  We discuss from a geometric point of view the connection between the
renormalization group flow for non--linear sigma models and the Ricci flow.
This offers new perspectives in providing a geometrical landscape for 2D
quantum field theories. In particular we argue that the structure of Ricci flow
singularities suggests a natural way for extending, beyond the weak coupling
regime, the embedding of the Ricci flow into the renormalization group flow.
