Towards non-reductive geometric invariant theory

We study linear actions of algebraic groups on smooth projective varieties X. A guiding goal for us is to understand the cohomology of "quotients" under such actions, by generalizing (from reductive to non-reductive group actions) existing methods involving Mumford's geometric invariant theory (GIT). We concentrate on actions of unipotent groups H, and define sets of stable points X^s and semistable points X^{ss}, often explicitly computable via the methods of reductive GIT, which reduce to the standard definitions due to Mumford in the case of reductive actions. We compare these with definitions in the literature. Results include (1) a geometric criterion determining whether or not a ring of invariants is finitely generated, (2) the existence of a geometric quotient of X^s, and (3) the existence of a canonical "enveloping quotient" variety of X^{ss}, denoted X//H, which (4) has a projective completion given by a reductive GIT quotient and (5) is itself projective and isomorphic to Proj(k[X]^H) when k[X]^H is finitely generated.Comment: 37 pages, 1 figure (parabola2.eps), in honor of Bob MacPherson's 60th birthda

Yang-Mills theory and Tamagawa numbers

Atiyah and Bott used equivariant Morse theory applied to the Yang-Mills functional to calculate the Betti numbers of moduli spaces of vector bundles over a Riemann surface, rederiving inductive formulae obtained from an arithmetic approach which involved the Tamagawa number of SL_n. This article surveys this link between Yang-Mills theory and Tamagawa numbers, and explains how methods used over the last three decades to study the singular cohomology of moduli spaces of bundles on a smooth complex projective curve can be adapted to the setting of A^1-homotopy theory to study the motivic cohomology of these moduli spaces.Comment: Accepted for publication in the Bulletin of the London Mathematical Societ

Graded linearisations

When the action of a reductive group on a projective variety has a suitable linearisation, Mumford's geometric invariant theory (GIT) can be used to construct and study an associated quotient variety. In this article we describe how Mumford's GIT can be extended effectively to suitable actions of linear algebraic groups which are not necessarily reductive, with the extra data of a graded linearisation for the action. Any linearisation in the traditional sense for a reductive group action induces a graded linearisation in a natural way. The classical examples of moduli spaces which can be constructed using Mumford's GIT are moduli spaces of stable curves and of (semi)stable bundles over a fixed nonsingular curve. This more general construction can be used to construct moduli spaces of unstable objects, such as unstable curves or unstable bundles (with suitable fixed discrete invariants in each case, related to their singularities or Harder--Narasimhan type).Comment: 20 pages. arXiv admin note: text overlap with arXiv:1607.0418

A qualitative study of staff perspectives of patient non-attendance in a regional primary healthcare setting.

BackgroundNon-attendance at health appointments reduces health service efficiency, is costly to services, and can risk patient health. Reminder systems are widely used to overcome forgetfulness, the most common reason for non-attendance; however, other factors, such as patient demographics and service accessibility, may also affect attendance rates.AimsThere is limited primary research on the reasons for patient non-attendance in the Australian healthcare setting, although the success of preventative health initiatives requires ongoing monitoring of patients. This study aims to improve our understanding of the Australian experience by examining staff perspectives.MethodThis qualitative study explored staff perspectives of the reasons for non-attendance in a large, regional general practice super clinic, which has a low socioeconomic catchment, and serves a large Aboriginal population.ResultsThe practical barriers to attendance of travel, cost, and waiting times had largely been overcome with transport provision, free medical care and responsive appointment times, but paradoxically, these were seen to devalue allocated appointments and reinforce the expectations of “on-demand” health care. For Aboriginal patients specifically, a distrust of authority, combined with poor health literacy was perceived to impact negatively on the uptake of diagnostic tests, filling of prescriptions, health monitoring, and adherence to medication.ConclusionThe results suggest a complex interplay between poor health literacy and low patient self-worth; a funding system that encourages “5-minute medicine” without enabling doctors to get to the root cause of patient problems or having the ability to provide health education

Encouraging translation and assessing impact of the Centre for Research Excellence in Integrated Quality Improvement: Rationale and protocol for a research impact assessment

Introduction: There is growing recognition among health researchers and funders that the wider benefits of research such as economic, social and health impacts ought to be assessed and valued alongside academic outputs such as peer-reviewed papers. Research translation needs to increase and the pathways to impact ought to be more transparent. These processes are particularly pertinent to the Indigenous health sector given continued concerns that Indigenous communities are over-researched with little corresponding improvement in health outcomes. This paper describes the research protocol of a mixed methods study to apply FAIT (Framework to Assess the Impact from Translational health research) to the Centre for Research Excellence in Integrated Quality Improvement (CRE-IQI). FAIT will be applied to five selected CRE-IQI Flagship projects to encourage research translation and assess the wider impact of that research. Methods and analysis: Phase I will develop a modified programme logic model for each Flagship project including identifying process, output and impact metrics so progress can be monitored. A scoping review will inform potential benefits. In phase II, programme logic models will be updated to account for changes in the research pathways over time. Audit and feedback will be used to encourage research translation and collect evidence of achievement of any process, output and interim impacts. In phase III, three proven methodologies for measuring research impact—Payback, economic assessment and narratives—will be applied. Data on the application of FAIT will be collected and analysed to inform and improve FAIT’s performance