Type I singularities and ancient solutions of homogeneous Ricci flow

We will present a class of compact and connected homogeneous

spaces such that the Ricci flow of invariant Riemannian metrics develops

type I singularities in finite time. We will describe the singular

behaviours that we can get, as we approach the singular time, and the Ricci

soliton that we obtain by blowing up the solution near the singularity.

Finally, we will investigate the existence of ancient solutions when the

isotropy representation decomposes into two inequivalent irreducible

summands.