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.