Resurgence numbers and convex regions associated to pairs of graded families of ideals

We discuss how to understand the asymptotic resurgence number of a pair of graded families of ideals from combinatorial data of their associated convex regions. When the families consist of monomial ideals, the convex regions being considered are the Newton–Okounkov regions of the families. When ideals in the second family are classical invariant ideals, for instance, determinantal ideals or ideals of Pfaffians, these convex regions are constructed from the associated Rees packages.