Norms on curves on surfaces classify Birkhoff cross sections.
problem Classifying Birkhoff cross sections on surfaces.
method Defining norms on homology groups and interpreting integer points.
result Integer points in dual unit balls classify isotopy classes of Birkhoff cross sections.
New method constructs Birkhoff sections for pseudo-Anosov flows with controlled complexity.
problem Constructing Birkhoff sections for pseudo-Anosov flows with specific properties.
method Uses connection between pseudo-Anosov flows and veering triangulations to explicitly construct sections with controlled complexity.
result Shows that any transitive pseudo-Anosov flow has a Birkhoff section with two boundary components.
The abstract proves that certain Reeb vector fields on 3-manifolds have Birkhoff sections.
problem Existence of Birkhoff sections for Reeb vector fields on 3-manifolds.
method Showed existence of Birkhoff sections for Reeb vector fields satisfying Kupka-Smale condition.
result Reeb vector fields on closed 3-manifolds with Kupka-Smale condition admit Birkhoff sections.
Geodesic flow on orbifolds has a genus 1 Birkhoff section.
problem Existence of Birkhoff sections for geodesic flows on orbifolds.
method Proved existence of a genus 1 Birkhoff section for geodesic flow on a specific class of 2-orbifolds.
result Geodesic flow on a 2-orbifold admits a Birkhoff section of genus 1.
Shows Anosov flows with genus one sections, supporting a conjecture.
problem Finding genus one Birkhoff sections for Anosov flows.
method Utilizes horizontal Goodman surgery operation and correspondence with veering triangulations.
result Provides evidence for Fried and Ghys conjecture.
The paper shows how different geodesic flows on surfaces can be mapped to each other.
problem Comparing pseudo-Anosov maps from various Birkhoff sections of a geodesic flow.
method Identifying canonical surfaces and expressing first-return maps as compositions of Dehn twists.
result First-return maps from different Birkhoff sections are equivalent and can be expressed using a fixed set of Dehn twists.
Paper shows how to transform certain flows into R-covered ones.
problem Transforming Anosov flows into R-covered ones.
method Goodman-Fried surgery along periodic points.
result Any topologically transitive Anosov flow can be transformed into an R-covered one.
We prove that the geodesic flow on the unit tangent bundle to every hyperbolic 2-orbifold that is a sphere with 3 or 4 singular points admits explicit genus one Birkhoff sections, and we determine the associated first return maps.
The study finds sufficient conditions for Reeb flows to have genus zero global surfaces of section.
problem Finding conditions for Reeb flows to have genus zero global surfaces of section.
method Analyzes linking assumptions on periodic orbits and ambient contact geometry.
result Reveals sufficient conditions for Reeb flows to have genus zero global surfaces of section.
New results on geodesic flows using curve shortening flow.
problem Stability and existence of geodesics in Riemannian surfaces.
method Curve shortening flow approach.
result Existence of infinitely many geodesics intersecting a given one in every primitive class.
Proof that certain Anosov flows are almost equivalent.
problem Proving equivalence of suspension Anosov flows.
method Constructing a genus-one Birkhoff section and analyzing its first-return map.
result Explicit bounds on distances between suspension Anosov flows.
New global section found for geodesic flows on convex hypersurfaces.
problem Finding global sections for geodesic flows on convex hypersurfaces.
method Constructing a global hypersurface of section with an isometric involution.
result Generalized Birkhoff annulus to higher dimensions.
This paper proves integrability of Birkhoff billiards inside convex cones.
problem Proving integrability of Birkhoff billiards in non-traditional shapes.
method Analyzing the billiard inside a convex cone, proving integrability using a first integral of degree two.
result The Birkhoff billiard inside a convex C3 cone is integrable. New method shows pseudo-Anosov flows on graph manifolds can be simplified.
problem Understanding pseudo-Anosov flows on graph manifolds.
method Constructing a partial Birkhoff section with genus one components that misses finitely many closed orbits.
result Every pseudo-Anosov flow on a graph manifold is almost equivalent to a totally periodic flow or a suspension Anosov flow.
The paper proves the existence of surfaces of section for geodesic flows on closed surfaces.
problem Existence of surfaces of section for geodesic flows on closed surfaces.
method Study of configurations of simple closed geodesics and use of the curve shortening flow.
result Construction of surfaces of section that intersect or have hyperbolic components in their boundary.
Survey of integrable billiard models and inequalities.
problem Understanding integrable billiard dynamics.
method Analysis of various billiard models.
result Isoperimetric inequality for Mather β-function.
Explains historical connections between vector bundle splitting and Riemann-Hilbert problems.
problem Vector bundle splitting over the Riemann sphere.
method Historical overview and connections to other mathematical problems.
result Explains the Riemann-Hilbert-Birkhoff problems and their relation to vector bundle splitting.
