Regularity theory for Type I Ricci flows

A  Ricci flow exhibits a Type I singularity if the curvature blows up at a certain rate near the singular time. Type I singularities are abundant and in fact it is conjectured that they are the generic singular behaviour for the Ricci flow on closed manifolds.

In this talk, I will describe some new integral curvature estimates for Type I flows, valid up to the singular time. These estimates partially extend to higher dimensions an estimate that was recently shown to hold in dimension three by Kleiner-Lott, using Ricci flow with surgery.

In this work we use the monotonicity formula available for Type I Ricci flows, adapting the technique of quantitative stratification of Cheeger-Naber to this setting.