Abstract: Mean curvature flow deforms a curve (or surface, or submanifold) in the direction specified by its mean curvature vector field. This is the direction in which length (or area, or volume) decreases most rapidly, and it is thus a very canonical way to obtain minimal submanifolds. For curves, it is often called Curve Shortening Flow.
Mean curvature flow is a very active and important field. Many beautiful theorems, particularly for the curve shortening flow, have been obtained in the past 30 years. However, at the same time there are still many unsolved questions. In this talk I will give a short introduction and survey of this interesting and beautiful field.