  Starting from a factorization theorem in effective field theory, we derive a
parton-shower equation for the resummation of non-global logarithms. We have
implemented this shower and interfaced it with a tree-level event generator to
obtain an automated framework to resum the leading logarithm of non-global
observables in the large-$N_c$ limit. Using this setup, we compute gap
fractions for dijet processes and isolation cone cross sections relevant for
photon production. We compare our results with fixed-order computations and LHC
measurements. We find that naive exponentiation is often not adequate,
especially when the vetoed region is small, since non-global contributions are
enhanced due to their dependence on the veto-region size. Since our parton
shower is derived from first principles and based on renormalization-group
evolution, it is clear what ingredients will have to be included to perform
resummations at subleading logarithmic accuracy in the future.
