arXiv subjects
Publications and source records attributed to Junsheng Zhang.
We complete the classification of non-K\"ahler steady pluriclosed soliton on compact complex surfaces, as initiated by Streets. The underlying complex structure must be a Hopf surface, with any finite primary cover being of class 1. Moreover, the soliton metric is unique up to biholomorphism.
In this paper, we establish several uniform estimates for K\"ahler--Ricci shrinkers without imposing any curvature assumptions. In particular, we prove: 1. a uniform lower bound for the entropy; 2. a uniform lower bound for the asymptotic volume ratio of K\"ahler--shrinkers with maximal volume growth; 3. a uniform lower bound for the scalar curvature on balls centered at a minimum point of the soliton potential for non-Gaussian shrinkers.
Turning a research idea into a complete paper requires more than text generation: the system must retrieve literature, design and execute experiments, revise claims according to evidence, produce publication-ready figures, and maintain consistency across a long generation process. We present Spark-to-Paper, an end-to-end research paper generation system implemented as thirteen composable skills inside an existing coding assistant, without requiring a separate agent platform or orchestration service. Spark-to-Paper separates model-based judgment from deterministic operations that can be directly executed and checked. It further separates experiment planning from reporting, so that required evidence is specified before results are observed and manuscript claims are revised according to measured outcomes. To improve reliability over long research trajectories, the system combines deterministic integrity checks with self-critique and bounds a failure mode we call the Self-Refutation Loop, in which repeated experiments continue to reject the original research objective. Spark-to-Paper also produces editable vector figures through programmatic plotting for experimental results and code-based reconstruction for generated method diagrams. Across eight controlled research topics, Spark-to-Paper achieves 99.5% citation validity and 96.4% figure editability. A controlled ablation increases fabrication detection from 14% for a single-pass draft to 92% with the full integrity and review stack, while adversarial review achieves 74% precision. The full system uses 11.9M tokens, costs $8.1 per manuscript, and requires 3.2 hours on average. These results show that end-to-end research paper generation can be implemented as a lightweight, composable workflow inside existing coding assistants while keeping experimental evidence central to how claims are accepted, revised, or abandoned.
We study the metric geometry of finite-time singularities of volume-noncollapsed K\"ahler-Ricci flows and the geometry at infinity of Ricci shrinkers. For a compact volume-noncollapsed K\"ahler-Ricci flow approaching its first singular time, we prove that the time slices converge to a unique Gromov-Hausdorff limit, canonically identified with the time-zero slice of the Ricci-flow spacetime completion. Its regular part is identified with the complement of the null locus, and we show that the singular set has Hausdorff codimension at least four. For K\"ahler-Ricci shrinkers, we relate the geometry at infinity to the associated Fano fibration. We prove local smooth convergence to a K\"ahler cone metric on the locus where the fibration is biholomorphic, and characterize asymptotic conicality by biholomorphicity outside a compact set. For Ricci shrinkers with bounded scalar curvature, we show that local compactness of the time-zero slice implies pointed Gromov-Hausdorff convergence of the full self-similar flow to that slice. As applications, we prove uniqueness of the tangent space at infinity for K\"ahler-Ricci shrinkers with bounded scalar curvature and Euclidean volume growth whose soliton vector field generates an $S^1$-action, and for all four-dimensional Ricci shrinkers with bounded scalar curvature.
Human motion follows a temporal hierarchical structure, transitioning from low-frequency global trajectories to high-frequency details. Inspired by the success of multi-level autoregressive models in computer vision, we propose MotionMAR, a coarse-to-fine framework for motion reconstruction from sparse observations. It first estimates the global trajectory of human motion and then gradually refines the temporal details. This architecture consists of four integrated components. The Temporal Multi-scale Tokenization (TMT) VQ-VAE encodes the data at multiple temporal resolutions, separating semantic motion from minor jitters. The Motion Autoregressive Network (MAN) operates in this latent space, predicting motion across scales. It first establishes the global structure through coarse indices and then generates finer indices to recover specific details. Meanwhile, the Scale-Aware Control (SAC) module integrates sparse tracking data to ensure the generated output aligns with actual observations. The Motion Refinement Network (MRN) subsequently smooths consecutive poses and eliminates quantization artifacts. Experiments show that MotionMAR achieves state-of-the-art accuracy on the AMASS dataset, providing a reliable and structure-aware approach for motion reconstruction. The source code is publicly available at http://www.lidarhumanmotion.net/motionmar/.
We show that the Gromov--Hausdorff convergence of non-collapsed polarized constant scalar curvature K\"ahler (cscK) surfaces can be realized as convergence in a Hilbert scheme. We also derive uniform estimates of Bergman kernels on the effective regular set. As an application, we establish the Zariski openness of cscK metrics for certain smooth polarized families, following the approach of Donaldson.
We prove that any singular K\"ahler--Ricci shrinker $X$ arising as a noncollapsed limit of K\"ahler--Ricci flows admits a natural structure of a polarized Fano fibration. We also show that it is simply connected, has unique tangent cones at every point, and is a smooth orbifold outside a subset of complex codimension at least three. As an application, we prove a new long-time pseudolocality theorem for almost-selfsimilar K\"ahler--Ricci flows.
