arXiv subjects

Qingyuan Jiang

Publications and source records attributed to Qingyuan Jiang.

At least 19 recordsLinked to original sources

arXiv2026

Continuum envelopes on Fargues-Fontaine curves and elliptic curves

In this paper, we apply the theory of Bridgeland stability conditions, which was motivated by ideas from string theory, to study the derived category of coherent sheaves on Fargues--Fontaine curves. This leads us to consider the quasi-coherent sheaves $\mathcal{O}(θ^{\pm})$ via the convergents of an irrational number $θ$. We define the continuum envelope $\mathrm{QCoh}_{\mathbb{R}}(X{FF})$ to be the smallest abelian subcategory of $\mathrm{QCoh}(X_{FF})$ containing $\mathrm{Coh}(X_{FF})$ and $\mathcal{O}(θ^{\pm})$. We study the homological algebra of $\mathrm{QCoh}_{\mathbb{R}}(X{FF})$ via Farey diagrams. We show that the homological properties of $\mathcal{O}(θ^{\pm})$ depend heavily on the Diophantine properties of $θ$. From this point of view, Fargues--Fontaine curves exhibit strong similarities to complex elliptic curves.

math.AG↗

arXiv2026

Semiorthogonal indecomposability for Hilbert schemes of points on integral locally planar curves

Let $C$ be an integral projective curve of arithmetic genus $g$ with locally planar singularities over an algebraically closed field. We prove that for every $1\leq n\leq g-1$, both $\mathrm{Perf}(\mathrm{Hilb}^n(C))$ and $\mathrm{D^b_{coh}}(\mathrm{Hilb}^n(C))$ are semiorthogonally indecomposable. We also establish the corresponding relative $S$-linear statement for a flat family of such curves over a connected base $S$, with admissibility required in the $\mathrm{D^b_{coh}}$ case. Our results hold in arbitrary characteristic.

math.AG↗

arXiv2026

Instantons on the Blown-up Surface and the Affine Vertex Algebra

We answer a long-standing question raised by Vafa--Witten on a relation between S-duality and conformal field theory, which related Yoshioka's blow-up formula and the WZW model for $\mathrm{SU}(r)$ at level $1$. Precisely, for the moduli space of Euler characteristics of rank $r$ instantons on the blow-up of an algebraic surface along a closed point, we construct the affine $\mathrm{gl}_r$-action on various cohomology theories, including the Grothendieck group of coherent sheaves, Hochschild homology groups, Chow groups and Hodge cohomology groups, and identifying the module as a basic representation. A key ingredient in our proof is a representation-theoretic reformulation of the theory of Grassmannians of Tor-amplitude $[0,1]$-perfect complexes studied by the first-named author in terms of the spin representation of the finite-dimensional Clifford algebra. This may be viewed as a finite analog of the question of Vafa--Witten via the Boson--Fermion correspondence.

math.AG↗

arXiv2026

Modular variants of p-adic fundamental sequence

In this article, we relate any Farey triangle in the extended upper half-plane to a variant of Colmez--Fontaine's fundamental lemma in $p$-adic Hodge theory. In particular, their original fundamental lemma corresponds to the fundamental Farey triangle $(\frac{1}{0},\frac{1}{1},\frac{0}{1})$.

math.NT↗

arXiv2025

Abel maps for integral curves via a derived perspective

We develop a general framework for Abel maps associated with a family $X/S$ of integral curves using derived algebraic geometry. For compactified Picard schemes, our approach yields relative quasi-smooth derived enhancements of the Quot schemes $\mathrm{Quot}_{ω/X/S}^d$ and, in the Gorenstein case, of the Hilbert schemes of points $\mathrm{Hilb}_{X/S}^d$ on $X/S$. These constructions naturally generalize to higher rank torsion-free sheaves and their coherent systems. We obtain unified semiorthogonal decompositions for the derived categories of these derived moduli spaces, broadly extending previous results for symmetric powers, varieties of linear series, and Thaddeus pairs to torsion-free sheaves on integral curves. Central to our approach are two novel tools of independent interest: the $\mathcal{Q}$-complex, a derived generalization of Grothendieck's $Q$-module and the Altman--Kleiman $H$-module, and a derived theory of moduli of extensions that extends Lange's classical framework.

