arXiv subjects

Aryaman Patel

Publications and source records attributed to Aryaman Patel.

11 recordsLinked to original sources

arXiv2026

A characterization of ball quotient stacks

We characterize smooth proper Deligne-Mumford stacks $\mathscr{X}$ that arise as compactifications of ball quotient stacks $[\mathbb{B}^d/\Gamma]$. Moreover, we show that every ball quotient admits a compactification whose boundary divisor $\mathscr{D}:=\mathscr{X}-[\mathbb{B}^d/\Gamma]$ is a disjoint union of quotient stacks $[A/G]$, where $A$ is an abelian variety and $G$ is a finite group. This generalizes a result of Deng-Cadorel. Our strategy combines Simpson's non-abelian Hodge correspondence for smooth proper DM-stacks, Mochizuki's generalization of the classical Simpson's correspondence to the log setting, and the uniformization results of Deng-Cadorel.

math.AG↗

arXiv2026

Hilti-Trimble-Oxford Dataset: 360 Visual-Inertial Benchmark with Floor Plan Priors for SLAM and Localization

Automated progress monitoring on construction sites is an active area of research and development. Robot and human-carried mapping systems have been developed to build 3D maps of building and infrastructure projects. While LiDAR-based mapping systems achieve high accuracy, the cost of LiDAR can be prohibitive. Consumer-grade cameras with wide field of view ("360 cameras") combined with embedded inertial measurement units (IMUs) provide a cost-effective alternative. To support change detection and progress monitoring, highly accurate visual Simultaneous Localization and Mapping (SLAM) and floor plan-referenced localization systems are required. In this paper we present a high-quality dataset collected at an active construction site, which captures realistic challenges such as variable lighting conditions, moving workers, fast motions, and repetitive structures. The dataset offers thirty visual-inertial sequences recorded across seven floors over an eight-month period of the construction project. Ground truth trajectories were collected using a high quality LiDAR-inertial SLAM system rigidly attached to the 360 camera. Additionally, we report the results of an open research challenge evaluating the best visual SLAM and localization systems from around the world. The Challenge attracted substantially higher participation in SLAM, with 62 teams compared to 22 in floor-plan-referenced localization, reflecting the broader maturity of SLAM methods. The higher errors in localization further highlight the difficulty of this task in construction and point to the need for continued research, which this dataset is intended to support. The dataset and the benchmark are publicly available at: https://hilti-trimble-challenge.com/dataset-2026.

cs.RO↗

arXiv2026

Semispecial tensors and quotients of the polydisc

Let $X$ be a complex-projective variety with klt singularities and ample canonical divisor. We prove that $X$ is a quotient of the polydisc by a group acting properly discontinuously and freely in codimension one if and only if $X$ admits a semispecial tensor with reduced hypersurface. This extends a result of Catanese and Di Scala to singular spaces, and answers a question raised by these authors. As a key step in the proof, we establish the Bochner principle for holomorphic tensors on klt spaces in the negative Kähler--Einstein case.

math.AG↗

arXiv2026

The Hitchin morphism for K-trivial varieties

We study the Hitchin morphism for higher dimensional varieties and show that, for a certain class of varieties which we call r-small, the set-theoretic image of the Hitchin morphism from the Dolbeault moduli space coincides with the spectral base. In other words, a stronger version of the conjecture of Chen and Ngô holds for this class of varieties, which includes K-trivial varieties. As part of the proof, we slightly modify the construction of spectral covers to obtain normal spectral covers.

math.AG↗

arXiv2026

Stratifying moduli spaces of Higgs bundles and the Hitchin morphism

We study the behavior of slope-stability of reflexive twisted sheaves over a normal projective variety $X$ under pullback along a cover. Slope-stability is always preserved if the cover does not factor via a quasi-étale cover. Fixing the rank, there is one quasi-étale cover that checks whether a twisted sheaf remains slope-stable on all Galois covers, yielding a stratification of the moduli space of slope-stable Higgs-bundles. As an application, we determine the image of the Hitchin morphism restricted to the smallest closed stratum of the Dolbeault moduli space when $X$ is smooth. This allows us to determine the image of the Hitchin morphism from the Dolbeault moduli space when $X$ is a hyperelliptic or abelian variety in characteristic $p\ge0$. In particular, we show that Chen-Ngô's conjecture holds for hyperelliptic varieties in characteristic $0$.

math.AG↗

arXiv2025

Slope zero tensors, uniformizing variations of Hodge structure and quotients of tube domains

