Mean Curvature Flow

A mean curvature flow is an evolving submanifold $M_t$ whose velocity is equal to its mean curvature. Mean curvature flow is in some respects the most natural evolution equation for a moving submanifold: it is the gradient flow of the area functional, as well as the analog of the heat equation for submanifolds. The lecture will survey mean curvature flow for a general audience.