Rational surfaces with a large group of automorphisms (following S. Cantat and I. Dolgachev)

We discuss classification of rational surfaces $X$ for which the image of the automorphisms group $Aut(X)$ in the group of linear transformations of the Picard group $Pic(X)$ is the largest possible. This answers a question raised by Arthur Coble in 1928, and can be rephrased in terms of periodic orbits of birational actions of infinite Coxeter groups.