  I discuss certain applications of the Ricci flow in physics. I first review
how it arises in the renormalization group (RG) flow of a nonlinear sigma
model. I then review the concept of a Ricci soliton and recall how a soliton
was used to discuss the RG flow of mass in 2-dimensions. I then present recent
results obtained with Oliynyk on the flow of mass in higher dimensions. The
final section discusses one way in which Ricci flow may arise in general
relativity, particularly for static metrics.
