  We study the Euclidean path integral of two-dimensional quantum gravity with
positive cosmological constant coupled to conformal matter with large and
positive central charge. The problem is considered in a semiclassical expansion
about a round two-sphere saddle. We work in the Weyl gauge whereby the
computation reduces to that for a (timelike) Liouville theory. We present
results up to two-loops, including a discussion of contributions stemming from
the gauge fixing procedure. We exhibit cancelations of ultraviolet divergences
and provide a path integral computation of the central charge for timelike
Liouville theory. Combining our analysis with insights from the DOZZ formula we
are led to a proposal for an all orders result for the two-dimensional
gravitational partition function on the two-sphere.
