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Xiang Tang

Publications and source records attributed to Xiang Tang.

At least 19 recordsLinked to original sources
arXiv2026

Text2Villa: Hierarchical Generation of 3D Indoor Environments with Physics-Aware Analysis-by-Synthesis

Generating 3D indoor scenes from natural language holds tremendous potential, yet existing methods predominantly fail to generate multi-room structures with vertical connectivity and arbitrary polygonal boundaries. Furthermore, they lack a deep grounding in continuous 3D physical laws, leading to severe geometric penetrations and floating artifacts. In this work, we propose Text2Villa, a novel hierarchical generative framework. At the macro level, we construct a multi-story dataset to fine-tune an autoregressive layout generator, ensuring the direct parsing of text into 3D building foundations featuring polygonal boundaries and multi-story connectivity. To enforce physical laws during micro-level asset arrangement, we introduce the Affordance-driven Physical-Semantic Scene Graph (A-PSSG) to explicitly abstract physical affordances (such as support surfaces and containment cavities) into node attributes, establishing strict geometric and semantic edge constraints. Guided by the A-PSSG, we formulate scene instantiation as a constrained closed-loop optimization problem following the analysis-by-synthesis paradigm. By integrating an underlying geometric collision detection engine with the high-level semantic reasoning of multimodal large language models (MLLMs), our heuristic solver dynamically executes physics-aware actions under the observation-evaluation-modification mechanism to effectively resolve mesh collisions, floating artifacts, and fine-grained cavity containment failures. Extensive experiments demonstrate that Text2Villa outperforms previous methods across various metrics, robustly generating high-fidelity and physically plausible villa-level 3D environments from text, thereby providing a reliable and interactive 3D content foundation for downstream applications.

cs.GR↗
arXiv2025

Higher Lefschetz formulas on {\Gamma}-proper manifolds

Let $\Gamma$ be a finitely generated discrete group acting properly and cocompactly on a smooth manifold M. By employing heat-kernel techniques we prove a geometric formula for the pairing of the index class associated to a $\Gamma$-equivariant Dirac operator $D$ with a delocalized cyclic cocycles $\tau$ in $HP^\bullet (\mathbb{C}\Gamma,\langle \gamma \rangle)$. Our formula takes place on the fixed point manifold $M^\gamma$ and should be regarded as a higher Lefschetz formula for $D$. The formula involves the Atiyah-Segal-Singer form and an explicit $Z_\gamma$-invariant form on $M^\gamma$ that is naturally associated to $\tau\in HP^\bullet (\mathbb{C}\Gamma,\langle \gamma \rangle)$

math.DG↗
arXiv2025

Superconnection and Orbifold Chern character

We use flat antiholomorphic superconnections to study orbifold Chern character following the method introduced by Bismut, Shen, and Wei. We show the uniqueness of orbifold Chern character by proving a Riemann-Roch-Grothendieck theorem for orbifold embeddings.

math.DG↗
arXiv2025

ZeroScene: A Zero-Shot Framework for 3D Scene Generation from a Single Image and Controllable Texture Editing

In the field of 3D content generation, single image scene reconstruction methods still struggle to simultaneously ensure the quality of individual assets and the coherence of the overall scene in complex environments, while texture editing techniques often fail to maintain both local continuity and multi-view consistency. In this paper, we propose a novel system ZeroScene, which leverages the prior knowledge of large vision models to accomplish both single image-to-3D scene reconstruction and texture editing in a zero-shot manner. ZeroScene extracts object-level 2D segmentation and depth information from input images to infer spatial relationships within the scene. It then jointly optimizes 3D and 2D projection losses of the point cloud to update object poses for precise scene alignment, ultimately constructing a coherent and complete 3D scene that encompasses both foreground and background. Moreover, ZeroScene supports texture editing of objects in the scene. By imposing constraints on the diffusion model and introducing a mask-guided progressive image generation strategy, we effectively maintain texture consistency across multiple viewpoints and further enhance the realism of rendered results through Physically Based Rendering (PBR) material estimation. Experimental results demonstrate that our framework not only ensures the geometric and appearance accuracy of generated assets, but also faithfully reconstructs scene layouts and produces highly detailed textures that closely align with text prompts.

cs.GR↗
arXiv2025

Symplectic Morse Theory and Witten Deformation

On symplectic manifolds, we introduce a Morse-type complex with elements generated by pairs of critical points of a Morse function. The differential of the complex consists of gradient flows and an integration of the symplectic structure over spaces of gradient flow lines. Using the Witten deformation method, we prove that the cohomology of this complex is independent of both the Riemannian metric and the Morse function used to define the complex and is in fact isomorphic to the cohomology of differential forms of Tsai, Tseng and Yau (TTY). We also obtain Morse-type inequalities that bound the dimensions of the TTY cohomologies by the number of Morse critical points and the interaction of symplectic structure with the critical points.

