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.
Study connects derivations and holonomy symmetries in heterotic geometries.
Derived geometry can be defined as the universal way to adjoin finite homotopical limits to a given category of manifolds compatibly with products and glueing. The point of this paper is to show that a construction closely resembling existing approaches to derived geometry in fact produces a geometry with this universa…
We explain how to translate several recent results in derived algebraic geometry to derived differential geometry. These concern shifted Poisson structures on NQ-manifolds, Lie groupoids, smooth stacks and derived generalisations, and include existence and classification of various deformation quantisations.
Researchers redefine spinor field derivatives in generalized geometry.
Perturbative string amplitudes are correctly derived from the string geometry theory, which is one of the candidates of a non-perturbative formulation of string theory. In order to derive non-perturbative effects rather easily, we formulate topological string geometry theory. We derive the perturbative partition functi…
Develops derived differential geometry for supermanifolds.
Foundations of derived geometry in smooth settings.
Introduces a new geometric framework for non-perturbative BV-theory.
New theory proves representability of PDE solutions without complex machinery.
Study of nonlinear PDEs using derived geometry and BV formalism.
New geometries derived from symplectic Monge-Ampère structures.
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.…
Recently Berman and Perry constructed a four-dimensional M-theory effective action which manifests SL(5) U-duality. Here we propose an underlying differential geometry of it, under the name `SL(5) U-geometry' which generalizes the ordinary Riemannian geometry in an SL(5) compatible manner. We introduce a `semi-covarian…
Study moduli spaces of elliptic PDEs using derived -geometry.
Simpler method derived for path geometries on surfaces, characterizing projective path geometries.
Enhances conformal geometry in higher dimensions with infinite-dimensional algebra.
Derives path-integrals for superstrings on curved backgrounds using string geometry theory.
Derives Levi-Civita connection formulas for specific geometries.
Develops Riemannian geometry for optimization on manifolds with detailed derivations.
Study improves understanding of solutions to complex equations in geometry.
Develops derived differential geometry theory.
The study sets limits on the complexity of Klein geometries.
Extends illumination bodies to non-Euclidean spaces and proves their volume derivative defines surface area.
Study derived Lie ∞-groupoids and algebroids in higher differential geometry.
This is a survey of the author's book "D-manifolds and d-orbifolds: a theory of derived differential geometry", available at http://people.maths.ox.ac.uk/~joyce/dmanifolds.html We introduce a 2-category dMan of "d-manifolds", new geometric objects which are 'derived' smooth manifolds, in the sense of the 'derived algeb…
The goal of this paper is to encode equivalently the fractional Lagrange dynamics as a nonholonomic almost Kahler geometry. We use the fractional Caputo derivative generalized for nontrivial nonlinear connections (N-connections) originally introduced in Finsler geometry, with further developments in Lagrange and Hamilt…
This is a long summary of the author's book "D-manifolds and d-orbifolds: a theory of derived differential geometry", available at http://people.maths.ox.ac.uk/~joyce/dmanifolds.html . A shorter survey paper on the book, focussing on d-manifolds without boundary, is arXiv:1206.4207, and readers just wanting a general o…
This paper proves equivalence between derived manifolds and differential graded manifolds.
Extends differential geometry concepts to manifolds with super tangent bundles.
Curved loxodromes on spheres are explained and their ODE derived.
Derives path integrals for perturbative strings on various backgrounds.
Derives localization formulas in Batalin-Vilkovisky formalism.
Our purpose is to use a Darboux homogenous derivative to understand the harmonic maps with values in homogeneous space. We present a characterization of these harmonic maps from the geometry of homogeneous space. Furthermore, our work covers all type of invariant geometry in homogeneous space.
It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwe…
UMAP connects to Information Geometry principles.
Introduces new connections in higher geometry.
After defining generalizations of the notions of covariant derivatives and geodesics from Riemannian geometry for reductive Cartan geometries in general, various results for reductive Cartan geometries analogous to important elementary results from Riemannian geometry are proven using these generalizations. In particul…
Normality equations describe Newtonian dynamical systems admitting normal shift of hypersurfaces. These equations were first derived in Euclidean geometry. Then very soon they were rederived in Riemannian and in Finslerian geometry. Recently I have found that normality equations can be derived in geometry given by clas…
The paper generalizes Cartan Geometry using Polacek and Siegel's approach.
We show that, locally, all geometric objects of Generalized Kahler Geometry can be derived from a function K, the "generalized Kahler potential''. The metric g and two-form B are determined as nonlinear functions of second derivatives of K. These nonlinearities are shown to arise via a quotient construction from an aux…
We develop a universal framework to study smooth higher orbifolds on the one hand and higher Deligne-Mumford stacks (as well as their derived and spectral variants) on the other, and use this framework to obtain a completely categorical description of which stacks arise as the functor of points of such objects. We choo…
We exploit the spinor description of four-dimensional Walker geometry, and conformal rescalings of such, to describe the local geometry of four-dimensional neutral geometries with algebraically degenerate self-dual Weyl curvature and an integrable distribution of alpha-planes (algebraically special real alpha-geometry)…
A new Lagrangian formulation of the Raychaudhuri equation in non-Riemannian geometry.
It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian dynamical system in a manifold, one can consider it as geometric equipment of this manif…
The -exterior derivative , which is the Finslerian generalization of the (usual) exterior derivative of Riemannian geometry, is defined. The notion of a -closed vector field is introduced and investigated. Various characterizations of -closed vector fields are established. Some results concerning $ød…
We study the classification of special almost hermitian manifolds in Gray and Hervella's type classes. We prove that the exterior derivatives of the symplectic form and the complex volume form contain all the information about the intrinsic torsion of the $\SUn(n)$-structure. Furthermore, we apply the obtained results …
This work is based on the talk delivered at Poisson 2008. We review the recent advances in Generalized Kahler geometry while stressing the use of Poisson and symplectic geometry. The derivation of the generalized Kahler potential is sketched and the relevant global issues are discussed.
We introduce a method in differential geometry to study the derivative operators of Siegel modular forms. By determining the coefficients of the invariant Levi-Civita connection on a Siegel upper half plane, and further by calculating the expressions of the differential forms under this connection, we get a non-holomor…