Classification of noncollapsed translators in $\mathbb{R}^4$

In this paper, we classify all noncollapsed singularity models for the mean curvature flow of 3-dimensional hypersurfaces in $\mathbb{R}^4$ or more generally $4$-manifolds. Specifically, prove that every translating hypersurface is either $\mathbb{R}\times$2d-bowl, a 3d round bowl, belongs to one-parameter family oval bowls constructed by Hoffman-Ilmanen-Martin-White.