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Nick Wright

Publications and source records attributed to Nick Wright.

At least 19 recordsLinked to original sources
arXiv2026

Geometry and topology of the tempered Iwahori-spherical representations of a split semisimple $p$-adic group

Let $\mathfrak{G}$ be a connected split $p$-adic group of type $B_n$, $C_n$ or $D_n$. Amongst the tempered representations of $\mathfrak{G}$ a key role is played by the Iwahori-spherical block. We provide a compact Hausdorff model for this space which allows us to compute the $K$-theory ranks for the corresponding $C^*$-algebra. The model, an extended quotient, is stratified by sectors. Underlying the approach of this paper is the interplay between the geometric extended quotient and the spectral extended quotient in the context of the ABPS conjecture. We give geometric descriptions of every sector thus equipping the spectrum with a cellular structure. We classify the geometric structures arising in our model, and specifically discover real projective spaces along with cones and suspensions of these. These examples require a minor modification to our homotopy sector conjecture: we show that Langlands dual sectors are rationally (indeed dyadically) homotopy equivalent in all cases ($A_n, B_n, C_n, D_n, E_6, E_7$ and $E_8$).

math.RT↗
arXiv2026

HRMOS: A High-Resolution Multi-Object Spectrograph for the VLT

This White Paper presents the scientific rationale and instrument concept for HRMOS (High-Resolution Multi-Object Spectrograph), a next-generation instrument proposed for the ESO Very Large Telescope within the VLT 2030 roadmap. Current and planned facilities offer either multi-object spectroscopy or ultra-high spectral resolution, but not both. HRMOS fills this gap by combining very high spectral resolution, multi-object capability, and radial-velocity stability, enabling transformative studies in Galactic and extragalactic astrophysics. The baseline design provides a resolving power of R = 80000, radial-velocity precision of 10 m s-1 (goal: 5 m s-1), simultaneous observations of 50-60 targets, and broad optical coverage down to 385 nm. These capabilities enable precise measurements of elemental abundances, isotopic ratios, line profiles, and radial velocities for large stellar samples, including crowded fields, star clusters, the Galactic bulge, and nearby dwarf galaxies. HRMOS will address key questions on the age of the oldest stellar populations through nucleocosmochronology, the formation and survival of planetary systems, the assembly history of the Milky Way and satellites, the origin of the heaviest elements, stellar evolution, and the chemical and dynamical properties of the interstellar and circumgalactic medium. It will bridge large spectroscopic surveys and the next generation of extremely large telescopes, with strong synergies with 4MOST, Gaia, TESS, PLATO, the proposed Haydn mission, and future ELT instruments. Building on VLT/FLAMES heritage, HRMOS represents a strategic investment for European astronomy in the 2030s.

astro-ph.IM↗
arXiv2024

Building weight-free F{\o}lner sets for Yu's Property A in coarse geometry

In this note we study the natural question of when the generalised F{\o}lner sets exhibiting property A can be chosen to be subsets of the space itself. We show that for many property A spaces $X$, this is indeed possible. Specifically this holds: for all discrete bounded geometry metric spaces which coarsely have all components unbounded; for all countable discrete groups; and for all box spaces.

math.MG↗
arXiv2024

O-TALC: Steps Towards Combating Oversegmentation within Online Action Segmentation

Online temporal action segmentation shows a strong potential to facilitate many HRI tasks where extended human action sequences must be tracked and understood in real time. Traditional action segmentation approaches, however, operate in an offline two stage approach, relying on computationally expensive video wide features for segmentation, rendering them unsuitable for online HRI applications. In order to facilitate online action segmentation on a stream of incoming video data, we introduce two methods for improved training and inference of backbone action recognition models, allowing them to be deployed directly for online frame level classification. Firstly, we introduce surround dense sampling whilst training to facilitate training vs. inference clip matching and improve segment boundary predictions. Secondly, we introduce an Online Temporally Aware Label Cleaning (O-TALC) strategy to explicitly reduce oversegmentation during online inference. As our methods are backbone invariant, they can be deployed with computationally efficient spatio-temporal action recognition models capable of operating in real time with a small segmentation latency. We show our method outperforms similar online action segmentation work as well as matches the performance of many offline models with access to full temporal resolution when operating on challenging fine-grained datasets.

cs.CV↗
arXiv2023

The Effects of Signal-to-Noise Ratio on Generative Adversarial Networks Applied to Marine Bioacoustic Data

In recent years generative adversarial networks (GANs) have been used to supplement datasets within the field of marine bioacoustics. This is driven by factors such as the cost to collect data, data sparsity and aid preprocessing. One notable challenge with marine bioacoustic data is the low signal-to-noise ratio (SNR) posing difficulty when applying deep learning techniques such as GANs. This work investigates the effect SNR has on the audio-based GAN performance and examines three different evaluation methodologies for GAN performance, yielding interesting results on the effects of SNR on GANs, specifically WaveGAN.

