  The recent progress in the Causal Dynamical Triangulations (CDT) approach to
quantum gravity indicates that gravitation is nonperturbatively renormalizable.
We review some of the latest results in 1+1 and 3+1 dimensions with special
emphasis on the 1+1 model. In particular we discuss a nonperturbative
implementation of the sum over topologies in the gravitational path integral in
1+1 dimensions. The dynamics of this model shows that the presence of
infinitesimal wormholes leads to a decrease in the effective cosmological
constant. Similar ideas have been considered in the past by Coleman and others
in the formal setting of 4D Euclidean path integrals. A remarkable property of
the model is that in the continuum limit we obtain a finite space-time density
of microscopic wormholes without assuming fundamental discreteness. This shows
that one can in principle make sense out of a gravitational path integral
including a sum over topologies, provided one imposes suitable kinematical
restrictions on the state-space that preserve large scale causality.
