  CDT is an attempt to formulate a non-perturbative lattice theory of quantum
gravity. We describe the phase diagram and analyse the phase transition between
phase B and phase C (which is the analogue of the de Sitter phase observed for
the spherical spatial topology). This transition is accessible to ordinary
Monte Carlo simulations when the topology of space is toroidal. We find that
the transition is most likely first order, but with unusual properties. The end
points of the transition line are candidates for second order phase transition
points where an UV continuum limit might exist.
