arXiv subjects

Andrea Conti

Publications and source records attributed to Andrea Conti.

At least 19 recordsLinked to original sources

arXiv2026

Small points in radical extensions of number fields

We study small points in radical extensions of algebraic fields. Given an algebraic extension $\mathbb{F}$ of $\mathbb{Q}$, a finitely generated subgroup $\Gamma\subseteq \mathbb{F}^\times$, and a rational prime $p$, we give a general criterion ensuring that $\mathbb{F}(\Gamma^{p-\mathrm{div}})\setminus \Gamma^{\mathrm{div}}$ has the Bogomolov property. This problem is motivated by a conjecture of R\'emond, formulated when $\mathbb{F}$ is a number field, predicting that such radical extensions contain no unexpected small points outside the divisible hull of the group used to generate them. As applications, we obtain new cases of R\'emond's conjecture for radical extensions generated by division points with respect to a finite set of primes, recovering and extending previous results of Amoroso and the third author. Our argument is based on a recent result on small points in $p$-adic Lie extensions.

math.NT↗

arXiv2026

The trianguline variety for reductive groups

We study the trianguline variety for split connected reductive groups. We generalize a theorem of Breuil, Hellmann, and Schraen about its local structure, establishing smoothness over the loci determined by various regularity conditions on the triangulation parameter, and normality at certain points outside of these smooth loci. Along the way, we prove a crystallinity criterion for $(\varphi,\Gamma_K)$-modules with $\mathsf G$-structure.

math.NT↗

arXiv2026

M5 branes wrapping $\mathbb{WCP}^2$ and spindles fibred over constant curvature Riemann surfaces

We classify AdS$_3$ solutions of the U(1) invariant sector of minimal $d=7$ supergravity. We find two classes of solutions preserving ${\cal N}=(2,0)$ supersymmetry for which the internal space M$_4$ is either a negative curvature Kahler-Einstein manifold or a circle fibration over $\Sigma\times \mathbb{R}$. For the later, in the case that $\Sigma$ has constant curvature, we reduce finding a solution to solving a single ODE that admits polynomial solutions. Among these are interesting solutions whose uplifts to $d=11$ describe M5 branes wrapping various $d=4$ orbifolds. These include a topological $\mathbb{CP}^2$ with 2 orbifold fixed points that we identify as the weighted projective space $\mathbb{WCP}^2_{[k,k,\ell]}$. We are also able to construct solutions with M5 branes that wrap a spindle fibred over constant curvature Riemann surfaces of arbitrary genus. Such solutions should provide holographic duals to the ${\cal N}=(2,0)$ SCFT associated to the M5 brane compactified to $d=2$ on these orbifolds. We match the holographic central charges of these solutions to a field theory computation in terms of anomaly polynomials and c-extremisation.

hep-th↗

arXiv2026

The Bogomolov property for $p$-supercuspidal eigenforms

We prove a lower bound on the Weil height, the so-called Bogomolov property, for the algebraic extensions of $\mathbb Q$ cut out by the adelic Galois representations attached to certain eigenforms whose local component at a prime $p$ is supercuspidal. To this end, we give a method for constructing metric inequalities over $p$-adic Lie extensions of fields over $\mathbb Q$ that are finitely ramified at $p$.

math.NT↗

arXiv2026

Water adsorption on a model silicate surface: wollastonite (100)

Water adsorption on silicate surfaces is a critical yet poorly understood process relevant to, e.g., mineral weathering and cement hydration. This study investigates the structure of water overlayers on a model calcium silicate, the lowest-energy (100) surface of wollastonite (CaSiO3). It combines atomically resolved non-contact atomic force microscopy (nc-AFM), acquired with qPlus sensors and functionalized tips in ultrahigh vacuum (UHV), with density functional theory (DFT) calculations employing the metaGGA r2SCAN+rVV10 functional. Adding incremental doses of water to the sample at cryogenic temperatures produces distinct structures governed by the competition between water-surface and water-water interactions. With two water molecules per surface unit cell, water-surface interactions dominate: In line with previous theoretical predictions, adsorbates follow the surface lattice. As the coverage increases, intermolecular hydrogen bonding competes with bonding to the surface, leading to the emergence of complex, coexisting patterns. While their small energy differences prevent an unambiguous identification of the most stable structure by DFT, the experimentally observed symmetries help constrain plausible structural models. Above a critical density of four water molecules per unit cell, water-water interactions prevail, and water clusters are formed. The results provide an atomic-scale framework for understanding water interactions with calcium silicate surfaces.