math.AG↗

arXiv2025

Part Segmentation and Motion Estimation for Articulated Objects with Dynamic 3D Gaussians

Part segmentation and motion estimation are two fundamental problems for articulated object motion analysis. In this paper, we present a method to solve these two problems jointly from a sequence of observed point clouds of a single articulated object. The main challenge in our problem setting is that the point clouds are not assumed to be generated by a fixed set of moving points. Instead, each point cloud in the sequence could be an arbitrary sampling of the object surface at that particular time step. Such scenarios occur when the object undergoes major occlusions, or if the dataset is collected using measurements from multiple sensors asynchronously. In these scenarios, methods that rely on tracking point correspondences are not appropriate. We present an alternative approach based on a compact but effective representation where we represent the object as a collection of simple building blocks modeled as 3D Gaussians. We parameterize the Gaussians with time-dependent rotations, translations, and scales that are shared across all time steps. With our representation, part segmentation can be achieved by building correspondences between the observed points and the Gaussians. Moreover, the transformation of each point across time can be obtained by following the poses of the assigned Gaussian (even when the point is not observed). Experiments show that our method outperforms existing methods that solely rely on finding point correspondences. Additionally, we extend existing datasets to emulate real-world scenarios by considering viewpoint occlusions. We further demonstrate that our method is more robust to missing points as compared to existing approaches on these challenging datasets, even when some parts are completely occluded in some time-steps. Notably, our part segmentation performance outperforms the state-of-the-art method by 13% on point clouds with occlusions.

cs.CV↗

arXiv2025

Rebalanced Multimodal Learning with Data-aware Unimodal Sampling

To address the modality learning degeneration caused by modality imbalance, existing multimodal learning~(MML) approaches primarily attempt to balance the optimization process of each modality from the perspective of model learning. However, almost all existing methods ignore the modality imbalance caused by unimodal data sampling, i.e., equal unimodal data sampling often results in discrepancies in informational content, leading to modality imbalance. Therefore, in this paper, we propose a novel MML approach called \underline{D}ata-aware \underline{U}nimodal \underline{S}ampling~(\method), which aims to dynamically alleviate the modality imbalance caused by sampling. Specifically, we first propose a novel cumulative modality discrepancy to monitor the multimodal learning process. Based on the learning status, we propose a heuristic and a reinforcement learning~(RL)-based data-aware unimodal sampling approaches to adaptively determine the quantity of sampled data at each iteration, thus alleviating the modality imbalance from the perspective of sampling. Meanwhile, our method can be seamlessly incorporated into almost all existing multimodal learning approaches as a plugin. Experiments demonstrate that \method~can achieve the best performance by comparing with diverse state-of-the-art~(SOTA) baselines.

cs.LG↗

arXiv2024

The Solution for Temporal Action Localisation Task of Perception Test Challenge 2024

This report presents our method for Temporal Action Localisation (TAL), which focuses on identifying and classifying actions within specific time intervals throughout a video sequence. We employ a data augmentation technique by expanding the training dataset using overlapping labels from the Something-SomethingV2 dataset, enhancing the model's ability to generalize across various action classes. For feature extraction, we utilize state-of-the-art models, including UMT, VideoMAEv2 for video features, and BEATs and CAV-MAE for audio features. Our approach involves training both multimodal (video and audio) and unimodal (video only) models, followed by combining their predictions using the Weighted Box Fusion (WBF) method. This fusion strategy ensures robust action localisation. our overall approach achieves a score of 0.5498, securing first place in the competition.

cs.CV↗

arXiv2024

Solution for OOD-CV UNICORN Challenge 2024 Object Detection Assistance LLM Counting Ability Improvement

This report provide a detailed description of the method that we explored and proposed in the ECCV OOD-CV UNICORN Challenge 2024, which focusing on the robustness of responses from large language models. The dataset of this competition are OODCA-VQA and SketchyQA. In order to test the robustness of the model. The organizer extended two variants of the dataset OODCV-Counterfactual and Sketchy-Challenging. There are several difficulties with these datasets. Firstly, the Sketchy-Challenging dataset uses some rarer item categories to test the model's generalization ability. Secondly, in the OODCV-Counterfactual dataset, the given problems often have inflection points and computational steps, requiring the model to recognize them during the inference process. In order to address this issue, we propose a simple yet effective approach called Object Detection Assistance Large Language Model(LLM) Counting Ability Improvement(ODAC), which focuses on using the object detection model to assist the LLM. To clarify, our approach contains two main blocks: (1)Object Detection Assistance. (2) Counterfactual Specific prompt. Our approach ranked second in the final test with a score of 0.86.

