Monday

Singularity formation plays an essential role in the analysis and applications of geometric flows. In mean curvature flow, singularities are modeled by self-shrinking solutions, or shrinkers. Many shrinkers have been constructed, but it has remained unclear whether they can actually be realized as singularities of compact mean curvature flows. We will see that every currently known smoothly embedded shrinker whose asymptotic behavior is understood does arise in this way, with potential applications to the construction of fattening examples in all dimensions. This is based on joint work with Jingwen Chen, Ao Sun, and Xinrui Zhao.