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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,657 papers · 148 categories

Differential Geometry

latest 9

Proves spacetime positive mass theorem with corners.

problem Proving a positive mass theorem for spacetime with corners.
method Deformation theorem with corner conditions, asymptotically flat initial data.
result Exterior end satisfies EPE \ge |P| in every dimension n3n \ge 3.

Unified framework for Riemannian deep learning across manifold-valued representations.

problem Deep learning on manifold-valued representations often relies on Euclidean approximations or costly geometric operations.
method Develops reusable neural modules, manifold-specific network architectures, and geometric designs.
result Generalizes batch normalization and multinomial logistic regression to broader classes of manifolds.

Develops relative harmonic metrics and deformation theory for Higgs and flat bundles on compact Kähler manifolds.

problem Analyzing harmonic metrics and deformations on Higgs and flat bundles on compact Kähler manifolds.
method Relative analytic theory, Sobolev completions, elliptic regularity, normalized gluing, plotwise smoothness, heat flow, harmonic filtrations, obstruction theory.
result Global smooth harmonic metrics exist for smooth stable Higgs families under certain conditions, and this theory extends to reduced singular parameter spaces.

Develops a unified theory of Yang-Mills and GR using generalized principal bundles.

problem Combining Yang-Mills theories and General Relativity into a single framework.
method Using generalized principal bundle theory, the authors develop a new approach to field theories.
result Recover General Relativity within the framework of generalized principal connections.

Paper proves existence of isometric immersions for negatively curved surfaces with unbounded second fundamental form.

problem Existence of isometric immersions for surfaces with negative Gaussian curvature.
method Reformulated Gauss--Codazzi equations into hyperbolic conservation laws, applied theories of invariant regions and compensated compactness.
result Established existence of W2,pW^{2,p}-isometric immersions for various families of metrics.

The paper explores spaces of Kähler and symplectic forms on 4-manifolds.

problem Investigating the properties of Kähler and symplectic forms on 4-manifolds.
method Analyzing the uniqueness, connectedness, and openness of spaces of Kähler forms and introducing holomorphically tamed symplectic forms.
result Formulated a parallel question for holomorphically tamed symplectic forms and related it to Kähler-type symplectic forms.

This paper classifies ball quotients of the complex projective plane.

problem Understanding the structure of the complex projective plane as a ball quotient.
method Analyzing the branch locus as a line arrangement and smooth normal-crossing curves.
result The orbifold structure of (P2,D)(\mathbb{P}^2,D) is isomorphic to either the Deligne-Mostow example or a certain degree 9 cover.

Geometric Topology

latest 9

Classifies degenerations of complex projective plane with rational singularities.

problem Classifying singularities of complex projective plane.
method Assuming Wahl's conjecture, classifies degenerations using rational homology disk smoothing.
result Classifies surfaces with rational singularities, including new degenerations with non-log canonical singularities.

The paper explores the geometry and dynamics of free splitting and free factor complexes for groups.

problem Understanding the large scale geometry and dynamics of free splitting and free factor complexes.
method Analyzing the actions of the relative outer automorphism group on these complexes and using tools like the Two Over All Theorem and filling paths.
result Hyperbolicity of the relative free splitting complex and relative free factor complex was proven.

New findings show infinitely many non-homeomorphic manifolds with same proper homotopy type.

problem Characterizing nonrigidity of open contractible manifolds.
method Construction of infinitely many pairwise nonhomeomorphic smooth open contractible manifolds.
result Existence of infinitely many pairwise nonhomeomorphic smooth open contractible manifolds with same proper homotopy type.

Study detects a specific type of link using annular Khovanov homology.

problem Detecting a specific type of three-strand weaving link.
method Combines braid detection with rigidity theorem to determine (σ1σ21)N(σ_1σ_2^{-1})^N up to conjugacy.
result Annular Khovanov homology detects the underlying unoriented annular link KNK_N.

The paper characterizes simple closed curves on surfaces using profinite rigidity.

problem Characterizing simple closed curves on surfaces using profinite rigidity.
method Proving that elements with the same images under all finite groups are simple closed curves.
result The set of simple closed curves is closed in the profinite topology of the surface group.

The pants graph of a non-orientable surface is quasi-isometric to its Teichmüller space.

problem Understanding the relationship between pants graphs and Teichmüller spaces of non-orientable surfaces.
method Constructing a map between pants graphs induced by lifting pants decompositions and proving quasi-isometric embeddings.
result The pants graph of a non-orientable surface is quasi-isometric to its Teichmüller space.

