Ancient curve shortening flows
There are a lot of different types of ancient curve shortening flows. However, it is known that the only convex ancient flows are shrinking circles, translating Grim Reaper curves, Angenent ovals, and static lines. So, it'd be interesting to classify ancient flows under an assumption weaker than convexity. In this talk, we will discuss about the classification of ancient curve shortening flows with finite entropy. In particular, we put emphasis on the uniqueness of tangent flow at negative infinity, which is the round circle or a straight line with multiplicity. This is a joint work with Dong-Hwi Seo, Wei-Bo Su, and Kai-Wei Zhao.