We study the local and global dynamics of mean curvature flow with spherical and cylindrical singularities. We find the most generic dynamic behavior of such singularities, and show that the singularities with the most generic dynamic behavior are robust. We also show that the most generic singularities are isolated and type-I. Among applications, we prove that the singular set structure of the generic mean convex mean curvature flow has certain patterns, and the level set flow starting from a generic mean convex hypersurface has low regularity. This is joint work with Jinxin Xue (Tsinghua University).
Ao Sun is a Dickson Instructor at the University of Chicago. He obtained Ph.D. from Massachusetts Institute of Technology in 2020 under the supervision of William Minicozzi. His research is mainly focused on geometry and partial differential equations, in particular geometric flows and minimal surfaces.
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