Zoom link: https://princeton.zoom.us/j/594605776

I will describe how parabolic smoothing properties of the Ricci flow from initial supercritical L^p integral curvature control, p>n/2, can be extended to the critical, scale-invariant L^{n/2} case using the W-functional and related entropies. Such smoothing occurs in both global and relatively local situations, the latter being motivated by Perelman's pseudolocality theorem.  As applications we have gap theorems for shrinking and steady solitons as well as Ricci-nonnegative noncompact manifolds based on scale-invariant hypotheses, in addition to a compactness result.

This is joint work with Pak-Yeung Chan and Man-Chun Lee.