Richard Bamler will talk on 9th March at 5pm UK time, 6pm Brussels time. Please note the unusual time! Richard’s title is “Compactness and partial regularity theory of Ricci flows in higher dimensions” and his abstract is below.
Compactness and partial regularity theory of Ricci flows in higher dimensions
We present a new compactness theory of Ricci flows. This theory states that any sequence of Ricci flows that is pointed in an appropriate sense, subsequentially converges to a synthetic flow. Under a natural non-collapsing condition, this limiting flow is smooth on the complement of a singular set of parabolic codimension at least 4. We furthermore obtain a stratification of the singular set with optimal dimensional bounds depending on the symmetries of the tangent flows. Our methods also imply the corresponding quantitative stratification result and the expected L^p-curvature bounds.
As an application we obtain a description of the singularity formation at the first singular time and a long-time characterization of immortal flows, which generalizes the thick-thin decomposition in dimension 3. We also obtain a backwards pseudolocality theorem and discuss several other applications.