Overpartition M2M2-rank differences, class number relations, and vector-valued mock Eisenstein series

We prove that the generating function of overpartition $M2$-rank differences is, up to coefficient signs, a component of the vector-valued mock Eisenstein series attached to a certain quadratic form. We use this to compute analogs of the class number relations for $M2$-rank differences. As applications we split the Kronecker-Hurwitz relation into its "even" and "odd" parts and calculate sums over Hurwitz class numbers of the form $\sum_{r \in \mathbb{Z}} H(n - 2r^2)$.Comment: 13 pages. v2 includes a notation and background section and changes some notatio

Environmental Water Markets: Restoring Streams Through Trade

This Policy Series explores the evolving institutional settings in western states1 for restoring and preserving instream flows. The focus is on how markets can provide an efficient and equitable solution for allocating water among increasingly competitive offstream and instream demands, while also providing economic incentives for improved water use efficiencies and conservation. This essay also identifies the underlying barriers that complicate or thwart water markets and provides thoughts on how they may be overcome

Stump's Forgiveness

To love someone, Eleonore Stump tells us, is to have two desires: a desire her objective good and a desire for union with her. In Atonement, Stump claims that loving someone—understood as having these desires—is necessary and sufficient for morally appropriate forgiveness. I offer several arguments against this claim

Colville to Goble: Some Thoughts on the Evolving Place of Photography in Canadian Military Art

This article focuses on the photographic work of two Canadian military artists whose careers are separated by half a century. Alex Colville (1920–2013) used photography in his work but rarely mentioned it and never publicly exhibited or acknowledged it. Elaine Goble (born 1956) bases all her work on photography, engages explicitly with it, acknowledges it, exhibits and donates it, but does not consider herself a professional photographer. An exploration of these two artists’ relationship with photography sheds some light on how attitudes to the medium have changed in recent decades. Photography’s new prominence in the digital age has affected artists, photographers, institutions, collectors, as well as art and photo historians, and encouraged reconsideration of past practices

G-valued crystalline representations with minuscule p-adic Hodge type

We study G-valued semi-stable Galois deformation rings where G is a reductive group. We develop a theory of Kisin modules with G-structure and use this to identify the connected components of crystalline deformation rings of minuscule p-adic Hodge type with the connected components of moduli of "finite flat models with G-structure." The main ingredients are a construction in integral p-adic Hodge theory using Liu's theory of $(\varphi, \widehat{G})$-modules and the local models constructed by Pappas and Zhu