The paper explores curvature types of surfaces in normed spaces.
problem Investigating curvature types of surfaces in normed spaces.
method Defining curvature types using a normal vector field and eigenvalues of the differential of the Gauss map.
result A compact surface with constant Minkowski Gaussian curvature is a Minkowski sphere.
Study shows nontrivial links as cross-sections of unknotted holomorphic disks.
problem Resolving parts of Kirby's list problem about nontrivial links.
method Using unknotted holomorphic disks in the four-ball to produce cross-sections.
result Many nontrivial links arise as cross-sections of unknotted holomorphic disks.
The study explores infinitesimal automorphisms of principal bundles and their implications.
problem Understanding infinitesimal automorphisms of principal bundles.
method Review of vector fields in complex-analytic setting, rationality results, and extension of Birkhoff-Grothendieck theorem.
result Conditions for rationality of complex manifolds and existence of Lie subgroups in principal bundles.
New dynamical system for convex curves solves integrable billiards conjecture.
problem Algebraic Birkhoff conjecture on integrable billiards.
method Introducing Angular billiard system.
result New results on algebraic Birkhoff conjecture.
Study polynomial integrals for Birkhoff billiards on spheres and hyperbolic planes.
problem Existence of polynomial integrals for Birkhoff billiards.
method Extension of S. Bolotin's method and use of Angular billiard.
result New obstructions on polynomial integrability.
The paper defines cross-section continuity for angular momentum definitions and finds the CWY definition valid.
problem Defining angular momentum at null infinity and ensuring its continuity across different cross-sections.
method Introducing cross-section continuity as a criterion and proving it for specific angular momentum definitions.
result The Chen-Wang-Yau definition of angular momentum satisfies cross-section continuity, while the Compere-Nichols modification does not.
The study identifies flat manifolds with unique cusp cross-sections in arithmetic hyperbolic manifolds.
problem Characterizing flat manifolds that have unique cusp cross-sections in arithmetic hyperbolic manifolds.
method Algebraic characterization of cusp cross-sections in arithmetic hyperbolic manifolds.
result Construction of flat manifolds with unique cusp cross-sections and proof of their existence in all dimensions n≥32. New algorithm improves asset ranking for better cross-sectional portfolios.
problem Sub-optimal ranking of assets in cross-sectional systematic strategies.
method Learning-to-rank algorithms to enhance portfolio construction.
result Modern machine learning ranking algorithms boost Sharpe Ratios by approximately threefold.
Set-Sequence model learns cross-sectional dynamics directly from time series data.
problem Predicting large cross-sections of time series data with latent cross-sectional dynamics.
method A model that learns cross-sectional structure directly, enhancing expressivity and eliminating manual feature engineering.
result Significantly outperforms strong baselines in equity portfolio optimization and loan risk prediction.
Conditions for flat manifolds as cusp cross-sections in arithmetic hyperbolic manifolds.
problem Determining when a flat manifold can be a cusp cross-section in arithmetic hyperbolic manifolds.
method Analyzing rational representations of holonomy groups and quasi-arithmetic manifolds.
result Conditions for a flat manifold to appear as a cusp cross-section in every commensurability class of arithmetic hyperbolic manifolds.
TQA improves prediction intervals for time series data by adjusting quantiles for both cross-sectional and longitudinal coverage.
problem Constructing reliable prediction intervals for cross-sectional time series data.
method Temporal Quantile Adjustment (TQA) method that adjusts the quantile in Conformal Prediction to account for both cross-sectional and longitudinal coverage.
result TQA improves longitudinal coverage while preserving cross-sectional coverage, as validated through extensive experimentation.
Paper proves ellipticity of certain Reeb orbits and estimates ECH spectrum on lens spaces.
problem Proving ellipticity of Reeb orbits in lens spaces and estimating ECH spectrum.
method Using rational self-linking number, Conley-Zehnder index, and ECH computations.
result First ECH spectrum on dynamically convex L(3,1) is estimated and shown to be equal to contact area infimum.
This is an elementary geometrical proof of Birkhoff theorem. It is hardly important, but the pictures behind are quite nice.
We establish that, for every hyperbolic orbifold of type (2, q, ∞) and for every orbifold of type (2, 3, 4g+2), the geodesic flow on the unit tangent bundle is left-handed. This implies that the link formed by every collection of periodic orbits (i) bounds a Birkhoff section for the geodesic flow, and (ii) is a …
The paper evaluates forecast accuracy of realized volatility measures in large cross-sections.
problem Forecast evaluation of realized volatility measures in large cross-sections of financial data.
method Equal predictive accuracy testing procedures, LASSO shrinkage, measurement error correction, cross-sectional jump component measures.
result The augmented HAR model outperforms the standard HAR model in forecasting realized volatility.
