arXiv subjects

Qingyun Zeng

Publications and source records attributed to Qingyun Zeng.

6 recordsLinked to original sources

arXiv2026

Higher Riemann-Hilbert Correspondence and Descent for Regular Foliations

Let ${\mathcal F}\subset TM$ be a regular foliation. We construct an $A_\infty$ integration functor from globally bounded finite-rank leafwise cohesive modules with locally constant fiber-cohomology rank to global plot-smooth infinity-local systems with the same regularity. The target retains the global higher-transport objects and sheafifies their raw Block--Smith Hom presheaves. The construction combines the Gugenheim--Arias Abad--Schätz iterated-integral map with the Lie-algebroid higher-holonomy formulas. For every $M$, integration is quasi-fully faithful. On each star-shaped foliated box, a strictly unital simplicial prism gives an explicit raw local inverse. If $M$ is compact, effective descent for cohesive modules and Čech descent for the target Hom sheaves promote the local comparison to an $A_\infty$ quasi-equivalence on the regular full subcategories; compact proper submersions give a distinguished class of examples. At every fixed finite amplitude, the local comparison also induces an equivalence of $\operatorname{Cat}_\infty$-valued hypersheafifications. No global raw-Hom comparison or analogous correspondence for singular foliations or general $L_\infty$-algebroids is asserted.

math.DG↗

arXiv2026

Superconnections, descent, and monodromy on transversely holomorphic foliations

Let $X$ carry a transversely holomorphic foliation, equivalently an elliptic involutive structure $V\subset T_{\mathbb C}X$, and let ${\mathcal O}_V$ be its sheaf of leafwise-constant, transversely holomorphic functions. We construct a finite superconnection model for the derived category of coherent ${\mathcal O}_V$-modules. The key input is a mixed local reduction for finite Maurer--Cartan objects over the mixed de Rham--Dolbeault dga $(\wedge^\bullet V^\vee,d_V)$: a multiplicative homotopy contracts the real directions, after which Block's Dolbeault gauge theorem removes the positive transverse form degrees. For compact $X$, this gives an exact equivalence between the homotopy category of bounded finite-rank flat $V$-superconnections and $D^b_{\mathrm{coh}}(X,{\mathcal O}_V)$, interpolating between the de Rham and Dolbeault realizations. We prove locally finite Čech descent under necessary uniform amplitude and rank bounds, identify the coherent heart with equivariant coherent analytic sheaves on a transverse monodromy groupoid, and characterize descent to ordinary holonomy. For a holomorphic suspension, we identify the full superconnection category, up to Morita equivalence, with the homotopy fixed points of the Dolbeault category of the transversal and derive an equivariant Ext spectral sequence. Examples on $S^1$ and $S^2$ delimit when ordinary monodromy $1$-groupoids can recover the derived category.

math.AG↗

arXiv2025

Derived Lie $\infty$-groupoids and algebroids in higher differential geometry

We study various problems arising in higher differential geometry using {\it derived Lie $\infty$-groupoids and algebroids}.We first study Lie $\infty$-groupoids in various categories of derived geometric objects in differential geometry, including derived manifolds, derived analytic spaces, derived noncommutative spaces, and derived Banach manifolds. We construct category of fibrant objects (CFO) structures in the category of derived Lie $\infty$-groupoids. Then we study $L_{\infty}$-algebroids which are the infinitesimal counterpart of derived Lie $\infty$-groupoids. We then study the homotopical algebras for derived Lie $\infty$-groupoids and algebroids and study their homotopy-coherent representations, which we call $\infty$-representations. We relate $\infty$-representations of $L_{\infty}$-algebroids to (quasi-) cohesive modules developed by Block, and $\infty$-representations of Lie $\infty$-groupoids to $\infty$-local system introduced by Block-Smith. Then we apply these tools in studying singular foliations and their characteristic classes. We construct Atiyah classes for $L_{\infty}$-algebroids pairs. We study singular foliations and their holonomies. We construct $Ł_{\infty}$-algebroids for holomorphic singular foliations, and then We study elliptic involutive structures and prove an dg-enhancement of $V$-analytic coherent sheaves. These examples inspire us to define {\it perfect singular foliations}, which is a subcategory of singular foliation but with better homological algebras. Next, we construct various Lie $\infty$-groupoids for singular foliations. Then we study foliations on stacks and higher groupoids. Finally, we prove an $A_{\infty}$ de Rham theorem for foliations, and Riemann-Hilbert correspondence for foliated $\infty$-local system foliated manifolds.

math.DG↗

arXiv2025

Financial sentiment analysis using FinBERT with application in predicting stock movement

In this study, we integrate sentiment analysis within a financial framework by leveraging FinBERT, a fine-tuned BERT model specialized for financial text, to construct an advanced deep learning model based on Long Short-Term Memory (LSTM) networks. Our objective is to forecast financial market trends with greater accuracy. To evaluate our model's predictive capabilities, we apply it to a comprehensive dataset of stock market news and perform a comparative analysis against standard BERT, standalone LSTM, and the traditional ARIMA models. Our findings indicate that incorporating sentiment analysis significantly enhances the model's ability to anticipate market fluctuations. Furthermore, we propose a suite of optimization techniques aimed at refining the model's performance, paving the way for more robust and reliable market prediction tools in the field of AI-driven finance.

q-fin.ST↗

arXiv2025

Taming SQL Complexity: LLM-Based Equivalence Evaluation for Text-to-SQL

The rise of Large Language Models (LLMs) has significantly advanced Text-to-SQL (NL2SQL) systems, yet evaluating the semantic equivalence of generated SQL remains a challenge, especially given ambiguous user queries and multiple valid SQL interpretations. This paper explores using LLMs to assess both semantic and a more practical "weak" semantic equivalence. We analyze common patterns of SQL equivalence and inequivalence, discuss challenges in LLM-based evaluation.

cs.CL↗

arXiv2020

Merging of Soap Bubbles and Why Surfactant Matters

The merging of two soap bubbles is a fundamental fluid mechanical process in foam formation. In the present experimental study the liquid films from two soap bubbles are brought together. Once the liquid layers initially separated by a gas sheet are bridged on a single spot the rapid merging of the two liquid films proceed. Thereby the connecting rim is rapidly accelerated into the separating gas layer. We show that due to the dimple formation the velocity is not uniform and the high acceleration causes initially a Rayleigh-Taylor instability of the liquid rim. At later times, the rim takes heals into a circular shape. However for sufficient high concentrations of the surfactant the unstable rim pinches off microbubbles resulting in a fractal dendritic structure after coalescence.

physics.flu-dyn↗