Humanoid robots have achieved significant progress in motion generation and control, exhibiting movements that appear increasingly natural and human-like. Inspired by the Turing Test, we propose the Motion Turing Test, a framework that evaluates whether human observers can discriminate between humanoid robot and human poses using only kinematic information. To facilitate this evaluation, we present the Human-Humanoid Motion (HHMotion) dataset, which consists of 1,000 motion sequences spanning 15 action categories, performed by 11 humanoid models and 10 human subjects. All motion sequences are converted into SMPL-X representations to eliminate the influence of visual appearance. We recruited 30 annotators to rate the human-likeness of each pose on a 0-5 scale, resulting in over 500 hours of annotation. Analysis of the collected data reveals that humanoid motions still exhibit noticeable deviations from human movements, particularly in dynamic actions such as jumping, boxing, and running. Building on HHMotion, we formulate a human-likeness evaluation task that aims to automatically predict human-likeness scores from motion data. Despite recent progress in multimodal large language models, we find that they remain inadequate for assessing motion human-likeness. To address this, we propose a simple baseline model and demonstrate that it outperforms several contemporary LLM-based methods. The dataset, code, and benchmark will be publicly released to support future research in the community.
We show that the normalized K\"ahler-Ricci flow on a compact K\"ahler manifold with semiample canonical bundle converges in the Gromov-Hausdorff topology to the metric completion of the twisted K\"ahler-Einstein metric on the canonical model, as conjectured by Song-Tian's analytic mimimal model program.
We prove a weaker version of the transcendental base-point freeness on compact K\"ahler manifolds. As a consequence, we derive the diameter lower bound for finite time singularities of K\"ahler-Ricci flow with non-Fano initial data.
We show that for a pointed Gromov-Hausdorff limit of non-collapsed Riemannian manifolds with bounded Ricci curvature, the local $b_1$ of the regular loci vanishes. We also discuss applications and some open questions.
In this paper, we build connections between K\"ahler-Ricci shrinkers, i.e., complete (possibly non-compact) shrinking gradient K\"ahler-Ricci solitons, and algebraic geometry. In particular, we (1). prove that a K\"ahler-Ricci shrinker is naturally a quasi-projective variety, using birational algebraic geometry; (2). formulate a conjecture relating the existence of K\"ahler-Ricci shrinkers and K-stability of polarized Fano fibrations, which unifies and extends the YTD type conjectures for K\"ahler-Einstein metrics, Ricci-flat K\"ahler cone metrics and compact K\"ahler-Ricci shrinkers; (3). formulate conjectures connecting tangent flows at singularities of K\"ahler-Ricci flows and algebraic geometry, via a 2-step degeneration for the weighted volume of a Fano fibration.
Let $(Z,p)$ be a pointed Gromov-Hausdorff limit of non-collapsing K\"ahler-Einstein metrics with uniformly bounded Ricci curvature. We show that the singular K\"ahler-Einstein metric on $Z$ is conical at $p$ if and only if $\mathcal C=W$ in Donaldson-Sun's two-step degeneration theory, assuming curvature grows at most quadratically near $p$. Let $(X,p)$ be a germ of an isolated log terminal algebraic singularity. Following Hein-Sun's approach, we show that if $\mathcal C=W$ in the two-step stable degeneration of $(X,p)$ and $\mathcal C$ has a smooth link, then every singular K\"ahler-Einstein metric on $X$ with non-positive Ricci curvature and bounded potential is conical at $p$.
In this note, we give examples that demonstrate a negative answer to the generalized numerical criterion problem for pairs.
We show that on a compact Kähler manifold all real $(1,1)$-classes admitting solutions to the supercritical deformed Hermitian-Yang-Mills equation form a both open and closed subset of those which satisfy the numerical condition proposed by Collins-Jacob-Yau. More importantly, we show by examples that it can be a proper subset. This disproves a conjecture made by Collins-Jacob-Yau.
We discover a "no semistability at infinity" phenomenon for complete Calabi-Yau metrics asymptotic to cones, by eliminating the possible appearance of an intermediate K-semistable cone in the 2-step degeneration theory developed by Donaldson and the first author. It is in sharp contrast to the setting of local singularities of Kähler-Einstein metrics. A byproduct of the proof is a polynomial convergence rate to the asymptotic cone for such manifolds, which bridges the gap between the general theory of Colding-Minicozzi and the classification results of Conlon-Hein.
We give an algebraic criterion for the existence of projectively Hermitian-Yang-Mills metrics on a holomorphic vector bundle $E$ over some complete non-compact Kähler manifolds $(X,ω)$, where $X$ is the complement of a divisor in a compact Kähler manifold and we impose some conditions on the cohomology class and the asymptotic behaviour of the Kähler form $ω$. We introduce the notion of stability with respect to a pair of $(1,1)$-classes which generalizes the standard slope stability. We prove that this new stability condition is both sufficient and necessary for the existence of projectively Hermitian-Yang-Mills metrics in our setting.
Knowledge graphs (KGs) on COVID-19 have been constructed to accelerate the research process of COVID-19. However, KGs are always incomplete, especially the new constructed COVID-19 KGs. Link prediction task aims to predict missing entities for (e, r, t) or (h, r, e), where h and t are certain entities, e is an entity that needs to be predicted and r is a relation. This task also has the potential to solve COVID-19 related KGs' incomplete problem. Although various knowledge graph embedding (KGE) approaches have been proposed to the link prediction task, these existing methods suffer from the limitation of using a single scoring function, which fails to capture rich features of COVID-19 KGs. In this work, we propose the MDistMult model that leverages multiple scoring functions to extract more features from existing triples. We employ experiments on the CCKS2020 COVID-19 Antiviral Drugs Knowledge Graph (CADKG). The experimental results demonstrate that our MDistMult achieves state-of-the-art performance in link prediction task on the CADKG dataset