We present a joint work with Richard Bamler.
We consider Ricci flows that satisfy certain scalar curvature bounds. It is found that the time derivative for the solution of the heat equation and the curvature tensor have better than expected bounds. Based on these, we derive a number results. They are: bounds on distance distortion at different times and Gaussian bounds for the heat kernel, backward pseudolocality, L^2-curvature bounds in
dimension 4.