Abstract: 

The DG Literature Workshop is an event for students and researchers interested in DG to come together and discuss papers recently uploaded to the arXiv. For our third workshop, we will be looking at “A note on the self-similarity of limit flows” by Beomjun Choi, Robert Haslhofer and Or Hershkovits which can be found at https://arxiv.org/abs/1910.02341. The abstract of the paper can be seen below.

“It is a fundamental open problem for the mean curvature flow, and in fact for many partial differential equations, whether or not all blowup limits are selfsimilar. In this short note, we prove that for the mean curvature flow of mean convex surfaces all limit flows are selfsimilar (static, shrinking or translating) if and only if there are only finitely many spherical singularities. More generally, using the solution of the mean convex neighborhood conjecture for neck singularities, we establish a local version of this equivalence for neck singularities in arbitrary dimension. In particular, we see that the ancient ovals occur as limit flows if and only if there is a sequence of spherical singularities converging to a neck singularity. ”

Anyone is welcome to attend, though we highly recommend reading through the paper once.