Differential Geometry Seminar | The mean curvature flow, singularities, and entropy

Abstract：

The mean curvature flow is an example of a geometric flow, where in this case one deforms a submanifold according to its mean curvature vector. Like many such flows though the mean curvature flow will develop singularities, where the flow “pinches.” The entropy, in the sense of Colding and Minicozzi, is an interesting area-like monotone quantity under the flow, for one because it can constrain what sorts of singularity models may arise, and has played an important role in many recent developments. In this talk after introducing the relevant notions we’ll discuss some of these results, including some joint work with S. Wang.