On fixed points of quantum gravity

We study the short distance behaviour of euclidean quantum gravity in the light of Weinberg's asymptotic safety scenario. Implications of a non-trivial ultraviolet fixed point are reviewed. Based on an optimised renormalisation group, we provide analytical flow equations in the Einstein-Hilbert truncation. A non-trivial ultraviolet fixed point is found for arbitrary dimension. We discuss a bifurcation pattern in the spectrum of eigenvalues at criticality, and the large dimensional limit of quantum gravity. Implications for quantum gravity in higher dimensions are indicated.