CR compactification for asymptotically locally complex hyperbolic almost Hermitian manifolds

In this article, we consider a complete, non-compact almost Hermitian manifold whose curvature is asymptotic to that of the complex hyperbolic plane. Under natural geometric conditions, we show that such a manifold arises as the interior of a compact almost complex manifold whose boundary is a strictly pseudoconvex CR manifold. Moreover, the geometric structure of the boundary can be recovered by analysing the expansion of the metric near infinity.Comment: 25 pages. Comments are welcom

Towards a standardized framework for AI-assisted, image-based monitoring of nocturnal insects

Automated sensors have potential to standardize and expand the monitoring of insects across the globe. As one of the most scalable and fastest developing sensor technologies, we describe a framework for automated, image-based monitoring of nocturnal insects—from sensor development and field deployment to workflows for data processing and publishing. Sensors comprise a light to attract insects, a camera for collecting images and a computer for scheduling, data storage and processing. Metadata is important to describe sampling schedules that balance the capture of relevant ecological information against power and data storage limitations. Large data volumes of images from automated systems necessitate scalable and effective data processing. We describe computer vision approaches for the detection, tracking and classification of insects, including models built from existing aggregations of labelled insect images. Data from automated camera systems necessitate approaches that account for inherent biases. We advocate models that explicitly correct for bias in species occurrence or abundance estimates resulting from the imperfect detection of species or individuals present during sampling occasions. We propose ten priorities towards a step-change in automated monitoring of nocturnal insects, a vital task in the face of rapid biodiversity loss from global threats

Géométrie asymptotiquement hyperbolique complexe et contraintes de courbure

In this thesis, we investigate the asymptotic geometric properties a class of complete and non compact Kähler manifolds we call asymptotically locally complex hyperbolic manifolds.The local geometry at infinity of such a manifold is modeled on that of the complex hyperbolic space, in the sense that its curvature is asymptotic to that of the model space.Under natural geometric assumptions, we show that this constraint on the curvature ensures the existence of a rich geometry at infinity: we can endow it with a strictly pseudoconvex CR boundary at infinity.Dans cette thèse, nous nous intéressons aux propriétés géométriques asymptotiques d'une classe de variétés kähleriennes complètes et non compactes, que l'on appelle variétés asymptotiquement localement hyperboliques complexes. On les nomme ainsi car leur géométrie locale à l'infini est modelée sur celle de l'espace hyperbolique complexe, au sens où leur courbure est asymptotique à la courbure de l'espace hyperbolique complexe.Nous montrons que sous des hypothèses naturelles de nature géométrique, cette condition de courbure assure l'existence d'une structure riche à l'infini similaire à celle de l'espace modèle : leur bord à l'infini est muni d'une structure de Cauchy-Riemann strictement pseudoconvexe

Asymptotic strictly pseudoconvex CR structure for asymptotically locally complex hyperbolic manifolds

47 pagesGiven a complete non-compact K\"ahler manifold whose curvature tensor is asymptotic to that of the complex hyperbolic space, we endow its boundary at infinity with a strictly pseudoconvex CR structure