Description:

TITLE: Ricci flow on non-compact Riemannian manifolds and curvature 
concentration.

ABSTRACT: The Ricci flow on Riemannian manifolds was introduced by Richard 
Hamilton in 1982 to approach fundamental problems in topology & geometry 
with parabolic PDE methods. It has since been applied successfully to 
longstanding problems on compact and non-compact manifolds. In this talk I 
will review the development of basic Ricci flow theory on complete 
non-compact manifolds then focus on the assumption of integral/weak 
curvature bounds. Results on long-time existence and convergence of the 
flow will provided when the initial Riemannian manifold satisfies certain 
scale-invariant conditions. The talk is based on joint work with Adam 
Martens.