| Abstract: |
| Ancient solutions play a central role in mean curvature flow, since they often arise as blow-up models near singularities. This leads to a natural program: by classifying ancient solutions, one hopes to organize the possible local pictures of singularity formation. In this talk, I will give an introduction to this viewpoint and describe several recent classification results, focusing in particular on ancient ovals and related rigidity phenomena in higher dimensions. I will also explain how such results fit into the broader effort to understand singularities through canonical models. |
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