Towards a theory of local Shimura varieties

This is a survey article that advertizes the idea that there should exist a theory of p-adic local analogues of Shimura varieties. Prime examples are the towers of rigid-analytic spaces defined by Rapoport-Zink spaces, and we also review their theory in the light of this idea. We also discuss conjectures on the $\ell$-adic cohomology of local Shimura varieties.Comment: 53 page

Mapping nn grid points onto a square forces an arbitrarily large Lipschitz constant

We prove that the regular $n\times n$ square grid of points in the integer lattice $\mathbb{Z}^{2}$ cannot be recovered from an arbitrary $n^{2}$-element subset of $\mathbb{Z}^{2}$ via a mapping with prescribed Lipschitz constant (independent of $n$). This answers negatively a question of Feige from 2002. Our resolution of Feige's question takes place largely in a continuous setting and is based on some new results for Lipschitz mappings falling into two broad areas of interest, which we study independently. Firstly the present work contains a detailed investigation of Lipschitz regular mappings on Euclidean spaces, with emphasis on their bilipschitz decomposability in a sense comparable to that of the well known result of Jones. Secondly, we build on work of Burago and Kleiner and McMullen on non-realisable densities. We verify the existence, and further prevalence, of strongly non-realisable densities inside spaces of continuous functions.Comment: 60 pages (43 pages of the main part, 13 pages of appendices), 10 figures. This is a revised version according to referees' comments. Our version of the proof of the theorem about bilipschitz decomposition of Lipschitz regular mappings was greatly simplified. To appear in GAF

Knowledge management in the voluntary sector: A focus on sharing project know-how and expertise

Voluntary sector organisations are operated principally by volunteers who are not obliged to share their knowledge, as might be expected in a for profit company, with a greater consequent loss of knowledge should individuals leave. This research examines how a volunteer-led organisation, the Campaign for Real Ale (CAMRA), acquires, stores and shares its project knowledge in the context of event management. Three annual CAMRA festivals of different sizes and maturity were selected to see how volunteers' knowledge is managed in the process of organising their festivals. Key festival officers were interviewed and focus groups, comprising of festival volunteers, were conducted. While the maturity of a festival and its size seemed to influence the ways in which knowledge was managed there were some commonalities between festivals. Evident was a strong master-apprentice model of learning with little formal training or record keeping except, that is, where legislation and accountability in treasury and health and safety functions were necessary. Trust between volunteers and their need to know and to share information appeared to be dependent, in part, on their perception and confidence in the success of the overarching project organisation, and this helped shape volunteers' knowledge sharing practices. Whilst there was evidence of a laissez-faire approach to codification and the sharing of knowledge, this was less so when volunteers recognised a genuine lack of knowledge which would hinder the success of their festival. The analysis also highlighted factors related to the sharing of knowledge that, it is suggested, have not been identified in the for-profit sector

Effects of screened Coulomb impurities on autoionizing two-electron resonances in spherical quantum dots

In a recent paper (Phys. Rev. B {\bf 78}, 075316 (2008)), Sajeev and Moiseyev demonstrated that the bound-to-resonant transitions and lifetimes of autoionizing states in spherical quantum dots can be controlled by varying the confinment strength. In the present paper, we report that such control can in some cases be compromised by the presence of Coulomb impurities. It is demonstrated that a screened Coulomb impurity placed in the vicinity of the dot center can lead to bound-to-resonant transitions and to avoided crossings-like behavior when the screening of the impurity charge is varied. It is argued that these properties also can have impact on electron transport through quantum dot arrays

Retrofitting O'Raifeartaigh Models with Dynamical Scales

We provide a method for obtaining simple models of supersymmetry breaking, with all small mass scales generated dynamically, and illustrate it with explicit examples. We start from models of perturbative supersymmetry breaking, such as O'Raifeartaigh and Fayet models, that would respect an $R$ symmetry if their small input parameters transformed as the superpotential does. By coupling the system to a pure supersymmetric Yang-Mills theory (or a more general supersymmetric gauge theory with dynamically small vacuum expectation values), these parameters are replaced by powers of its dynamical scale in a way that is naturally enforced by the symmetry. We show that supersymmetry breaking in these models may be straightforwardly mediated to the supersymmetric Standard Model, obtain complete models of direct gauge mediation, and comment on related model building strategies that arise in this simple framework.Comment: 15 pages, harvmac bi