cond-mat.mtrl-sci↗

arXiv2026

The Unreconstructed {\alpha}-Al$_{2}$O$_{3}$(0001) Surface is Inhomogeneous and Rough

Alumina (Al$_{2}$O$_{3}$) is a key material for thin-film growth and heterogeneous catalysis, where the atomic surface structure critically impacts performance. Using noncontact atomic force microscopy (nc-AFM) combined with density functional theory (DFT) calculations, we challenge the common assumption that the unreconstructed $\alpha$-Al$_{2}$O$_{3}$(0001) surface is atomically flat and uniformly Al-terminated. This widely accepted bulk termination satisfies polarity compensation requirements but results in highly undercoordinated surface Al cations at the surface. Despite substantial inward relaxation of these Al cations, we find that the (1 ${\times}$ 1) surface remains inherently metastable, relative to the thermodynamically stable $(\sqrt{31} \times \sqrt{31})R\pm9\deg$ surface reconstruction that forms at high temperatures above 1000 {\deg}C. Nc-AFM imaging of the unreconstructed surface reveals a rough and disordered morphology, with only nanometer-scale regions exhibiting the ordered Al-terminated (1 $\times$ 1) structure. Our results show that the unreconstructed Al$_{2}$O$_{3}$(0001) surface is intrinsically inhomogeneous, reconciling conflicting experimental observations and challenging the validity of commonly used atomistic models.

cond-mat.mtrl-sci↗

arXiv2026

$\mathcal L$-invariants and deep congruences between newforms

We study congruences modulo powers of a prime $p$ between pairs of $p$-new modular Hecke eigenforms of level $\Gamma_0(p)$ and same weight $k$. Based on explicit computations, we conjecture that every such eigenform $f$ admits a twin to which it is congruent modulo a surprisingly high power of $p$, whose exponent is close to the opposite of the valuation of the $\mathcal L$-invariant of $f$, and whose Atkin--Lehner sign is opposite to that of $f$. This is a new phenomenon that is not explained by the known results on the $p$-adic variation of eigenforms. Inspired by the global picture, we formulate a local conjecture describing congruences between semistable representations of fixed weight, varying $\mathcal L$-invariant, and opposite Atkin--Lehner signs. We give some theoretical evidence towards our conjectures.

math.NT↗

arXiv2025

Transfer Learning (Il)liquidity

The estimation of the Risk Neutral Density (RND) implicit in option prices is challenging, especially in illiquid markets. We introduce the Deep Log-Sum-Exp Neural Network, an architecture that leverages Deep and Transfer learning to address RND estimation in the presence of irregular and illiquid strikes. We prove key statistical properties of the model and the consistency of the estimator. We illustrate the benefits of transfer learning to improve the estimation of the RND in severe illiquidity conditions through Monte Carlo simulations, and we test it empirically on SPX data, comparing it with popular estimation methods. Overall, our framework shows recovery of the RND in conditions of extreme illiquidity with as few as three option quotes.

q-fin.MF↗

arXiv2025

Monodromy Defects in Maximally Supersymmetric Yang-Mills Theories from Holography

We study three Type II supergravity solutions holographically dual to codimension-2 supersymmetric defects in $(p+1)$-dimensional SU($N$) maximally supersymmetric Yang-Mills theory ($p=2,3,4$). In all of these cases, the defects have a non-trivial monodromy for the maximal abelian subgroup for the SO($9-p$) R-symmetry. Such solutions are obtained by considering branes wrapping spindle configurations, changing the parameters (which alters the coordinate domain), and imposing suitable boundary conditions. We provide a prescription to compute the entanglement entropy of the effective theory on the defect. We find the resulting quantity to be proportional to the free energy of the ambient theory. A similar analysis is performed for the D5-brane wrapping a spindle, but we find that changing the coordinate domain does not lead to a defect solution, but rather to a circle compactification.