cs.SD↗
arXiv2022

Towards Automatic Cetacean Photo-Identification: A Framework for Fine-Grain, Few-Shot Learning in Marine Ecology

Photo-identification (photo-id) is one of the main non-invasive capture-recapture methods utilised by marine researchers for monitoring cetacean (dolphin, whale, and porpoise) populations. This method has historically been performed manually resulting in high workload and cost due to the vast number of images collected. Recently automated aids have been developed to help speed-up photo-id, although they are often disjoint in their processing and do not utilise all available identifying information. Work presented in this paper aims to create a fully automatic photo-id aid capable of providing most likely matches based on all available information without the need for data pre-processing such as cropping. This is achieved through a pipeline of computer vision models and post-processing techniques aimed at detecting cetaceans in unedited field imagery before passing them downstream for individual level catalogue matching. The system is capable of handling previously uncatalogued individuals and flagging these for investigation thanks to catalogue similarity comparison. We evaluate the system against multiple real-life photo-id catalogues, achieving mAP@IOU[0.5] = 0.91, 0.96 for the task of dorsal fin detection on catalogues from Tanzania and the UK respectively and 83.1, 97.5% top-10 accuracy for the task of individual classification on catalogues from the UK and USA.

cs.CV↗
arXiv2022

Hand Guided High Resolution Feature Enhancement for Fine-Grained Atomic Action Segmentation within Complex Human Assemblies

Due to the rapid temporal and fine-grained nature of complex human assembly atomic actions, traditional action segmentation approaches requiring the spatial (and often temporal) down sampling of video frames often loose vital fine-grained spatial and temporal information required for accurate classification within the manufacturing domain. In order to fully utilise higher resolution video data (often collected within the manufacturing domain) and facilitate real time accurate action segmentation - required for human robot collaboration - we present a novel hand location guided high resolution feature enhanced model. We also propose a simple yet effective method of deploying offline trained action recognition models for real time action segmentation on temporally short fine-grained actions, through the use of surround sampling while training and temporally aware label cleaning at inference. We evaluate our model on a novel action segmentation dataset containing 24 (+background) atomic actions from video data of a real world robotics assembly production line. Showing both high resolution hand features as well as traditional frame wide features improve fine-grained atomic action classification, and that though temporally aware label clearing our model is capable of surpassing similar encoder/decoder methods, while allowing for real time classification.

cs.CV↗
arXiv2022

Centralisers, complex reflection groups and actions in the Weyl group $E_6$

The compact, connected Lie group $E_6$ admits two forms: simply connected and adjoint type. As we previously established, the Baum-Connes isomorphism relates the two Langlands dual forms, giving a duality between the equivariant K-theory of the Weyl group acting on the corresponding maximal tori. Our study of the $A_n$ case showed that this duality persists at the level of homotopy, not just homology. In this paper we compute the extended quotients of maximal tori for the two forms of $E_6$, showing that the homotopy equivalences of sectors established in the $A_n$ case also exist here, leading to a conjecture that the homotopy equivalences always exist for Langlands dual pairs. In computing these sectors we show that centralisers in the $E_6$ Weyl group decompose as direct products of reflection groups, generalising Springer's results for regular elements, and we develop a pairing between the component groups of fixed sets generalising Reeder's results. As a further application we compute the $K$-theory of the reduced Iwahori-spherical $C^*$-algebra of the p-adic group $E_6$, which may be of adjoint type or simply connected.

math.GR↗
arXiv2020

NDD20: A large-scale few-shot dolphin dataset for coarse and fine-grained categorisation

We introduce the Northumberland Dolphin Dataset 2020 (NDD20), a challenging image dataset annotated for both coarse and fine-grained instance segmentation and categorisation. This dataset, the first release of the NDD, was created in response to the rapid expansion of computer vision into conservation research and the production of field-deployable systems suited to extreme environmental conditions -- an area with few open source datasets. NDD20 contains a large collection of above and below water images of two different dolphin species for traditional coarse and fine-grained segmentation. All data contained in NDD20 was obtained via manual collection in the North Sea around the Northumberland coastline, UK. We present experimentation using standard deep learning network architecture trained using NDD20 and report baselines results.

cs.CV↗
arXiv2019

The Northumberland Dolphin Dataset: A Multimedia Individual Cetacean Dataset for Fine-Grained Categorisation

Methods for cetacean research include photo-identification (photo-id) and passive acoustic monitoring (PAM) which generate thousands of images per expedition that are currently hand categorised by researchers into the individual dolphins sighted. With the vast amount of data obtained it is crucially important to develop a system that is able to categorise this quickly. The Northumberland Dolphin Dataset (NDD) is an on-going novel dataset project made up of above and below water images of, and spectrograms of whistles from, white-beaked dolphins. These are produced by photo-id and PAM data collection methods applied off the coast of Northumberland, UK. This dataset will aid in building cetacean identification models, reducing the number of human-hours required to categorise images. Example use cases and areas identified for speed up are examined.