math.SG↗
arXiv2025

Simplicial sheaves of modules and Morita invariance of groupoid cohomology

In this article we develop a unified framework for proving Morita invariance of cohomology theories associated to Lie groupoids. Our approach is to view these cohomology theories as arising from sheaves of modules on the nerve of the groupoid. We establish criteria for when such sheaves of modules give rise to Morita invariant cohomology theories.

math.DG↗
arXiv2025

Higher Orbital Integrals on Motion Groups and Mackey Deformation

We present an explicit construction of cyclic cocycles on Cartan motion groups, which can be viewed as generalizations of orbital integrals. We show that the higher orbital integral on a real reductive group associated with a semisimple element converges to the corresponding one on the associated Cartan motion group.

math.KT↗
arXiv2025

Towards Geometric and Textural Consistency 3D Scene Generation via Single Image-guided Model Generation and Layout Optimization

In recent years, 3D generation has made great strides in both academia and industry. However, generating 3D scenes from a single RGB image remains a significant challenge, as current approaches often struggle to ensure both object generation quality and scene coherence in multi-object scenarios. To overcome these limitations, we propose a novel three-stage framework for 3D scene generation with explicit geometric representations and high-quality textural details via single image-guided model generation and spatial layout optimization. Our method begins with an image instance segmentation and inpainting phase, which recovers missing details of occluded objects in the input images, thereby achieving complete generation of foreground 3D assets. Subsequently, our approach captures the spatial geometry of reference image by constructing pseudo-stereo viewpoint for camera parameter estimation and scene depth inference, while employing a model selection strategy to ensure optimal alignment between the 3D assets generated in the previous step and the input. Finally, through model parameterization and minimization of the Chamfer distance between point clouds in 3D and 2D space, our approach optimizes layout parameters to produce an explicit 3D scene representation that maintains precise alignment with input guidance image. Extensive experiments on multi-object scene image sets have demonstrated that our approach not only outperforms state-of-the-art methods in terms of geometric accuracy and texture fidelity of individual generated 3D models, but also has significant advantages in scene layout synthesis.

cs.GR↗
arXiv2025

Heat kernel, large-time behavior, and representation theory

Given a real reductive group $G$, the purpose of this paper is to show an asymptotic formula of the large-time behavior of the $G$-trace of the heat operator on the associated symmetric spaces. Together with Carmona's proof on Vogan's lambda map, our results provide a geometric counterpart of Vogan's minimal $K$-type theory.

math.DG↗
arXiv2025

Delocalized eta invariants of the signature operator on G-proper manifolds

Let $G$ be a connected, linear real reductive group and let $X$ be a cocompact $G$-proper manifold without boundary. We define delocalized eta invariants associated to a $L^2$-invertible perturbed Dirac operator $D_X+A$ with $A$ a suitable smoothing perturbation. We also investigate the case in which $D_X$ is not invertible but $0$ is isolated in the $L^2$-spectrum of $D_X$. We prove index formulas relating these delocalized eta invariants to Atiyah-Patodi-Singer delocalized indices on $G$-proper manifolds with boundary. In order to achieve this program we give a detailed account of both the large and small time behaviour of the heat-kernel of perturbed Dirac operators, as a map from the positive real line to the algebra of Lafforgue integral operators. We apply these results to the definition of rho-numbers associated to $G$-homotopy equivalences between closed $G$-proper manifolds and to the study of their bordism properties. We also define delocalized signatures of manifolds with boundary satisfying an invertibility assumption on the differential form Laplacian of the boundary in middle degree and prove an Atiyah-Patodi-Singer formula for these delocalized signatures.

math.DG↗
arXiv2025

Recent Advances in 3D Object and Scene Generation: A Survey

In recent years, the demand for 3D content has grown exponentially with the intelligent upgrade of interactive media, extended reality (XR), and Metaverse industries. In order to overcome the limitations of traditional manual modeling approaches, such as labor-intensive workflows and prolonged production cycles, revolutionary advances have been achieved through the convergence of novel 3D representation paradigms and artificial intelligence generative technologies. In this survey, we conduct a systematic review of the cutting-edge achievements in static 3D object and scene generation, as well as establish a comprehensive technical framework through systematic categorization. We start our analysis with mainstream 3D object representations. Subsequently, we delve into the technical pathways of 3D object generation based on four mainstream deep generative models: Variational Autoencoders, Generative Adversarial Networks, Autoregressive Models, and Diffusion Models. Regarding scene generation, we focus on three dominant paradigms: layout-guided generation, lifting based on 2D priors, and rule-driven modeling. Finally, we critically examine persistent challenges in 3D generation and propose potential research directions for future investigation. This survey aims to provide readers with a structured understanding of state-of-the-art 3D generation technologies while inspiring researchers to undertake more exploration in this domain.

