Abstract: Perturbative calculations of entanglement entropy have found a number of recent applications in understanding field theory, holography, and quantum gravity. In this talk, I will discuss a class of excited states of a CFT formed from a Euclidean path integral with nonlocal multitrace insertions, with an eye toward understanding their entanglement structure holographically. Such states are argued to have good semiclassical holographic duals, but can possess nontrivial bulk entanglement structure at order N^0. A surprising feature of these states is that divergences occur quite generically in the perturbative expansion of their entanglement entropy. These divergences signal a nonanalyticity in the expansion, and must be resummed in computing the full expression for the entropy. This resummation is challenging in general, but I will describe some simplified examples in which it may be tractable. In the process, I will also give some general techniques for diagnosing when such nonanalyticities occur, and point to some indications that they may in general be calculable. This talk is based on arXiv:1904.01584 and ongoing work.