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

Seshadri constants and Grassmann bundles over curves

Let $X$ be a smooth complex projective curve, and let $E$ be a vector bundle on $X$ which is not semistable. For a suitably chosen integer $r$, let $\text{Gr}(E)$ be the Grassmann bundle over $X$ that parametrizes the quotients of the fibers of $E$ of dimension $r$. Assuming some numerical conditions on the Harder-Narasimhan filtration of $E$, we study Seshadri constants of ample line bundles on $\text{Gr}(E)$. In many cases, we give the precise value of Seshadri constant. Our results generalize various known results for ${\rm rank}(E)=2$.Comment: Final version; Annales Inst. Fourier (to appear

The Scientific Reach of Multi-Ton Scale Dark Matter Direct Detection Experiments

The next generation of large scale WIMP direct detection experiments have the potential to go beyond the discovery phase and reveal detailed information about both the particle physics and astrophysics of dark matter. We report here on early results arising from the development of a detailed numerical code modeling the proposed DARWIN detector, involving both liquid argon and xenon targets. We incorporate realistic detector physics, particle physics and astrophysical uncertainties and demonstrate to what extent two targets with similar sensitivities can remove various degeneracies and allow a determination of dark matter cross sections and masses while also probing rough aspects of the dark matter phase space distribution. We find that, even assuming dominance of spin-independent scattering, multi-ton scale experiments still have degeneracies that depend sensitively on the dark matter mass, and on the possibility of isospin violation and inelasticity in interactions. We find that these experiments are best able to discriminate dark matter properties for dark matter masses less than around 200 GeV. In addition, and somewhat surprisingly, the use of two targets gives only a small improvement (aside from the advantage of different systematics associated with any claimed signal) in the ability to pin down dark matter parameters when compared with one target of larger exposure.Comment: 23 pages; updated to match PRD versio

Psychology Education in the Post-Covid World

A major aim of psychology education is to train students in psychological literacy – the ability to apply psychological knowledge to everyday activities. In this paper we explore how well this has been achieved in recent years. As a result of Covid-19 the focus of teaching in recent months has inevitably been on developing online methods of teaching and attempts to develop psychological literacy have of necessity received less attention. However, we argue that the developments enforced by Covid-19 actually open up a range of new possibilities and that psychological literacy can benefit from these changes. In particular, we suggest that much of the transmission of psychological knowledge can continue to take place online and that universities should become places where the focus is on the application of that knowledge

Universal families on moduli spaces of principal bundles on curves

Let H be a connected semisimple linear algebraic group defined over C and X a compact connected Riemann surface of genus at least three. Let M'X(H) be the moduli space parametrising all topologically trivial stable principal H-bundles over X whose automorphism group coincides with the centre of H. It is a Zariski open dense subset of the moduli space of stable principal H-bundles. We prove that there is a universal principal H-bundle over X × M'X(H) if and only if H is an adjoint group (i.e., the centre of H is trivial)

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