Rank 3 rigid representations of projective fundamental groups

Let X be a smooth complex projective variety with basepoint x. We prove that every rigid integral irreducible representation $\pi_1(X,x)\to SL (3,{\mathbb C})$ is of geometric origin, i.e., it comes from some family of smooth projective varieties. This partially generalizes an earlier result by K. Corlette and the second author in the rank 2 case and answers one of their questions.Comment: v3, 49 pages; final version, to appear in Compositio Mat

Teaching social work in times of change

Social Work, a profession with explicit academic and practice links to social policy, is undergoing profound change and transformation. ( DOH 2009) As part of this ongoing critique, the teaching of social work is being increasingly questioned by the general public, employers and government. Over the last two years innovative research at the University of Lincoln, jointly undertaken by a team of academic researchers and former social work students, has been analysing the efficacy of teaching methods and university support systems. In particular, the effectiveness of the social work undergraduate degree programme in equipping graduates for the demands of front line practice is being evaluated. The paper draws on key themes identified by the research and shares findings relating to; • Good practice in teaching and learning; including what students value most from lecturers and how academics can best support students • The use of students in research; opportunities and pitfall

What is the object of the encapsulation of a process?

Several theories have been proposed to describe the transition from process to object in mathematical thinking. Yet, what is the nature of this ''object'' produced by the ''encapsulation'' of a process? Here, we outline the development of some of the theories (including Piaget, Dienes, Davis, Greeno, Dubinsky, Sfard, Gray, and Tall) and consider the nature of the mental objects (apparently) produced through encapsulation and their role in the wider development of mathematical thinking. Does the same developmental route occur in geometry as in arithmetic and algebra? Is the same development used in axiomatic mathematics? What is the role played by imagery

Composition of dissolved organic matter within a lacustrine environment

Freshwater dissolved organic matter (DOM) is a complex mixture of chemical components that are central to many environmental processes, including carbon and nitrogen cycling. However, questions remain as to its chemical characteristics, sources and transformation mechanisms. Here, we employ 1- and 2-D nuclear magnetic resonance (NMR) spectroscopy to investigate the structural components of lacustrine DOM from Ireland, and how it varies within a lake system, as well as to assess potential sources. Major components found, such as carboxyl-rich alicyclic molecules (CRAM) are consistent with those recently identified in marine and freshwater DOM. Lignin-type markers and protein/peptides were identified and vary spatially. Phenylalanine was detected in lake areas influenced by agriculture, whereas it is not detectable where zebra mussels are prominent. The presence of peptidoglycan, lipoproteins, large polymeric carbo- hydrates and proteinaceous material supports the substantial contribution of material derived from microorganisms. Evidence is provided that peptidoglycan and silicate species may in part originate from soil microbes

The significance of seniority for women managers’ interpretations of organizational restructuring

This paper examines the impact of restructuring within the transport and logistics sector on women managers working at senior and less senior (middle/junior management) levels of the organization. The majority of women experienced increased performance pressures and heavier workloads as well as an increase in working hours. At the same time, there were pressures to work at home (i.e. week-ends and evenings) and reduced opportunities to work from home (i.e. during normal office hours). Management level emerged as an important factor in how these changes were interpreted. Senior managers perceived more positive outcomes in terms of increased motivation and loyalty. Despite a longer working week, they were less likely to report low morale as an outcome from long hours. In fact, irrespective of management level, women working shorter hours were more likely to report low morale as an outcome. Results are discussed in relation to literature on restructuring and careers, in terms of perceptual framing and in relation to different levels of investment in the organization

Impacts of European livestock production: nitrogen, sulphur, phosphorus and greenhouse gas emissions, land-use, water eutrophication and biodiversity

Livestock production systems currently occupy around 28% of the land surface of the European Union (equivalent to 65% of the agricultural land). In conjunction with other human activities, livestock production systems affect water, air and soil quality, global climate and biodiversity, altering the biogeochemical cycles of nitrogen, phosphorus and carbon. Here, we quantify the contribution of European livestock production to these major impacts. For each environmental effect, the contribution of livestock is expressed as shares of the emitted compounds and land used, as compared to the whole agricultural sector. The results show that the livestock sector contributes significantly to agricultural environmental impacts. This contribution is 78% for terrestrial biodiversity loss, 80% for soil acidification and air pollution (ammonia and nitrogen oxides emissions), 81% for global warming, and 73% for water pollution (both N and P). The agriculture sector itself is one of the major contributors to these environmental impacts, ranging between 12% for global warming and 59% for N water quality impact. Significant progress in mitigating these environmental impacts in Europe will only be possible through a combination of technological measures reducing livestock emissions, improved food choices and reduced food waste of European citizens

Making sense of ‘mastery’: Understandings of a policy term among a sample of teachers in England

This paper considers the term ‘mastery’ as used in mathematics education across different times and locations. A case study from England is offered to show how these pedagogical approaches morph as they move from one territory to another, in the context of each territory’s history. The paper first examines English policy documents, research and published curricula for their use of the term. This suggests that ‘mastery’ in England has become associated with mathematics teaching practices used in high-performing territories such as Singapore and Shanghai (China). But the efforts to transport approaches predominately from East Asian sources, against the background of an existing Western set of meanings for the term, has led to considerable inconsistency in interpretations and definitions of the ‘mastery approach’. A subsequent case study of eight teachers involved in developing mastery approaches in England explores how they make sense of ‘mastery’ in the context of these inconsistent messages. We suggest that this generates challenges for teachers tasked with implementing mastery approaches, with the danger that anything can be done in the name of mastery