Perturbed geodesics on the moduli space of flat connections and Yang-Mills theory

If we consider the moduli space of flat connections of a non trivial principal SO(3)-bundle over a surface, then we can define a map from the set of perturbed closed geodesics, below a given energy level, into families of perturbed Yang-Mills connections depending on a small parameter. In this paper we show that this map is a bijection and maps perturbed geodesics into perturbed Yang-Mills connections with the same Morse index.Comment: 58 pages, 3 figure

Singular projective varieties and quantization

By the quantization condition compact quantizable Kaehler manifolds can be embedded into projective space. In this way they become projective varieties. The quantum Hilbert space of the Berezin-Toeplitz quantization (and of the geometric quantization) is the projective coordinate ring of the embedded manifold. This allows for generalization to the case of singular varieties. The set-up is explained in the first part of the contribution. The second part of the contribution is of tutorial nature. Necessary notions, concepts, and results of algebraic geometry appearing in this approach to quantization are explained. In particular, the notions of projective varieties, embeddings, singularities, and quotients appearing in geometric invariant theory are recalled.Comment: 21 pages, 3 figure

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

Double marking revisited

In 2002, the Qualifications and Curriculum Authority (QCA) published the report of an independent panel of experts into maintaining standards at Advanced Level (A-Level). One of its recommendations was for: ‘limited experimental double marking of scripts in subjects such as English to determine whether the strategy would signi-ficantly reduce errors of measurement’ (p. 24). This recommendation provided the impetus for this paper which reviews the all but forgotten literature on double marking and considers its relevance now

Quantization of Fayet-Iliopoulos Parameters in Supergravity

In this short note we discuss quantization of the Fayet-Iliopoulos parameter in supergravity theories. We argue that in supergravity, the Fayet-Iliopoulos parameter determines a lift of the group action to a line bundle, and such lifts are quantized. Just as D-terms in rigid N=1 supersymmetry are interpreted in terms of moment maps and symplectic reductions, we argue that in supergravity the quantization of the Fayet-Iliopoulos parameter has a natural understanding in terms of linearizations in geometric invariant theory (GIT) quotients, the algebro-geometric version of symplectic quotients.Comment: 21 pages, utarticle class; v2: typos and tex issue fixe

Cooperative Interactions between TLR4 and TLR9 Regulate Interleukin 23 and 17 Production in a Murine Model of Gram Negative Bacterial Pneumonia

Toll like receptors play an important role in lung host defense against bacterial pathogens. In this study, we investigated independent and cooperative functions of TLR4 and TLR9 in microbial clearance and systemic dissemination during Gram-negative bacterial pneumonia. To access these responses, wildtype Balb/c mice, mice with defective TLR4 signaling (TLR4lps-d), mice deficient in TLR9 (TLR9−/−) and TLR4/9 double mutant mice (TLR4lps-d/TLR9−/−) were challenged with K. pneumoniae, then time-dependent lung bacterial clearance and systemic dissemination determined. We found impaired lung bacterial clearance in TLR4 and TLR9 single mutant mice, whereas the greatest impairment in clearance was observed in TLR4lps-d/TLR9−/− double mutant mice. Early lung expression of TNF-α, IL-12, and chemokines was TLR4 dependent, while IFN-γ production and the later expression of TNF-α and IL-12 was dependent on TLR9. Classical activation of lung macrophages and maximal induction of IL-23 and IL-17 required both TLR4 and TLR9. Finally, the i.t. instillation of IL-17 partially restored anti-bacterial immunity in TLR4lps-d/TLR9−/− double mutant mice. In conclusion, our studies indicate that TLR4 and TLR9 have both non-redundant and cooperative roles in lung innate responses during Gram-negative bacterial pneumonia and are both critical for IL-17 driven antibacterial host response

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 Paracoccus denitrificans NarK-like nitrate and nitrite transporters—probing nitrate uptake and nitrate/nitrite exchange mechanisms

Nitrate and nitrite transport across biological membranes is often facilitated by protein transporters that are members of the major facilitator superfamily. Paracoccus denitrificans contains an unusual arrangement whereby two of these transporters, NarK1 and NarK2, are fused into a single protein, NarK, which delivers nitrate to the respiratory nitrate reductase and transfers the product, nitrite, to the periplasm. Our complementation studies, using a mutant lacking the nitrate/proton symporter NasA from the assimilatory nitrate reductase pathway, support that NarK1 functions as a nitrate/proton symporter while NarK2 is a nitrate/nitrite antiporter. Through the same experimental system, we find that Escherichia coli NarK and NarU can complement deletions in both narK and nasA in P. denitrificans, suggesting that, while these proteins are most likely nitrate/nitrite antiporters, they can also act in the net uptake of nitrate. Finally, we argue that primary sequence analysis and structural modelling do not readily explain why NasA, NarK1 and NarK2, as well as other transporters from this protein family, have such different functions, ranging from net nitrate uptake to nitrate/nitrite exchange

Mixed Hodge polynomials of character varieties

We calculate the E-polynomials of certain twisted GL(n,C)-character varieties M_n of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n,F_q) and a theorem proved in the appendix by N. Katz. We deduce from this calculation several geometric results, for example, the value of the topological Euler characteristic of the associated PGL(n,C)-character variety. The calculation also leads to several conjectures about the cohomology of M_n: an explicit conjecture for its mixed Hodge polynomial; a conjectured curious Hard Lefschetz theorem and a conjecture relating the pure part to absolutely indecomposable representations of a certain quiver. We prove these conjectures for n = 2.Comment: with an appendix by Nicholas M. Katz; 57 pages. revised version: New definition for homogeneous weight in Definition 4.1.6, subsequent arguments modified. Some other minor changes. To appear in Invent. Mat