Have there been any applications of perfectoid theory to Iwasawa theory? At a first glance, this seems like a natural choice. For instance, the field $\mathbb Q_p(\mu_p^{1/p^\infty})$ is studied in both theories (the class group in Iwasawa theory and as a natural example of a perfectoid field (possibly after completion)).

Can we use the tilting correspondence to get information about class groups as in Iwasawa theory?