Statistical ML

latest 9

A new method combines simple binary classifiers to build complex multiclass classifiers, achieving performance limits in a Gaussian setting.

problem Building a sophisticated multiclass classifier from simple binary decisions.
method Combining O(logK)O(\log K) simple binary classifiers to form a KK-class classifier.
result Explicit performance bounds across various decoding and dimensional regimes for a stylized Gaussian setting.

A new algorithm improves posterior sampling for linear inverse problems.

problem Efficiently sampling from posterior distributions in noisy linear inverse problems.
method Proposes \pddim, a DDIM-type sampler that separately samples along singular directions of the measurement operator.
result The method converges to the Bayesian posterior conditioned on the measurements.

New PINNs method improves accuracy in computing Mean Escape Time from bounded domains.

problem Computing Mean Escape Time from bounded domains with high accuracy.
method Boundary-adapted Physics-Informed Neural Networks (PINNs) with exact Dirichlet boundary enforcement.
result Derivation of H2(Ω)H^2(Ω) a priori error bounds for PINNs with normalized distance approximations.

Study compares different scoring rules for machine-learned weather forecasts, finding scale-awareness improves forecast realism.

problem Improving the accuracy of machine-learned probabilistic weather forecasts.
method Comparison of scoring rules (CRPS, fair global energy score, graph energy score) and analysis of their impact on forecast field spectra.
result Scale-awareness improves forecast realism, particularly in the tropics.

Deep learning predicts adhesive forces in soft viscoelastic contacts quickly and accurately.

problem Predicting the full time-resolved force trajectory of adhesive soft viscoelastic contacts is computationally expensive and impractical.
method Trained a deep learning model to predict the full force evolution from a prescribed displacement history, using FMS representation and various architectures.
result Best-performing model predicts complete force trajectory with low error metrics and fast inference time.

The paper optimizes regret using covariance between costs and decisions.

problem Optimizing expected regret in decision-making problems.
method Developed derivative theory of covariance regret functional, derived Gâteaux derivative, and extended to constrained optimization.
result Gradient of covariance regret is the cost covariance matrix, with implications for portfolio optimization.

Paper uses algebraic signatures to identify probabilistic structures in empirical data.

problem Identifying probabilistic structure from observed binomials in empirical probability tensors.
method Treating vanishing binomials as algebraic signatures, matching signatures to identify models without parameter estimation.
result The method successfully identified rank-one structures in real language data, revealing interpretable sets of words.

Quant Finance

latest 9

Quantum GBS boosts asset clustering for robust statistical arbitrage portfolios.

problem Identifying co-moving assets from correlation matrices for statistical arbitrage.
method Mapping S&P 500 correlation data to GBS-compatible adjacency matrices, benchmarking classical and quantum clustering algorithms.
result Quantum GBS generates superior alpha during high volatility periods, persisting under low-loss conditions.

DSPM models control noise volatility, improving financial data analysis.

problem Financial returns exhibit volatility clustering, challenging traditional models.
method DSPM uses a tempered-stable subordinator to control noise volatility, preserving kurtosis and autocorrelation.
result DSPM models accurately capture volatility clustering and noise mechanisms.

The paper models Gasoil options using Brent benchmarks, improving volatility estimation.

problem Inability to directly model illiquid Gasoil options market.
method Jointly models Brent and Gasoil futures prices with a correlated Bachelier model, estimating volatility spread.
result The proposed framework accurately maps Brent implied volatilities to Gasoil implied volatilities.

OMD monitors stock market dynamics through matrix trajectories, revealing crisis patterns and sector rotations.

problem Understanding and predicting stock market dynamics during crises.
method Applying OMD to S&P 500 returns over three crises, analyzing distance matrices and their spectra.
result Market dynamics show coherent changes during crises, with sector-specific patterns and volatility clustering.

The study compares parametric and nonparametric models for estimating mean-variance mixtures and finds that nonparametric models perform better.

problem Estimating the distribution of a normal mean-variance mixture under uncertainty.
method Comparison of six parametric mixing laws with a grid nonparametric maximum likelihood estimator, using a paired block bootstrap for score comparison.
result Nonparametric models outperform parametric models in estimating the distribution of a normal mean-variance mixture.

Develops portfolio theory without probabilistic analysis, focusing on pathwise decomposition.

problem Ensuring market viability without probabilistic assumptions.
method Uses pathwise decomposition and trend extractors to replace semimartingale decomposition.
result Growth-numéraire and viability equivalences are similar but not identical in pathwise setting.

Firms miscount their customers who stop buying without saying goodbye.

problem Counting non-contractual customers accurately.
method Estimating repeat purchase probabilities and extrapolating to infinite time.
result The count of alive customers is only partially identified, with a wide range of estimates.