arXiv subjects

Florent Dupont

Publications and source records attributed to Florent Dupont.

4 recordsLinked to original sources

arXiv2026

Chern classes of Laughlin bundles on the quasihole moduli space

We study fractional quantum Hall states with quasihole excitations, on Riemann surfaces of arbitrary genus. For configurations with $m$ quasiholes we construct a vector bundle above the $m$-th symmetric power of the curve so that the fiber at a point $\lbrace w_1,\dots,w_m \rbrace$ corresponds to the state with quasiholes localized at these positions. We determine the Chern character of this bundle via the Grothendieck-Riemann-Roch theorem and show that in the completely filled state, i.e. when the number of particles is maximal, the vector bundle is compatible with the condition of projective flatness. Furthermore, we obtain a generalization of this result to the case of multiple layers and multiple quasihole types. In genus zero and one, we construct explicit wave-functions and verify that the curvature of the associated Chern connection reproduces the predicted Chern classes. The Chern classes obtained match, term by term, the predicted decomposition of the Berry phase under quasihole exchange, into an extensive Aharonov--Bohm contribution and a fractional statistical contribution.

math.AG↗

arXiv2025

Chern classes of the multilayer fractional quantum Hall bundle on Riemann surfaces

The so-called multilayer wave functions were introduced in the study of the fractional Quantum Hall effect by Halperin and others. They are defined with the help of a symmetric matrix $K$ in $M^k(\mathbb{N})$, which encodes the couplings between the $k$ layers where particles live. We study the multilayer quantum states in the case where each layer is a Riemann surface of genus $g$. These states form a vector bundle over the Jacobian variety of the Riemann surface, or the space of Aharonov-Bohm fluxes in physics terminology. Burban-Klevtsov have determined the rank and first Chern class of this bundle when $g=1$, and Klevtsov-Zvonkine computed the Chern character of this bundle in the single layer case for any genus. We generalize the latter approach to the multilayer case and compute the Chern character of the multilayer bundle for any genus, and any possible number of non-localized quasi-holes, under the assumption that the bilinear form associated to $K-I$ is non negative. The key tools are the Grothendieck-Riemann-Roch formula, Berezin integration and Wick's formula for exterior algebras. We show that when all quasi-holes are localized, the Chern character is compatible with the bundle being projectively flat. Furthermore, for those configurations, the conductance becomes independent of the genus and is equal to the sum of the coefficients of the inverse matrix $K^{-1}$, proving two conjectures by Keski-Vakkuri and Wen. We also find the relation linking $K$, the genus of the surface, the magnetic field and the number of non-localized quasi holes in each layer, which was studied under the name of ''shift formula''. Finally, we study conditions on the matrix $K$ under which states having only localized quasi-holes maximize the total particle number, as well as the asymptotics for large magnetic fields in this scenario.

math.AG↗

arXiv2023

Textured Mesh Quality Assessment: Large-Scale Dataset and Deep Learning-based Quality Metric

Over the past decade, 3D graphics have become highly detailed to mimic the real world, exploding their size and complexity. Certain applications and device constraints necessitate their simplification and/or lossy compression, which can degrade their visual quality. Thus, to ensure the best Quality of Experience (QoE), it is important to evaluate the visual quality to accurately drive the compression and find the right compromise between visual quality and data size. In this work, we focus on subjective and objective quality assessment of textured 3D meshes. We first establish a large-scale dataset, which includes 55 source models quantitatively characterized in terms of geometric, color, and semantic complexity, and corrupted by combinations of 5 types of compression-based distortions applied on the geometry, texture mapping and texture image of the meshes. This dataset contains over 343k distorted stimuli. We propose an approach to select a challenging subset of 3000 stimuli for which we collected 148929 quality judgments from over 4500 participants in a large-scale crowdsourced subjective experiment. Leveraging our subject-rated dataset, a learning-based quality metric for 3D graphics was proposed. Our metric demonstrates state-of-the-art results on our dataset of textured meshes and on a dataset of distorted meshes with vertex colors. Finally, we present an application of our metric and dataset to explore the influence of distortion interactions and content characteristics on the perceived quality of compressed textured meshes.

cs.GR↗

arXiv2021

Multi-resolution deep learning pipeline for dense large scale point clouds

Recent development of 3D sensors allows the acquisition of extremely dense 3D point clouds of large-scale scenes. The main challenge of processing such large point clouds remains in the size of the data, which induce expensive computational and memory cost. In this context, the full resolution cloud is particularly hard to process, and details it brings are rarely exploited. Although fine-grained details are important for detection of small objects, they can alter the local geometry of large structural parts and mislead deep learning networks. In this paper, we introduce a new generic deep learning pipeline to exploit the full precision of large scale point clouds, but only for objects that require details. The core idea of our approach is to split up the process into multiple sub-networks which operate on different resolutions and with each their specific classes to retrieve. Thus, the pipeline allows each class to benefit either from noise and memory cost reduction of a sub-sampling or from fine-grained details.

cs.CV↗