cs.GR↗
arXiv2024

Boulder migration in the Khonsu region of comet 67P/Churyumov-Gerasimenko

European Space Agency's Rosetta mission is the only space mission that performed long-term monitoring of comet at close distances. Its over two years' rendezvous with comet 67P/Churyumov-Gerasimenko revealed diverse evolutionary processes of the cometary nucleus. One of the most striking events is the migration of a 30-m boulder in the southern hemisphere region of Khonsu. Previous works found the boulder's 140-m displacement occurred during the three months from August to October 2015, and several triggering mechanisms were proposed, including outburst at the boulder site, seismic vibrations from nearby activities, or surface erosion of the slope beneath the boulder. In this work, we further analyze this impressive event by analysing imaging data from Rosetta's OSIRIS camera. We constrained the boulder's migration time to within 14 hours and derived a detailed timeline of the boulder migration event and local dust activities. High-resolution thermophysical modelling shows significant dichotomy in the thermal history of the boulder's southern and northern sides, which could have triggered or facilitated its migration via its own volatile activity.

astro-ph.EP↗
arXiv2024

Generation of 10 kT Axial Magnetic Fields Using Multiple Conventional Laser Beams: A Sensitivity Study for kJ PW-Class Laser Facilities

Strong multi-kilotesla magnetic fields have various applications in high-energy density science and laboratory astrophysics, but they are not readily available. In our previous work [Y. Shi et al., Phys. Rev. Lett. 130, 155101 (2023)], we developed a novel approach for generating such fields using multiple conventional laser beams with a twist in the pointing direction. This method is particularly well-suited for multi-kilojoule petawatt-class laser systems like SG-II UP, which are designed with multiple linearly polarized beamlets. Utilizing three-dimensional kinetic particle-in-cell simulations, we examine critical factors for a proof-of-principle experiment, such as laser polarization, relative pulse delay, phase offset, pointing stability, and target configuration, and their impact on magnetic field generation. Our general conclusion is that the approach is very robust and can be realized under a wide range of laser parameters and plasma conditions. We also provide an in-depth analysis of the axial magnetic field configuration, azimuthal electron current, and electron and ion orbital angular momentum densities. Supported by a simple model, our analysis shows that the axial magnetic field decays due to the expansion of hot electrons.

physics.plasm-ph↗
arXiv2024

Mapping Cone and Morse Theory

On a smooth manifold, we associate to any closed differential form a mapping cone complex. The cohomology of this mapping cone complex can vary with the de Rham cohomology class of the closed form. We present a novel Morse theoretical description for the mapping cone cohomology. Specifically, we introduce a Morse complex for the mapping cone complex which is generated by pairs of critical points with the differential defined by gradient flows and an integration of the closed form over spaces of gradient flow lines. We prove that the cohomology of our cone Morse complex is isomorphic to the mapping cone cohomology and hence independent of both the Riemannian metric and the Morse function used to define the complex. We also obtain sharp inequalities that bound the dimension of the mapping cone cohomology in terms of the number of Morse critical points and the properties of the specified closed form. Our results are widely applicable, especially for any manifold equipped with a geometric structure described by a closed differential form. We also obtain a bound on the difference between the number of Morse critical points and the Betti numbers.

math.DG↗
arXiv2023

Higher orbital integrals, rho numbers and index theory

Let $G$ be a connected, linear real reductive group. We give sufficient conditions ensuring the well-definedness of the delocalized eta invariant $η_g (D_X)$ associated to a Dirac operator $D_X$ on a cocompact $G$-proper manifold $X$ and to the orbital integral $τ_g$ defined by a semisimple element $g\in G$. Along the way, we give a detailed account of the large time behaviour of the heat kernel and of its short time bahaviour near the fixed point set of $g$. We prove that such a delocalized eta invariant enters as the boundary correction term in an index theorem computing the pairing between the index class and the 0-degree cyclic cocycle defined by $τ_g$ on a $G$-proper manifold with boundary. More importantly, we also prove a higher version of such a theorem, for the pairing of the index class and the higher cyclic cocycles defined by the higher orbital integral $Φ^P_g$ associated to a cuspidal parabolic subgroup $P<G$ with Langlands decomposition $P=MAN$ and a semisimple element $g\in M$. We employ these results in order to define (higher) rho numbers associated to $G$-invariant positive scalar curvature metrics.

math.DG↗
arXiv2023

On the Connes-Kasparov isomorphism, I: The reduced C*-algebra of a real reductive group and the K-theory of the tempered dual

This is the first of two papers dedicated to the computation of the reduced C*-algebra of a connected, linear, real reductive group up to Morita equivalence, and the verification of the Connes-Kasparov conjecture for these groups. These results were originally announced by Antony Wassermann in 1987. In Part I we shall give details of the C*-algebraic Morita equivalence, and then compute the Connes-Kasparov morphism subject to some results in tempered representation theory that we shall prove in Part II using tools from David Vogan's classification of the tempered dual.

math.RT↗
arXiv2022

Helton-Howe Trace, Connes-Chern character and Quantization

We study the Helton-Howe trace and the Connes-Chern character for Toeplitz operators on weighted Bergman spaces via the idea of quantization. We prove a local formula for the large $t$-limit of the Connes-Chern character as the weight goes to infinity. And we show that the Helton-Howe trace of Toeplitz operators is independent of the weight $t$ and obtain a local formula for the Helton-Howe trace for all weighted Bergman spaces using harmonic analysis and quantization.

math.FA↗