Ancient Ricci flows of bounded girth

I will describe how to construct a new family of ancient solutions to the Ricci flow on spheres of all dimensions. The two dimensional example is just the King—Rosenau solution (aka “the sausage model”) which near spacetime infinity resembles two cigar solitons joined by a stationary cylinder. The higher dimensional examples are new, and resemble a family of cigar $(n-2)$-planes centred at every point of an $(n-2)$-sphere of radius $\sim-2t$, joined by the stationary cylinder $S^1\times\mathbb{R}^{n-1}$.