de Sitter (AdS) space by solving
numerically the four-dimensional spherically symmetric
Einstein-massless-scalar field equations with a negative cosmological
constant. Our results suggest that AdS spacetime is unstable under
arbitrarily small generic perturbations. We conjecture that this
instability is triggered by a resonant mode mixing which gives rise to
diffusion of energy from low to high frequencies. A brief summary of our
results can be found in arXiv:1104.3702.