cs.CV↗

arXiv2024

Map-Aware Human Pose Prediction for Robot Follow-Ahead

In the robot follow-ahead task, a mobile robot is tasked to maintain its relative position in front of a moving human actor while keeping the actor in sight. To accomplish this task, it is important that the robot understand the full 3D pose of the human (since the head orientation can be different than the torso) and predict future human poses so as to plan accordingly. This prediction task is especially tricky in a complex environment with junctions and multiple corridors. In this work, we address the problem of forecasting the full 3D trajectory of a human in such environments. Our main insight is to show that one can first predict the 2D trajectory and then estimate the full 3D trajectory by conditioning the estimator on the predicted 2D trajectory. With this approach, we achieve results comparable or better than the state-of-the-art methods three times faster. As part of our contribution, we present a new dataset where, in contrast to existing datasets, the human motion is in a much larger area than a single room. We also present a complete robot system that integrates our human pose forecasting network on the mobile robot to enable real-time robot follow-ahead and present results from real-world experiments in multiple buildings on campus. Our project page, including supplementary material and videos, can be found at: https://qingyuan-jiang.github.io/iros2024_poseForecasting/

cs.RO↗

arXiv2023

Brill-Noether theory of Hilbert schemes of points on surfaces

We show that Brill--Noether loci in Hilbert scheme of points on a smooth connected surface $S$ are non-empty whenever their expected dimension is positive, and that they are irreducible and have expected dimensions. More precisely, we consider the loci of pairs $(I, s)$ where $I$ is an ideal that locally at the point $s$ of $S$ needs a given number of generators. We give two proofs. The first uses Iarrobino's descriptionof the Hilbert--Samuel stratification of local punctual Hilbert schemes, and the second is based on induction via birational relationships between different Brill--Noether loci given by nested Hilbert schemes.

math.AG↗

arXiv2023

Onboard View Planning of a Flying Camera for High Fidelity 3D Reconstruction of a Moving Actor

Capturing and reconstructing a human actor's motion is important for filmmaking and gaming. Currently, motion capture systems with static cameras are used for pixel-level high-fidelity reconstructions. Such setups are costly, require installation and calibration and, more importantly, confine the user to a predetermined area. In this work, we present a drone-based motion capture system that can alleviate these limitations. We present a complete system implementation and study view planning which is critical for achieving high-quality reconstructions. The main challenge for view planning for a drone-based capture system is that it needs to be performed during motion capture. To address this challenge, we introduce simple geometric primitives and show that they can be used for view planning. Specifically, we introduce Pixel-Per-Area (PPA) as a reconstruction quality proxy and plan views by maximizing the PPA of the faces of a simple geometric shape representing the actor. Through experiments in simulation, we show that PPA is highly correlated with reconstruction quality. We also conduct real-world experiments showing that our system can produce dynamic 3D reconstructions of good quality. We share our code for the simulation experiments in the link: https://github.com/Qingyuan-Jiang/view_planning_3dhuman

cs.RO↗

arXiv2023

Derived categories of Quot schemes of locally free quotients

This paper studies the derived category of the Quot scheme of rank $d$ locally free quotients of a sheaf $\mathscr{G}$ of homological dimension $\le 1$ over a scheme $X$. In particular, we propose a conjecture about the structure of its derived category and verify the conjecture in various cases. This framework allows us to relax certain regularity conditions on various known formulae -- such as the ones for blowups (along Koszul-regular centers), Cayley's trick, standard flips, projectivizations, and Grassmannain-flips -- and supplement these formulae with the results on mutations and relative Serre functors. This framework also leads us to many new phenomena such as virtual flips, and structural results for the derived categories of (i) $\mathrm{Quot}_2$ schemes, (ii) flips from partial desingularizations of $\mathrm{rank}\le 2$ degeneracy loci, and (iii) blowups along determinantal subschemes of codimension $\le 4$.

