Ricci flow and positivity of curvatures on manifolds with boundary

In this talk, we would discuss how to construct a canonical solution to Ricci flow on manifolds with boundary given an arbitrary initial metric. This solution behaves well with respect to natural curvature conditions for Ricci flow on closed manifolds. Our construction has the advantage of preserving various important curvature conditions along the flow under natural assumptions on the boundary. As an application, this produces pleasant topological consequences for manifolds with boundary.