Complex algebraic compactifications of the moduli space of Hermitian-Yang-Mills connections on a projective manifold

In this paper we study the relationship between three compactifications of the moduli space of Hermitian-Yang-Mills connections on a fixed Hermitian vector bundle over a projective algebraic manifold of arbitrary dimension. Via the Donaldson-Uhlenbeck-Yau theorem, this space is analytically isomorphic to the moduli space of stable holomorphic vector bundles, and as such it admits an algebraic compactification by Gieseker-Maruyama semistable torsion-free sheaves. A recent construction due to the first and third authors gives another compactification as a moduli space of slope semistable sheaves. In the present article, following fundamental work of Tian generalising the analysis of Uhlenbeck and Donaldson in complex dimension two, we define a gauge theoretic compactification by adding certain ideal connections at the boundary. Extending work of Jun Li in the case of bundles on algebraic surfaces, we exhibit comparison maps from the sheaf theoretic compactifications and prove their continuity. The continuity, together with a delicate analysis of the fibres of the map from the moduli space of slope semistable sheaves allows us to endow the gauge theoretic compactification with the structure of a complex analytic space.Comment: minor changes to the exposition based on referee's comments; final version to appear in Geometry & Topology; 95 page

Direct Detection of Leptophilic Dark Matter in a Model with Radiative Neutrino Masses

We consider an electro-weak scale model for Dark Matter (DM) and radiative neutrino mass generation. Despite the leptophilic nature of DM with no direct couplings to quarks and gluons, scattering with nuclei is induced at the 1-loop level through photon exchange. Effectively, there are charge-charge, dipole-charge and dipole-dipole interactions. We investigate the parameter space consistent with constraints from neutrino masses and mixing, charged lepton-flavour violation, perturbativity, and the thermal production of the correct DM abundance, and calculate the expected event rate in DM direct detection experiments. We show that current data from XENON100 start to constrain certain regions of the allowed parameter space, whereas future data from XENON1T has the potential to significantly probe the model.Comment: 24 pages, 8 figures, 2 tables, discussion of large theta13 added, version to appear in PR

Compact moduli spaces for slope-semistable sheaves

We resolve pathological wall-crossing phenomena for moduli spaces of sheaves on higher-dimensional base manifolds. This is achieved by considering slope-semistability with respect to movable curves rather than divisors. Moreover, given a projective n-fold and a curve C that arises as the complete intersection of n-1 very ample divisors, we construct a modular compactification of the moduli space of vector bundles that are slope-stable with respect to C. Our construction generalises the algebro-geometric construction of the Donaldson-Uhlenbeck compactification by Joseph Le Potier and Jun Li. Furthermore, we describe the geometry of the newly construced moduli spaces by relating them to moduli spaces of simple sheaves and to Gieseker-Maruyama moduli spaces.Comment: v1: 41 pages, the threefold case, general case pending; v2: 51 pages, new features: generalisation of results to base manifolds of arbitrary dimension, identification of equivalence relation represented by the moduli space, comparison with Gieseker moduli spaces; v3: 50 pages, small corrections, updated references; a slightly shortened version will appear in "Algebraic Geometry

Sensor systems for a changing ocean

The papers in this special section focus on sensor system deployment in the field of oceanography. Oceans regulate the Earth's climate and are integral to all known sources of life. Ocean processes are of biological, geological, chemical, or physical nature, occurring at micro- to kilometer scales, from less than seconds to centuries, turning the understanding and the sustainable management of the ocean into a multiscale and multidisciplinary effort. Collection of in situ observation of a volume that covers over 70% of the planet is also inherently challenging and remains generally difficult and costly in time and resources, with so far a rather unsatisfactory result, in particular with respect to space-time resolution. Over the past decade, there has been a steady crescendo of interest to support the development of a truly integrated and sustainably funded Ocean Observing System. This will be achieved with more long-term measurements of key parameters but is impaired by the costs and lack of reliability of ocean sensors in general.Postprint (author's final draft

Long baseline (LBL) positioning system for the crawler tele-operated underwater vehicle in OBSEA observatory

Peer Reviewe

Data acquisition system for volcano monitoring with real-time transmission, low cost and low power consumption

Postprint (published version