Local stability of Einstein metrics under the Ricci iteration

A Ricci iteration is a sequence of Riemannian metrics on a manifold such that every metric in the sequence is equal to the Ricci curvature of the next metric. These sequences of metrics were introduced by Rubinstein to provide a discretisation of the Ricci flow. In this talk, I will discuss the relationship between the Ricci iteration and the Ricci flow. I will also describe a recent result concerning the existence and convergence of Ricci iterations close to certain Einstein metrics. (Joint work with Max Hallgren)