Uniqueness of convex ancient solutions to mean curvature flow in R3

A well-known question of Perelman concerns the classification of noncompact ancient solutions to the Ricci flow in dimension 3 which have positive sectional curvature and are -noncollapsed. In this paper, we solve the analogous problem for mean curvature flow in R3, and prove that the rotationally symmetric bowl soliton is the only noncompact ancient solution of mean curvature flow in R3 which is strictly convex and noncollapsed.