  Using perfectoid algebras, we introduce a mixed characteristic analog of the
multiplier ideal, respectively test ideal, from characteristic zero,
respectively $p > 0$, in the case of a regular ambient ring. We prove several
properties about this ideal such as subadditivity. We then use these techniques
to derive a uniform bound on the growth of symbolic powers of radical ideals in
all excellent regular rings. The analogous result was shown in equal
characteristic by Ein-Lazarsfeld-Smith and Hochster-Huneke.