We prove an equivalence between two approaches to characterizing complex-projective varieties $X$ with klt singularities and ample canonical divisor that are uniformized by bounded symmetric domains. In order to do so, we show how to construct a uniformizing variation of Hodge structure from a slope zero tensor and vice versa. As a consequence, we generalize various uniformization results of Catanese and Di Scala to the singular setting. For example, we prove that $X$ is a quotient of a bounded symmetric domain of tube type by a group acting properly discontinuously and freely in codimension one if and only if $X$ admits a slope zero tensor. As a key step in the proof, we establish the compactness of the holonomy group of the singular K\"{a}hler--Einstein metric on $X_{\mathrm{reg}}$.

math.AG↗

arXiv2024

Uniformization of klt pairs by bounded symmetric domains

Given a complex-projective klt pair $(X, Δ)$ with standard coefficients and such that $K_X + Δ$ is ample, we determine necessary and sufficient conditions for the pair $(X, Δ)$ to be uniformized by a bounded symmetric domain. As an application, we obtain characterizations of orbifold quotients of the polydisc and of the four classical irreducible bounded symmetric domains in terms of Miyaoka-Yau-type Chern equalities.

math.AG↗

arXiv2024

Reflexive symmetric differentials and quotients of bounded symmetric domains

For each classical irreducible bounded symmetric domain $\mathcal{D}$, Klingler has computed the minimum number $m_{\mathcal{D}}$ such that any smooth projective quotient $X=\mathcal{D}/Γ$, for $Γ\in\textrm{Aut}^0(\mathcal{D})$, satisfies $H^0(X,\mathrm{Sym}^iΩ^1_X)=0$ for $0<i<m_{\mathcal{D}}$. In this article, we extend Klingler's result to the case when $X$ is normal and projective. This, together with a normal version of Arapura's result about the relationship between the vanishing of global symmetric differentials on $X$ and the rigidity of finite dimensional representations of $π_1(X)$, gives rigidity statements for representations of $π_1(X)$ and $π_1(X_{reg})$ in a low dimensional range, when $X$ is a normal projective quotient of a bounded symmetric domain.

math.AG↗

arXiv2023

Solution to Advanced Manufacturing Process Problems using Cohort Intelligence Algorithm with Improved Constraint Handling Approaches

Recently, various Artificial Intelligence (AI) based optimization metaheuristics are proposed and applied for a variety of problems. Cohort Intelligence (CI) algorithm is a socio inspired optimization technique which is successfully applied for solving several unconstrained & constrained real-world problems from the domains such as design, manufacturing, supply chain, healthcare, etc. Generally, real-world problems are constrained in nature. Even though most of the Evolutionary Algorithms (EAs) can efficiently solve unconstrained problems, their performance degenerates when the constraints are involved. In this paper, two novel constraint handling approaches based on modulus and hyperbolic tangent probability distributions are proposed. Constrained CI algorithm with constraint handling approaches based on triangular, modulus and hyperbolic tangent is presented and applied for optimizing advanced manufacturing processes such as Water Jet Machining (WJM), Abrasive Jet Machining (AJM), Ultrasonic Machining (USM) and Grinding process. The solutions obtained using proposed CI algorithm are compared with contemporary algorithms such as Genetic Algorithm, Simulated Annealing, Teaching Learning Based Optimization, etc. The proposed approaches achieved 2%-127% maximization of material removal rate satisfying hard constraints. As compared to the GA, CI with Hyperbolic tangent probability distribution achieved 15%, 2%, 2%, 127%, and 4% improvement in MRR for AJMB, AJMD, WJM, USM, and Grinding processes, respectively contributing to the productivity improvement. The contributions in this paper have opened several avenues for further applicability of the proposed constraint handling approaches for solving complex constrained problems.

cs.NE↗

arXiv2023

Uniformization of complex projective klt varieties by bounded symmetric domains

Using classical results from Hodge theory and more contemporary ones valid for complex projective varieties with Kawamata log terminal (klt) singularities, we deduce necessary and sufficient conditions for such varieties to be uniformized by each of the four irreducible Hermitian symmetric spaces of non compact type. We also deduce necessary and sufficient conditions for uniformization by a polydisk, which generalizes a classical result of Simpson.

math.AG↗

arXiv2019

A Correspondence Between Maximal Surfaces and Timelike Minimal Surfaces in $\mathbb{L}^3$

We show that to every maximal surface with conelike singularities in Lorentz-Minkowski space $\mathbb{L}^3$ that can be locally represented as the graph of a smooth function, there exists a corresponding timelike minimal surface in $\mathbb{L}^3$. There exists a linear transformation between such a maximal surface and its corresponding timelike minimal surface and it maps the singularities of one to the singularities of the other. Moreover, this transformation establishes a one-one correspondence between such maximal surfaces and timelike minimal surfaces and also preserves the one-one property of the Gauss map. This leads to a Kobayashi type theorem for timelike minimal surfaces in $\mathbb{L}^3$. Finally, we derive some non-trivial identities using existing Euler-Ramanujan identities, and some familiar timelike minimal surfaces in parametric form.

math.DG↗