*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.