** **

**Abstract:**

Ricci
flow is a generalization of the heat equation for Riemannian

metrics.
It plays a role in quantum field theory and string theory,

and
has proven to be a useful tool in the study of three-manifold

topology.
I will start with an introduction, from a physicist's

viewpoint,
to the flow and its general properties. I will then discuss

novel
applications of the flow to the geometry of black holes and to

the
numerical solution of the Einstein equation.