Translators for Mean Curvature Flow

A translator for mean curvature flow is a hypersurface $M$ with the property that translation is a mean curvature flow. That is, if the translation is $t\rightarrow M+t\vec{v}$, then the normal component of the velocity vector $\vec{v}$ is equal to the mean curvature $\vec{ H}$. I will discuss recent joint work with Tom Ilmanen, Francisco Martin and Brian White, specifically our classification of the the complete translators in $R^3$ that are graphical, and the construction of new families of complete translators that are not graphical.