math.AG↗

arXiv2023

Derived projectivizations of complexes

In this paper, we study the counterpart of Grothendieck's projectivization construction in the context of derived algebraic geometry. Our main results are as follows: First, we define the derived projectivization of a connective complex, study its fundamental properties such as finiteness properties and functorial behaviors, and provide explicit descriptions of their relative cotangent complexes, We then focus on the derived projectivizations of complexes of perfect-amplitude contained in $[0,1]$. In this case, we prove a generalized Serre's theorem, a derived version of Beilinson's relations, and establish semiorthogonal decompositions for their derived categories. Finally, we show that many moduli problems fit into the framework of derived projectivizations, such as moduli spaces that arise in Hecke correspondences. We apply our results to these situations.

math.AG↗

arXiv2023

Derived Grassmannians and derived Schur functors

This paper develops two theories, the geometric theory of derived Grassmannians (and flag schemes) and the algebraic theory of derived Schur (and Weyl) functors, and establishes their connection, a derived generalization of the Borel-Weil-Bott theorem. More specifically: (1) The theory of derived Grassmannians and flag schemes is the natural extension of the theory of derived projectivizations [arXiv:2202.11636] and generalizes Grothendieck's theory of Grassmannians and flag schemes of sheaves to the case of complexes. We establish their fundamental properties and study various natural morphisms among them. (2) The theory of derived Schur and Weyl functors extends the classical theory of Schur and Weyl module functors studied in $\mathrm{GL}_n(\mathbb{Z})$-representation theory to the case of complexes. We show that these functors have excellent functorial properties and satisfy derived generalizations of classical formulae such as Cauchy's decomposition formula, direct-sum decomposition formula and Littlewood-Richardson rule. We also generalize various results from the case of derived symmetric powers to derived Schur functors, such as Illusie-Lurie's décalage isomorphism. (3) These two theories are connected by a derived version of the Borel-Weil-Bott theorem, which generalizes the classical Borel-Weil-Bott theorem and calculates the derived pushforwards of tautological perfect complexes on derived flag schemes in terms of derived Schur functors when the complexes have perfect-amplitude $\le 1$ and positive ranks.

math.AG↗

arXiv2023

Derived Categories of Derived Grassmannians

This paper establishes semiorthogonal decompositions for derived Grassmannians of perfect complexes with Tor-amplitude in $[0,1]$. This result verifies the author's Quot formula conjecture [J21a] and generalizes and strengthens Toda's result in [Tod23]. We give applications of this result to various classical situations such as blowups of determinantal ideals, reducible schemes, and varieties of linear series on curves. Our approach utilizes the framework of derived algebraic geometry, allowing us to work over arbitrary base spaces over $\mathbb{Q}$. It also provides concrete descriptions of Fourier-Mukai kernels in terms of derived Schur functors.

math.AG↗

arXiv2021

Derived category of projectivizations and flops

In this paper, we prove a generalization of Orlov's projectivization formula for the derived category $D^b_{\rm coh} (\mathbb{P}(\mathscr{E}))$, where $\mathscr{E}$ does not need to be a vector bundle; Instead, $\mathscr{E}$ is a coherent sheaf which locally admits two-step resolutions. As a special case, this also gives Orlov's generalized universal hyperplane section formula. As applications, (i) we obtain a blowup formula for blowup along codimension two Cohen-Macaulay subschemes, (ii) we obtain new "flop-flop=twist" results for a large class of flops obtained by crepant resolutions of degeneracy loci. As another consequence, this gives a perverse Schober on C. (iii) we give applications of the above results to symmetric powers of curves and $Θ$-flops, following Toda.

math.AG↗

arXiv2021

On the Chow theory of projectivizations

In this paper, we prove a decomposition result for the Chow groups of projectivizations of coherent sheaves of homological dimension $\le 1$. In this process, we establish the decomposition of Chow groups for the cases of Cayley's trick and standard flips. Moreover, we apply these results to study the Chow groups of symmetric powers of curves, nested Hilbert schemes of surfaces, and the varieties resolving Voisin maps for cubic fourfolds.

math.AG↗