Toward a Theory of Ricci Flow in Dimension 4

Explore a lecture on the advancements in Ricci flow theory in dimension 4, presented by Richard Bamler at the Hausdorff Center for Mathematics. Discover how Ricci flow with surgery has been instrumental in 3-dimensional topology, particularly in verifying the Poincaré and Geometrization Conjectures by Perelman approximately 20 years ago. Learn about recent progress in higher-dimensional Ricci flow through new compactness and partial regularity theory, which offers fresh geometric perspectives on singularity formation and long-term flow behavior. The first part of this one-hour talk examines this innovative theory and its implications for studying singularities in dimension 4, while the second part presents new research conducted jointly with Eric Chen on resolving conical singularities, potentially enabling surgery construction or "flow through singularities" in four dimensions.