We will show that any translator arising as a blow-up limit of a two-convex mean curvature flow in $\mathbb{R}^{n+1}$, $n\geq 3$, is rotationally symmetric. Our main contribution is to show that the blow-down of the translator is a unique shrinking cylinder; the result then follows by work of Haslhofer (who considered the embedded case). Time permitting, we shall discuss the extension of this result to a large class of other (fully nonlinear) flows. This work is joint with Theodora Bourni.

We present a new (2016) local result for the Ricci flow which holds in three dimensions. This result is joint work with Peter Topping.