Stability of Affine G-varieties and Irreducibility in Reductive Groups

Let $G$ be a reductive affine algebraic group, and let $X$ be an affine algebraic $G$-variety. We establish a (poly)stability criterion for points $x\in X$ in terms of intrinsically defined closed subgroups $H_{x}$ of $G$, and relate it with the numerical criterion of Mumford, and with Richardson and Bate-Martin-R\"ohrle criteria, in the case $X=G^{N}$. Our criterion builds on a close analogue of a theorem of Mundet and Schmitt on polystability and allows the generalization to the algebraic group setting of results of Johnson-Millson and Sikora about complex representation varieties of finitely presented groups. By well established results, it also provides a restatement of the non-abelian Hodge theorem in terms of stability notions.Comment: 29 pages. To appear in Int. J. Math. Note: this version 4 is identical with version 2 (version 3 is empty

Brauer group of moduli spaces of pairs

We show that the Brauer group of any moduli space of stable pairs with fixed determinant over a curve is zero.Comment: 12 pages. Final version, accepted in Communications in Algebr

Reflections on ten years of using economics games and experiments in teaching

In this paper, the author reflects on his 10 years’ experience of using games and experiments and in the process develops a type of practitioner’s guide. The existing quantitative and qualitative evidence on the impact of using games on student learning is reviewed. On balance, a positive effect, on measures of attainment, is found in the literature. Given these findings, it is surprising that there is also evidence in the UK and US that they are not widely used. Some factors are discussed that might deter tutors from employing them. Unsurprisingly, one of these is the additional cost, which might make the use of online games seem more attractive, given the way results can be automatically recorded. However, some relatively low-cost paper-based games were found to have significant advantages. In particular, they appear to facilitate social interaction which has a positive impact on student motivation and learning. One popular and effective paper-based game is discussed in some detail. A number of recommendations are provided on how to implement the game in order to maximise the learning benefits it can provide. Some ideas on how to maximise the learning benefits from using games more generally are also considered

Struggling and juggling: a comparison of assessment loads in research and teaching-intensive universities

In spite of the rising tide of metrics in UK higher education, there has been scant attention paid to assessment loads, when evidence demonstrates that heavy demands lead to surface learning. Our study seeks to redress the situation by defining assessment loads and comparing them across research-and teaching intensive universities. We clarify the concept of ‘assessment load’ in response to findings about high volumes of summative assessment on modular degrees. We define assessment load across whole undergraduate degrees, according to four measures: the volume of summative assessment; volume of formative assessment; proportion of examinations to coursework; number of different varieties of assessment. All four factors contribute to the weight of an assessment load, and influence students’ approaches to learning. Our research compares programme assessment data from 73 programmes in 14 UK universities, across two institutional categories. Research-intensives have higher summative assessment loads and a greater proportion of examinations; teaching-intensives have higher varieties of assessment. Formative assessment does not differ significantly across both university groups. These findings pose particular challenges for students in different parts of the sector. Our study questions the wisdom that ‘more’ is always better, proposing that lighter assessment loads may make room for ‘slow’ and deep learning

Elemental boron doping behavior in silicon molecular beam epitaxy

Boron-doped Si epilayers were grown by molecular beam epitaxy (MBE) using an elemental boron source, at levels up to 2×1020 cm−3, to elucidate profile control and electrical activation over the growth temperature range 450–900 °C. Precipitation and surface segregation effects were observed at doping levels of 2×1020 cm−3 for growth temperatures above 600 °C. At growth temperatures below 600 °C, excellent profile control was achieved with complete electrical activation at concentrations of 2×1020 cm−3, corresponding to the optimal MBE growth conditions for a range of Si/SixGe1−x heterostructures

Protection afforded by heat shock protein 60 from Francisella tularensis is due to copurified lipopolysaccharide.

Heat shock proteins (Hsps) have attracted significant attention as protective antigens against a range of diseases caused by bacterial pathogens. However, more recently there have been suggestions that the protective response is due to the presence of peptide components other than Hsps. We have shown that mice that had been immunized with purified heat shock protein 60 (Hsp60) isolated from Francisella tularensis were protected against a subsequent challenge with some strains of the bacterium. However, this protection appeared to be due to trace amounts of lipopolysaccharide, which were too low to be detected by using the Limulus amoebocyte lysate assay. This finding raises the possibility that the protection afforded by other bacterial Hsp60 proteins may be due to trace quantities of polysaccharide antigens carried by and acting in conjunction with the Hsps

Stratifying quotient stacks and moduli stacks

Recent results in geometric invariant theory (GIT) for non-reductive linear algebraic group actions allow us to stratify quotient stacks of the form [X/H], where X is a projective scheme and H is a linear algebraic group with internally graded unipotent radical acting linearly on X, in such a way that each stratum [S/H] has a geometric quotient S/H. This leads to stratifications of moduli stacks (for example, sheaves over a projective scheme) such that each stratum has a coarse moduli space.Comment: 25 pages, submitted to the Proceedings of the Abel Symposium 201

A functorial construction of moduli of sheaves

We show how natural functors from the category of coherent sheaves on a projective scheme to categories of Kronecker modules can be used to construct moduli spaces of semistable sheaves. This construction simplifies or clarifies technical aspects of existing constructions and yields new simpler definitions of theta functions, about which more complete results can be proved.Comment: 52 pp. Dedicated to the memory of Joseph Le Potier. To appear in Inventiones Mathematicae. Slight change in the definition of the Kronecker algebra in Secs 1 (p3) and 2.2 (p6), with corresponding small alterations elsewhere, to make the constructions work for non-reduced schemes. Section 6.5 rewritten. Remark 2.6 and new references adde

The usability of description logics: understanding the cognitive difficulties presented by description logics

Description Logics have been extensively studied from the viewpoint of decidability and computational tractability. Less attention has been given to their usability and the cognitive difficulties they present, in particular for those who are not specialists in logic. This paper reports on a study into the difficulties associated with the most commonly used Description Logic features. Psychological theories are used to take account of these. Whilst most of the features presented no difficulty to participants, the comprehension of some was affected by commonly occurring misconceptions. The paper proposes explanations and remedies for some of these difficulties. In addition, the time to confirm stated inferences was found to depend both on the maximum complexity of the relations involved and the number of steps in the argument