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 constructs new structures for manifolds using connections and combinations.
We describe arbitrary multiplicative differential forms on Lie groupoids infinitesimally, i.e., in terms of Lie algebroid data. This description is based on the study of linear differential forms on Lie algebroids and encompasses many known integration results related to Poisson geometry. We also revisit multiplicative…
Extends Infinitesimal Jackknife for model covariance, enhancing ensemble model analysis.
Local formulas integrate multiplicative forms on Lie groupoids.
In this work, we study Lie groupoids equipped with multiplicative foliations and the corresponding infinitesimal data. We determine the infinitesimal counterpart of a multiplicative foliation in terms of its core and sides together with a partial connection satisfying special properties, giving rise to the concept of I…
Paper develops a novel approach for optimal control using kernel methods.
The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of geometric symmetry of a linearly singular differential equation is introduced as a trans…
The construction (by Kapranov) of the space of infinitesimal paths on a manifold is extended to include higher dimensional infinitesimal objects, encoding contractions of infinitesimal loops. This full infinitesimal groupoid is shown to have the algebra of polyvector fields as its non-linear cohomology.
Study on bending knots and energy changes in 3D space.
In this paper, we establish an infinitesimal equivariant index formula in the noncommutative geometry framework using Greiner's approach to heat kernel asymptotics. An infinitesimal equivariant index formula for odd dimensional manifolds is also given. We define infinitesimal equivariant eta cochains, prove their regul…
Cauchy used infinitesimals in differential geometry and integral geometry.
Metric spaces with certain curvature properties are universally infinitesimally Hilbertian.
Weiss and, independently, Mazzeo and Montcouquiol recently proved that a 3--dimensional hyperbolic cone-manifold (possibly with vertices) with all cone angles less than is infinitesimally rigid. On the other hand, Casson provided 1998 an example of an infinitesimally flexible cone-manifold with some of the cone an…
VB-groupoids can be thought of as vector bundle objects in the category of Lie groupoids. Just as Lie algebroids are the infinitesimal counterparts of Lie groupoids, VB-algebroids correspond to the infinitesimal version of VB-groupoids. In this work we address the problem of the existence of a VB-groupoid admitting a g…
In this paper, we prove that infinitesimal equivariant Chern-Connes characters are well-defined. We decompose an equivariant index as a pairing of infinitesimal equivariant Chern-Connes characters with the Chern character of an idempotent matrix. We compute the limit of infinitesimal equivariant Chern- Connes character…
Paper generalizes connections between Lie groups and affine connections.
Deformation theory for holomorphic Cartan geometries studied.
Ancient formula connects volume forms and infinitesimal square volumes in manifolds.
New examples of rigid Lie foliations with dense leaves found.
The paper tests hypotheses on two Lévy process-driven streams of observations.
Lie algebroids are like infinitesimal Lie groupoids.
New classification of hypersurfaces with conformal variations.
Using standard analysis only, we present an extension of the real field containing nilpotent infinitesimals. On the one hand we want to present a very simple setting to formalize infinitesimal methods in Differential Geometry, Analysis and Physics. On the other hand we want to show that these infinitesim…
We study infinitesimal conformal deformations of a triangulated surface in Euclidean space and investigate the change in its extrinsic geometry. A deformation of vertices is conformal if it preserves length cross-ratios. On one hand, conformal deformations generalize deformations preserving edge lengths. On the other h…
In category theory, logic and geometry cooperate with each other producing what is known under the name Synthetic Differential Geometry (SDG). The main difference between SDG and standard differential geometry is that the intuitionistic logic of SDG enforces the existence of infinitesimal objects which essentially modi…
We study infinitesimal Einstein deformations on compact flat manifolds and on product manifolds. Moreover, we prove refinements of results by Koiso and Bourguignon which yield obstructions on the existence of infinitesimal Einstein deformations under certain curvature conditions.
The paper presents a method for detecting jump sizes in crude oil prices.
The paper studies infinitesimal variations of submanifolds in Euclidean space.
We study tensors on Lie groupoids suitably compatible with the groupoid structure, called {\em multiplicative}. Our main result gives a complete description of these objects only in terms of infinitesimal data. Special cases include the infinitesimal counterparts of multiplicative forms, multivector fields and holomorp…
New method discovers symmetries in differential equations from data.
Study of Teichmüller space geometry using infinitesimal and global methods.
In this paper, an obstruction against the integrability of certain infinitesimal solitonic deformations is given. Using this obstruction, we show that the complex projective spaces of even complex dimension are rigid as Ricci solitons although they have infinitesimal solitonic deformations.
Study Poisson algebras for Hamiltonian systems linearization.
In this paper we study infinitesimal and finite flexibility for generic semidiscrete surfaces. We prove that generic 2-ribbon semidiscrete surfaces have one degree of infinitesimal and finite flexibility. In particular we write down a system of differential equations describing isometric deformations in the case of exi…
Study of infinitesimal rigidity in hyperbolic manifolds.
Novel framework for learning infinitesimal generator of stochastic processes.
The paper proposes a method to compute higher infinitesimals in numerical and symbolic analysis.
Conditions are given under which an infinitesimal automorphism of a torsion-free connection preserving a symplectic form is necessarily a symplectic vector field. An example is given of a compact symplectic manifold admitting a flat symplectic connection and an infinitesimal automorphism that is not symplectic.
New method classifies hypersurfaces that can bend infinitesimally.
Develops second order infinitesimal structures on Teichmüller space.
A local description of the non-flat infinitesimally bendable Euclidean hypersurfaces was recently given by Dajczer and Vlachos \cite{DaVl}. From their classification, it follows that there is an abundance of infinitesimally bendable hypersurfaces that are not isometrically bendable. In this paper we consider the case o…
Continuous Lorentzian metrics yield infinitesimal Minkowskian spacetimes.
Study variational properties of cone structures with infinitesimal symmetry.
We study non-flat planar 3-webs with infinitesimal symmetries. Using multi-dimensional Schwarzian derivative we give a criterion for linearization of such webs and present a projective classification thereof. Using this classification we show that the Gronwall conjecture is true for 3-webs admitting infinitesimal symme…
Study infinitesimally tight Lagrangian orbits in symplectic manifolds.
A new method for approximating CV and bootstrap with higher-order infinitesimal jackknife.
The study examines non-continuous Riemannian metrics on manifolds and their infinitesimal properties.
The paper extends Noether's theorem to contact systems, finding dissipated quantities instead of conserved ones.