cs.CV↗
arXiv2018

Coarse median algebras: The intrinsic geometry of coarse median spaces and their intervals

This paper establishes a new combinatorial framework for the study of coarse median spaces, bridging the worlds of asymptotic geometry, algebra and combinatorics. We introduce a simple and entirely algebraic notion of coarse median algebra which simultaneously generalises the concepts of bounded geometry coarse median spaces and classical discrete median algebras. We study the coarse median universe from the perspective of intervals, with a particular focus on cardinality as a proxy for distance. In particular we prove that the metric on a quasi-geodesic coarse median space of bounded geometry can be constructed up to quasi-isometry using only the coarse median operator. Finally we develop a concept of rank for coarse median algebras in terms of the geometry of intervals and show that the notion of finite rank coarse median algebra provides a natural higher dimensional analogue of Gromov's concept of $\delta$-hyperbolicity.

math.MG↗
arXiv2017

Poincar\'e duality and Langlands duality for extended affine Weyl groups

In this paper we construct an equivariant Poincar\'e duality between dual tori equipped with finite group actions. We use this to demonstrate that Langlands duality induces a rational isomorphism between the group $C^*$-algebras of extended affine Weyl groups at the level of $K$-theory.

math.KT↗
arXiv2017

A four point characterisation for coarse median spaces

Coarse median spaces simultaneously generalise the classes of hyperbolic spaces and median algebras, and arise naturally in the study of the mapping class groups and many other contexts. One issue with their definition as originally conceived by Bowditch is the need to establish median approximations for all finite subsets of the space, an approach which allowed the definition of rank (a proxy for dimension) in terms of the dimensions of the approximating spaces. Here we provide a simplification of the definition in terms of a $4$-point condition analogous to the $4$-point condition defining hyperbolicity. We show how to define rank in this context, and use this to give a direct proof that rank $1$ geodesic coarse median spaces are $\delta$-hyperbolic, bypassing Bowditch's use of asymptotic cones. A key ingredient of the proof is a new definition of intervals in coarse median spaces and an analysis of their interaction with geodesics.

math.MG↗
arXiv2016

A characterization for asymptotic dimension growth

We give a characterization for asymptotic dimension growth. We apply it to CAT(0) cube complexes of finite dimension, giving an alternative proof of N. Wright's result on their finite asymptotic dimension. We also apply our new characterization to geodesic coarse median spaces of finite rank and establish that they have subexponential asymptotic dimension growth. This strengthens a recent result of J. Spakula and N. Wright.

math.MG↗
arXiv2016

Stratified Langlands duality in the $A_n$ tower

Let $\mathbf{S}_k$ denote a maximal torus in the complex Lie group $\mathbf{G} = \mathrm{SL}_n(\mathbb{C})/C_k$ and let $T_k$ denote a maximal torus in its compact real form $\mathrm{SU}_n(\mathbb{C})/C_k$, where $k$ divides $n$. Let $W$ denote the Weyl group of $\mathbf{G}$, namely the symmetric group $\mathfrak{S}_n$. We elucidate the structure of the extended quotient $\mathbf{S}_k // W$ as an algebraic variety and of $T_k // W$ as a topological space, in both cases describing them as bundles over unions of tori. Corresponding to the invariance of $K$-theory under Langlands duality, this calculation provides a homotopy equivalence between $T_k // W$ and its dual $T_{\frac{n}{k}} // W$. Hence there is an isomorphism in cohomology for the extended quotients which is stratified as a direct sum over conjugacy classes of the Weyl group. We use our formula to compute a number of examples.

math.KT↗
arXiv2016

Coarse medians and Property A

We prove that uniformly locally finite quasigeodesic coarse median spaces of finite rank and at most exponential growth have Property A. This offers an alternative proof of the fact that mapping class groups have property A.

math.MG↗
arXiv2014

The local spectrum of the Dirac operator for the universal cover of $SL_2(\mathbb R)$

Using representation theory, we compute the spectrum of the Dirac operator on the universal covering group of $SL_2(\mathbb R)$, exhibiting it as the generator of $KK^1(\mathbb C, \mathfrak A)$, where $\mathfrak A$ is the reduced $C^*$-algebra of the group. This yields a new and direct computation of the $K$-theory of $\mathfrak A$. A fundamental role is played by the limit-of-discrete-series representation, which is the frontier between the discrete and the principal series of the group. We provide a detailed analysis of the localised spectra of the Dirac operator and compute the Dirac cohomology.

math.RT↗