Nonuniqueness in Mean Curvature Flow

Mean curvature flow is the gradient flow of area functional that decreases the area in the steepest way. In general the flow will develop singularities in finite time. It is known that there may not be a unique way to continue the flow through singularities. In this talk, we will discuss some global features of the space of mean curvature flows that emerge from cone-like singularities. This is joint with Jacob Bernstein.