Quasiconformal homogeneity after Gehring and Palks

In a very influential paper Gehring and Palka introduced the notions of quasiconformally homogeneous and uniformly quasiconformally homogeneous subsets of Euclidean space. Their motivation was to provide a characterization of quasi-disks, i.e. domains which are quasiconformally homeomorphic to the unit disk. As a generalization, Bonfert-Taylor, Canary, Martin and Taylor initiated the study of uniformly quasiconformally homogeneous hyperbolic manifolds. In this paper, we review the theory of quasiconformally homogeneous subsets of Euclidean and uniformly quasiconformally homogeneous hyperbolic manifolds. We finish with a discussion of open problems in the theory.Comment: To be published in a volume of Computational Methods and Function Theory dedicated to the memory of Fred Gehrin

The relationship between international migration, trade, and development: some paradoxes and findings

The interactions among trade, international migration, and economic development in migrant-sending areas are complex, and paradoxes abound. This paper summarizes global trends in world migration and remittances, discusses some paradoxes surrounding the trade-migration-development relationship, and reports findings from new research on Mexico-to-U.S. migration, using data from rural Mexico. It concludes with some thoughts about designing policies to raise the development potential of remittances in migrant-sending areas.Emigration and immigration ; International trade ; Economic development ; Developing countries ; Emigrant remittances ; Mexico

On Lower Bounds for ss-multiplicities

A recent continuous family of multiplicity functions on local rings was introduced by Taylor interpolating between Hilbert-Samuel and Hilbert-Kunz multiplicities. The obvious goal is to use this as a tool for deforming results from one to the other. The values in this family which do not match these classic variants however are not known yet to be well-behaved. This article explores lower bounds for these intermediate multiplicities as well as gives evidence for analogies of the Watanabe-Yoshida minimality conjectures for unmixed singular rings.Comment: 10 page