Local dynamics and shape of mean curvature flow passing through a singularity

A central question in geometric flow is to understand how the geometry and topology change after passing through singularities. I will explain how the local dynamics influence the shape of the flow near a singularity, and how the geometry and topology of the flow will change after passing through a singularity with generic dynamics. This talk is based on joint work with Zhihan Wang and Jinxin Xue.