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We discuss two-dimensional quantum gravity coupled to conformal matter andfixed area in a semiclassical large and negative matter central charge limit.In this setup the gravity theory -- otherwise highly fluctuating -- admits around two-sphere saddle. We discuss the two-sphere partition function up totwo-loop order from the path integral perspective. This amounts to studyingFeynman diagrams incorporating the fixed area constraint on the roundtwo-sphere. In particular we find that all ultraviolet divergences cancel tothis order. We compare our results with the two-sphere partition functionobtained from the DOZZ formula.

The two-sphere partition function in two-dimensional quantum gravity at fixed area