(Non)uniqueness questions in mean curvature flow

Mean curvature flow is the negative gradient flow of the volume functional which decreases the volume of (hyper)surfaces in the steepest way. Starting from any closed surface, the flow exists uniquely for a short period of time, but always develops singularities in finite time. In this talk, we discuss some non-uniqueness problems of the mean curvature flow passing through singularities. The talk is mainly prepared for non-specialists of geometric flows.