The jumping coefficients of non-Q-Gorenstein multiplier ideals

De Fernex and Hacon associated a multiplier ideal sheaf to a pair $(X,
\mathfrak a^c)$ consisting of a normal variety and a closed subscheme,
which generalizes the usual notion where the canonical divisor $K_X$ is
assumed to be Q-Cartier. I will discuss some of the properties of the
jumping numbers associated to these multiplier ideals.
The set of jumping numbers of a pair is unbounded, countable and satisfies
a certain periodicity property. Furthermore, the jumping numbers form a
discrete set of real numbers if the locus where $K_X$ fails to be Q-Cartier
is zero-dimensional. In particular, discreteness holds whenever $X$ is a
threefold with rational singularities.