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.
Lecture notes introduce differential geometry using sheaves and differential operators.
Studies projective geometry and partial differential equations prolongation.
A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra)…
Explains curves and surfaces in differential geometry.
Quaternionic differential geometry expands geometric concepts using quaternions.
PINNs solve differential geometry problems in complex shapes.
These notes introduce key techniques in differential geometry for curves and surfaces.
Lecture notes on geodesics in differential geometry.
In our previous paper entitled "Axiomatic differential geometry -towards model categories of differential geometry-, we have given a category-theoretic framework of differential geometry. As the first part of our series of papers concerned with differential-geometric developments within the above axiomatic scheme, this…
Developed a theory of ultradifferentiable sheafs with applications.
Survey of geometry developments, including complex structures on surfaces.
Study surfaces with constant ratio of principal curvatures in Euclidean and isotropic geometries.
Introduces tractors for basic examples and modern differential calculus.
In this paper is proposed a kind of model theory for our axiomatic differential geometry. It is claimed that smooth manifolds, which have occupied the center stage in differential geometry, should be replaced by functors on the category of Weil algebras. Our model theory is geometrically natural and conceptually motiva…
Extends differential geometry concepts to manifolds with super tangent bundles.
Diffeology extends differential geometry to complex spaces.
The study sets limits on the complexity of Klein geometries.
The paper explores quaternionic curves using differential geometry.
Parametric Cartan theory of exterior differential systems, and explicit cohomology of projective manifolds reveal united rationality features of differential algebraic geometry.
We study the fundamental properties of curvature in groupoids within the framework of synthetic differential geometry. As is usual in synthetic differential geometry, its combinatorial nature is emphasized. In particular, the classical Bianchi identity is deduced from its combinatorial one.
Global homotopies upgrade classical map in differential geometry.
Projective geometry aids in analyzing fields near compact manifolds.
Segre embedding was introduced by C. Segre (1863--1924) in his famous 1891 article \cite{segre}. The Segre embedding plays an important roles in algebraic geometry as well as in differential geometry, mathematical physics, and coding theory. In this article, we survey main results on Segre embedding in differential geo…
In this paper, as the second in our series of papers on differential geometry of microlinear Frolicher spaces, we study differenital forms. The principal result is that the exterior differentiation is uniquely determined geometrically, just as grad (ient), div (ergence) and rot (ation) are uniquely determined geometric…
Explains Cartan geometries for graduate students.
Formalizes synthetic differential geometry in Lean.
Groupoids provide a more appropriate framework for differential geometry than principal bundles. Synthetic differential geometry is the avant-garde branch of differential geometry, in which nilpotent infinitesimals are available in abundance. The principal objective in this paper is to show within our favorite framewor…
We give a brief review of a research made in the field of differential geometry in Estonia in the period from the beginning of the 19th century to the present time. The biographic data of mathematicians who made a valuable contribution to the development of differential geometry in Estonia in mentioned period are prese…
The paper uses complex-valued functions to simplify plane differential geometry and kinematics.
We give an abstract formulation of the formal theory partial differential equations (PDEs) in synthetic differential geometry, one that would seamlessly generalize the traditional theory to a range of enhanced contexts, such as super-geometry, higher (stacky) differential geometry, or even a combination of both. A moti…
Algebraic geometry replaces manifolds in differential geometry.
Review of metallic Riemannian geometry advances.
The relation between differential geometry of surfaces and some Heisenberg ferromagnet models is considered.
Symmetry-breaking in three differential geometry conjectures.
A connection between differential geometry and soliton equations is discussed
Some differential equations are considered in the context of Synthetic Differential Geometry. Here, this means that not only nilpotent infinitesimals, but also the formation of function spaces, is exploited. In particular, we utilize distribution spaces in our study of wave and heat equations.
Advances M-polyfolds for complex geometry applications.
Criteria for smoothness of ambiskew polynomial rings.
Explains conformal symmetry with examples in geometry and analysis.
Introduces non-regular spacetime geometry without smooth calculus.
This book is a textbook for the basic course of differential geometry. It is recommended as an introductory material for this subject.
Proof confirms preservation of projective limits in synthetic differential geometry.
The field of multiple view geometry has seen tremendous progress in reconstruction and calibration due to methods for extracting reliable point features and key developments in projective geometry. Point features, however, are not available in certain applications and result in unstructured point cloud reconstructions.…
Quantum complexity lowerbound proved using differential geometry.
Survey talk on certain aspects of the subject, stressing the neighbor relation as a basic notion in differential geometry.
We discuss in some generality aspects of noncommutative differential geometry associated with reality conditions and with differential calculi. We then describe the differential calculus based on derivations as generalization of vector fields, and we show its relations with quantum mechanics. Finally we formulate a gen…
String backgrounds and D-branes do not possess the structure of Lorentzian manifolds, but that of manifolds with area metric. Area metric geometry is a true generalization of metric geometry, which in particular may accommodate a B-field. While an area metric does not determine a connection, we identify the appropriate…
The paper examines smoothness in diffusion algebra.