CPTD improves prediction intervals in time series regression with cross-sectional data.
problem Constructing valid prediction intervals in time series regression with a cross-section.
method Conformal Prediction with Temporal Dependence (CPTD) for post-hoc, light-weight approach.
result CPTD maintains cross-sectional validity while improving longitudinal coverage.
Unified model learns from both time-series and cross-sectional momentum features.
problem Separate time-series and cross-sectional momentum strategies do not consider concurrent relationships.
method Spatio-Temporal Momentum strategies using neural networks to combine both types of momentum.
result Simple neural network with single fully connected layer generates trading signals for all assets.
Paper finds conditions for finite-dimensional vector spaces of cross-sections.
problem Finite-dimensional vector spaces of cross-sections for holomorphic bundles.
method Analyzes complex vector spaces of holomorphic cross-sections over elliptic orbits.
result Provides a sufficient condition for vector spaces to be finite dimensional.
Study on stability of surfaces in null cones under area-preserving variations.
problem Investigating stability of spacelike cross sections of null cones.
method Area-preserving variations, Hawking energy analysis, spherical cross sections.
result Only round spheres are stable cross sections of the standard Minkowski lightcone.
Proposes Equity2Vec for cross-sectional asset pricing.
problem Sub-optimal performance due to missing cross-sectional effects and heterogeneous data.
method End-to-end deep learning framework with Equity2Vec for graph-based interactions and all alpha sources.
result Outperforms state-of-the-art approaches in real-world stock market datasets.
Model learns aging rates from single cross-sectional data.
problem Cross-sectional data limits traditional time-series methods.
method Latent-variable model with order-isomorphic nonlinear function.
result Reconstructs aging rates from single cross-sectional data.
Motivated by a question of Hirzebruch on the possible topological types of cusp cross-sections of Hilbert modular varieties, we give a necessary and sufficient condition for a manifold M to be diffeomorphic to a cusp cross-section of a Hilbert modular variety. Specialized to Hilbert modular surfaces, this proves that e…
Method constructs discrete surfaces with negative curvature.
problem Creating discrete surfaces with negative Gaussian curvature.
method Birkhoff decomposition and nonlinear d'Alembert formula.
result Simple algorithm for Birkhoff decomposition.
Examines differential smoothness in a specific skew PBW extension family.
problem Differential smoothness in skew PBW extensions.
method Investigates a specific family of skew PBW extensions.
result Results on differential smoothness of the family.
The cross curvature flow preserves negative sectional curvature in 3-manifolds for all time.
problem Preserving negative sectional curvature in 3-manifolds under the cross curvature flow.
method Maximum principle to prove long-time existence of the flow.
result The flow exists for all time and converges to a hyperbolic metric.
Deep learning predicts cross-sectional stock prices for practical investment.
problem Predicting stock prices using cross-sectional factors.
method Deep learning model for daily stock price prediction.
result Profitable investment framework demonstrated in Japanese stock market.
Paper analyzes Birkhoff relaxation for graph alignment, providing theoretical guarantees.
problem Finding vertex correspondence between two graphs to maximize edge overlap.
method Birkhoff relaxation as a convex relaxation of the quadratic assignment problem (QAP).
result Theoretical guarantees on the performance of Birkhoff relaxation under specific conditions.
Paper uses cross-sectional data to estimate VSL, reducing confidence intervals by a factor of 3.
problem Estimating VSL with cross-sectional data using Garen's IV approach.
method Garen's instrumental variable (IV) approach, proxy for risk attitude.
result Confidence intervals reduced by a factor of 3 using proxy.
We use integrable systems techniques to study the singularities of timelike non-minimal constant mean curvature (CMC) surfaces in the Lorentz-Minkowski 3-space. The singularities arise at the boundary of the Birkhoff big cell of the loop group involved. We examine the behaviour of the surfaces at the big cell boundary,…
Classifies Nil 3-manifolds as cross-sections of complex hyperbolic surfaces.
problem Identifying Nil 3-manifolds as cross-sections of complex hyperbolic surfaces.
method Comprehensive classification of commensurability classes of cusped, arithmetic, and non-arithmetic complex hyperbolic 2-manifolds.
result Some Nil 3-manifolds are cross-sections in every commensurability class, while others are cross-sections in only one.
Machine learning portfolios perform well with simple imputation of missing data.
problem Handling missing values in machine learning portfolios constructed from cross-sectional return predictors.
method Simple imputation with cross-sectional means compared to rigorous expectation-maximization methods.
result Simple imputation performs well due to the structure of missing data.