Louis Yudowitz, KTH Royal Institute of Technology
Introduced by Richard Hamilton in 1982, Ricci flow has been used to solve a variety of problems in geometry and topology.
A vital part of such proofs is a good understanding of finite time singularities. While we have such an understanding in dimensions 2 and 3, singularity models in higher dimensions are still relatively mysterious. This is partially due to the existence of singularity models which are singular themselves.
In this talk, we will prove bubble tree convergence of certain shrinking singularity models, which involves a detailed analysis of the singular set when it consists of isolated points.
As a consequence, we will recover any topology lost due to the formation of the singular points, as well as prove a qualitative classification result. The above results also apply to positive Einstein manifolds, as they are special cases of Ricci shrinkers.
This is all based on a joint work with Reto Buzano.