Zoom-Meeting: https://wwu.zoom.us/j/97461739978 Abstract: Ricci flow is a tool for smoothing metrics: from pointwise curvature bound to higher derivative bound or from integral bound to pointwise bound. This has be- en especially successful for L p pinching with p > n/2. In joint work with Eric Chen and Rugang Ye, we obtain an L n/2 -curvature pinching sphere theorem for Yamabe me- trics and Gromov?s almost flat manifolds theorem. These generalize the earlier works of Hebey?Vaugon and Dai-Petersen-Wei which require L p pinching for p > n/2.