hep-th↗

arXiv2025

Monodromy Defects in Massive Type IIA

In this paper we study solutions to massive Type IIA supergravity which we propose are dual to co-dimension 2 monodromy defects in 6d (1,0) CFTs realised in NS5-D6-D8 brane systems, as well as in the 5d Sp(N) fixed point theory. In the first case the defects are studied holographically as solutions to 7d $U(1)$ gauged supergravity that asymptote locally to its maximally supersymmetric $\text{AdS}_7$ vacuum away from the defects. In the second case they are dual to solutions to 6d $U(1)^2$ gauged supergravity that asymptote to its maximally supersymmetric $\text{AdS}_6$ vacuum. These solutions are then uplifted to massive Type IIA supergravity using known consistent truncations previously constructed in the literature. We compute the defect entanglement entropy and provide evidence that for the 3d defects, the entanglement entropy can be written as a linear combination of the free energy and conformal weight of the defect. Finally, we construct new co-dimension 2 monodromy defects in 6d and 5d CFTs compactified on Riemann surfaces and/or spindles.

hep-th↗

arXiv2025

Defect entanglement entropy for superconformal monodromy defects

We compute the defect entanglement entropy for co-dimension two superconformal monodromy defects in well known maximally symmetric holographic theories of various dimension. In each case we explicitly relate the universal part of the defect entanglement entropy to field theory data characterising the defect conformal field theory. We provide evidence that, unlike in the bulk theories in which the defects reside, the universal part of the defect entanglement entropy does not necessarily decrease along a renormalisation group flow.

hep-th↗

arXiv2025

Supersymmetric $\mathbb{WCP}^n$, AdS near horizons and orbifolds

We construct and study the supersymmetry properties of the weighted projective spaces $\mathbb{WCP}^2$ and $\mathbb{WCP}^3$. These are topologically $\mathbb{CP}^n$ with $n+1$ orbifold singularities and as such are higher dimensional analogues of the ``spindle'' or $\mathbb{WCP}^1$. We use these to construct interesting supersymmetric orbifolds of canonical near horizon geometries of relevance to the AdS/CFT correspondence. Interestingly, for certain tunings of their integer weights, and unlike the spindle, $\mathbb{WCP}^{2}$ and $\mathbb{WCP}^{3}$ are compatible with supersymmetry beyond the realm of gauged supergravity. This allows one to construct interesting supersymmetric solutions in type II supergravity such as AdS$_5\times\mathbb{WCP}^{2}\times\text{S}^1$ and AdS$_4\times \mathbb{WCP}^3$ via duality, in which $\mathbb{WCP}^n$ appears without a connection fibred over it. We also leverage our results to construct a supersymmetric AdS$_3$ solution containing a topological $\mathbb{T}^{(1,1)}$ space with 4 orbifold singularities.

hep-th↗

arXiv2025

ToF-Splatting: Dense SLAM using Sparse Time-of-Flight Depth and Multi-Frame Integration

Time-of-Flight (ToF) sensors provide efficient active depth sensing at relatively low power budgets; among such designs, only very sparse measurements from low-resolution sensors are considered to meet the increasingly limited power constraints of mobile and AR/VR devices. However, such extreme sparsity levels limit the seamless usage of ToF depth in SLAM. In this work, we propose ToF-Splatting, the first 3D Gaussian Splatting-based SLAM pipeline tailored for using effectively very sparse ToF input data. Our approach improves upon the state of the art by introducing a multi-frame integration module, which produces dense depth maps by merging cues from extremely sparse ToF depth, monocular color, and multi-view geometry. Extensive experiments on both synthetic and real sparse ToF datasets demonstrate the viability of our approach, as it achieves state-of-the-art tracking and mapping performances on reference datasets.

cs.CV↗

arXiv2025

$\mathcal{N}=6$ supersymmetric AdS$_2 \times \mathbb{CP}^3\times \Sigma_2 $

We perform a complete classification of AdS$_2$ solutions of Type II supergravity realising $\mathcal{N}=6$ supersymmetry and OSp$(6|2)$ superconformal symmetry on backgrounds that are foliations of AdS$_2 \times \mathbb{CP}^3$ over a Riemann surface $\Sigma_2$. Such solutions only exist in type IIB supergravity and are in 1 to 1 correspondence with a fourth order PDE that can be locally solved in terms of two holomorphic functions. Particular solutions in the class are the T-duals of the $\text{AdS}_3\times \mathbb{CP}^3$ and $\text{AdS}_2\times \text{S}^7$ solutions to massive Type IIA supergravity found in the literature. We discuss the field theory interpretation of the two sub-classes of solutions related to $\text{AdS}_3\times \mathbb{CP}^3$ by Abelian and non-Abelian T-duality, which provide explicit examples for the Riemann surface an annulus or a strip. In the second case we interpret the solutions as holographic duals to baryon vertex configurations realised in D2-brane box models.

