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*NEW EVENT TIME* September 11, 2019 4:00pm to 5:00 pm�� Fine Hall 314����

We prove that any ancient weak solution of the mean curvature flow, whose blowdown for $t \to -\infty$ is $S^{n-1} x R$, is either a round shrinking cylinder, a translating bowl soliton, or an ancient oval. As a consequence, we confirm the mean convex neighborhood conjecture for neck singularities in arbitrary dimension.

To show this, we introduce a novel variant of the moving plane method, which we call “moving plane method without assuming smoothness” - where smoothness and symmetry are established in tandem.�� We expect this method to have many future applications in geometric analysis.

This is joint work with Kyeongsu Choi, Or Hershkovits and Brian White.