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.
The paper tackles isotropy of symplectic forms using Hodge flows.
New GPs model edge functions on complex networks, capturing divergence and curl.
Researchers compute de Rham cohomology of geodesic flow foliations on hyperbolic surfaces.
We consider maps between Riemannian manifolds in which the map is a stationary point of the nonlinear Hodge energy. The variational equations of this functional form a quasilinear, nondiagonal, nonuniformly elliptic system which models certain kinds of compressible flow. Conditions are found under which singular sets o…
We compute the sum of the positive Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow. The computation is based on the analytic Riemann-Roch Theorem and uses a comparison of determinants of flat and hyperbolic Laplacians when the underlying Riemann surface degenerates.
Method detects trajectory outliers using Hodge Laplacian embeddings.
The Hodge star mean curvature flow on a 3-dimension Riemannian or pseudo-Riemannian manifold, the geometric Airy flow on a Riemannian manifold, the Schrodingier flow on Hermitian manifolds, and the shape operator curve flow on submanifolds are natural non-linear dispersive curve flows in geometric analysis. A curve flo…
In this paper we study the heat equation (of Hodge-Laplacian) deformation of -forms on a Kähler manifold. After identifying the condition and establishing that the positivity of a -form solution is preserved under such an invariant condition we prove the sharp differential Harnack (in the sense of Li-Ya…
This paper explores vortices and harmonic flows on compact surfaces, using Hodge decomposition.
A new method splits surface flow discretizations into streamfunctions and harmonic fields.
We propose a number of techniques for obtaining a global ranking from data that may be incomplete and imbalanced -- characteristics almost universal to modern datasets coming from e-commerce and internet applications. We are primarily interested in score or rating-based cardinal data. From raw ranking data, we construc…
Study examines money flow network among firms' accounts in a Japanese region.
Proves spectral gap bounds for Teichmüller geodesics on flat surfaces.
The paper studies Hodge structures on contact manifolds and their cohomology.
Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We s…
Study reveals structure of Bitcoin's crypto flow network.
New proofs of Cheeger-like inequalities for coexact 1-forms on hyperbolic manifolds.
The Hodge star mean curvature flow on a 3-dimensional Riemannian or pseudo-Riemannian manifold is a natural nonlinear dispersive curve flow in geometric analysis. A curve flow is integrable if the local differential invariants of a solution to the curve flow evolve according to a soliton equation. In this paper, we sho…
The paper shows that certain geometric structures remain unchanged under specific twists.
Decomposes financial networks to reveal cause-effect hierarchies during crises.
Let F be a riemannian flow on a closed manifold M. We study the behavior of the first eigenvalues of the Hodge Laplacian acting on differential forms under adiabatic collapsing of the flow. We show that the number of small eigenvalues is related to the basic cohomology of F, and give spectral criteria for the vanishing…
The basic Dolbeault cohomology groups of a Sasakian manifold M are invariants of its characteristic foliation F (the orbit foliation of the Reeb flow). We show some fundamental properties of this cohomology, which are useful for its computation. In the first part of the article, we show that the basic Hodge numbers, th…
Proves compact Cauchy horizons have constant surface gravity under null energy condition.
A kinematic method selects the deformation Laplacian for fluid dynamics on Riemannian manifolds.
The paper proves wave operator existence and completeness for Hodge Laplacians.
Determinants remain constant along specific families of differential operators.
Study on -structures using Laplacian coflow and solitons.
A leafwise Hodge decomposition was proved by Sanguiao for Riemannian foliations of bounded geometry. Its proof is explained again in terms of our study of bounded geometry for Riemannian foliations. It is used to associate smoothing operators to foliated flows, and describe their Schwartz kernels. All of this is extend…
Proves Hodge structures on modular functors, providing formulas for Hodge numbers.
We give hodge structures on quasitoric orbifolds. We define orbifold hodge numbers and show a correspondence of orbifold hodge numbers for crepant resolutions of quasitoric orbifolds. In short we extend hodge structures to a non complex setting .
The paper studies topological properties of Ricci shrinkers using weighted cohomology.
Study on Hodge theory for almost complex manifolds.
It has been shown that for each Killing-Yano (KY)-form accepted by an -dimensional (pseudo)Riemannian manifold of arbitrary signature, two basic gravitational currents can be defined. Conservation of the currents are explicitly proved by showing co-exactness of the one and co-closedness of the other. Some general ge…
We determine the structure of the Hodge ring, a natural object encoding the Hodge numbers of all compact Kaehler manifolds. As a consequence of this structure, there are no unexpected relations among the Hodge numbers, and no essential differences between the Hodge numbers of smooth complex projective varieties and tho…
We refine the Morgan's work on mixed Hodge structures on Sullivan's --minimal models by using non-abelian Hodge theory. As an application, we give explicit representatives of real unipotent variations of mixed Hodge structures over compact K"ahler manifolds.
On a smooth, compact and oriented manifold without boundary, we give a complete description of the correlation function of a Morse-Smale gradient flow satisfying a certain nonresonance assumption. This is done by analyzing precisely the spectrum of the generator of such a flow acting on certain anisotropic spaces of cu…
Novel Hodge theory developed for Carrollian bundles, addressing black hole event horizons.
We derive a numerical method for Darcy flow, hence also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedr…
Geometric model for Hodge filtered complex cobordism constructed.
Introduces a new Hodge theory using vector fields on manifolds.
Resolves conjectures on non-abelian Hodge loci for quasi-projective varieties.
Proves a tropical version of Clemens-Schmid sequence for tropical varieties.
We give a way of constructing real variations of mixed Hodge structures over compact Kähler manifolds by using mixed Hodge structures on Sullivan's -minimal models of certain differential graded algebras associated with real variations of Hodge structures.
Discretizes Hodge-Dirac operators on a torus.
Paper introduces magnetic Hodge Laplacian for differential forms.
For any positive integer m and any dimension n, we show that any n-dimensional Hodge diamond with values in Z/mZ is attained by the Hodge numbers of an n-dimensional smooth complex projective variety. As a corollary, there are no polynomial relations among the Hodge numbers of n-dimensional smooth complex projective va…
The paper proves formulas and theorems for statistical de Rham Hodge operators on manifolds with boundary.
Hodge theory applied to tropical curves.