We use the Folding Theorem of [Bis15] to construct an entire function f in class B and a wandering domain U of f such that f restricted to f n (U ) is univalent, for all n ≥ 0. The components of the wandering orbit are bounded and surrounded by the postcritical set.

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Abstract. The zero forcing number, maximum nullity and path cover number of a (simple, undirected) graph are parameters that are important in the study of minimum rank problems. We investigate the effects on these graph parameters when an edge is subdivided to obtain a so-called edge subdivision graph. An open question raised by Barrett et al. is answered in the negative, and we provide additional evidence for an affirmative answer to another open question in that paper [W. Barrett, R. Bowcutt, M. Cutler, S. Gibelyou, and K. Owens. Minimum rank of edge subdivisions of graphs. Electronic Journal of Linear Algebra, 18:530-563, 2009.]. It is shown that there is an independent relationship between the change in maximum nullity and zero forcing number caused by subdividing an edge once. Bounds on the effect of a single edge subdivision on the path cover number are presented, conditions under which the path cover number is preserved are given, and it is shown that the path cover number and the zero forcing number of a complete subdivision graph need not be equal.

We construct embeddings of Bers slices of ideal polygon reflection groups into the classical family of univalent functions Σ. This embedding is such that the conformal mating of the reflection group with the anti-holomorphic polynomial z → z d is the Schwarz reflection map arising from the corresponding map in Σ. We characterize the image of this embedding in Σ as a family of univalent rational maps. Moreover, we show that the limit set of every Kleinian reflection group in the closure of the Bers slice is naturally homeomorphic to the Julia set of an anti-holomorphic polynomial.