hep-th↗

arXiv2025

Bogomolov property for Galois representations with big local image

An algebraic extension of the rational numbers is said to have the $\textit{Bogomolov property}$ (B) if the absolute logarithmic Weil height of its non-torsion elements is uniformly bounded from below. Given a continuous representation $\rho$ of the absolute Galois group $G_{\mathbb{K}}$ of a number field ${\mathbb{K}}$, one says that $\rho$ has (B) if the subfield of $\overline{\mathbb{Q}}$ fixed by $\mathrm{ker}\,\rho$ has (B). We prove that, if $\rho:G_{\mathbb{K}} \to \mathrm{GL}_d({\mathbb{Z}}_p)$ maps an inertia subgroup at a prime above $p$ surjectively onto an open subgroup of $\mathrm{GL}_d({\mathbb{Z}}_p)$, then $\rho$ has (B). More generally, we show that if the image of inertia is open in the image of the decomposition group, the normal closure of the local image is sufficiently large in the global one, and a certain condition on the center of $\rho(G_{\mathbb{K}})$ satisfied, then $\rho$ has (B). In particular, no assumption on the modularity of $\rho$ is needed, contrary to previous work of Habegger and Amoroso--Terracini. We provide several examples both in modular and non-modular cases. Our methods rely on a result of Sen comparing the ramification and Lie filtrations on the $p$-adic Lie group $\rho(G_{\mathbb{K}})$.

math.NT↗

arXiv2024

Satellite-Terrestrial Quantum Networks and the Global Quantum Internet

This paper will explore the design and implementation of quantum networks in space integrated with quantum networks on Earth. We propose a three-layer approach, involving GEO and LEO satellites integrated with terrestrial ground stations. We first analyze the channel conditions between the three layers, and then highlight the key role of LEO satellites in the integrated space-terrestrial system - namely the source of entanglement distribution between specified terrestrial stations via direct downlink quantum-optical channels. The GEO satellites in the considered system are used primarily as coordination stations, managing and directing the LEO satellites regarding the positioning and timing of entanglement distribution. Complexity, in the form of entanglement distillation and quantum-state correction, is concentrated at the terrestrial stations, and teleportation is used as the primary quantum channel in the LEO uplinks and the inter-terrestrial channels. Although our designs are futuristic in that they assume limited quantum memory at the transceivers, we also discuss some near-term uses of our network in which no quantum memory is available.

quant-ph↗

arXiv2024

Depth on Demand: Streaming Dense Depth from a Low Frame Rate Active Sensor

High frame rate and accurate depth estimation plays an important role in several tasks crucial to robotics and automotive perception. To date, this can be achieved through ToF and LiDAR devices for indoor and outdoor applications, respectively. However, their applicability is limited by low frame rate, energy consumption, and spatial sparsity. Depth on Demand (DoD) allows for accurate temporal and spatial depth densification achieved by exploiting a high frame rate RGB sensor coupled with a potentially lower frame rate and sparse active depth sensor. Our proposal jointly enables lower energy consumption and denser shape reconstruction, by significantly reducing the streaming requirements on the depth sensor thanks to its three core stages: i) multi-modal encoding, ii) iterative multi-modal integration, and iii) depth decoding. We present extended evidence assessing the effectiveness of DoD on indoor and outdoor video datasets, covering both environment scanning and automotive perception use cases.

cs.CV↗

arXiv2024

${\cal N}=(4,4)$ supersymmetric AdS$_3$ solutions in $d=11$

We derive necessary and sufficient conditions for AdS$_3$ solutions of $d=11$ supergravity to preserve ${\cal N}=(1,1)$ supersymmetry in terms of G-structures. Such solutions necessarily support an SU(3)-structure on the internal 8-manifold M$_8$, in terms of which we phrase the conditions for supersymmetry preservation. We use this to derive the local form of all ${\cal N}=(4,4)$ supersymmetric AdS$_3$ solutions in $d=11$, for which M$_8$ decomposes as a foliation of a 3-sphere over a 5 dimensional base. There are 3 independent classes, 2 of which preserve the small superconformal algebra and one preserving its large counterpart for which M$_5$ contains a second 3-sphere. We show that for each solution with large (4,4) supersymmetry there are two corresponding solutions with small $(4,4)$, one for which M$_5$ maintains its 3-sphere, one where this blows up to $\mathbb{R}^3$ which can be compactified to $\mathbb{T}^3$. We use our results to construct several new solutions that lie within our derived classes as well as recovering some existing solutions.

hep-th↗