Results 1 to 10 of about 2,055,605 (307)
On the Relationship Between Differential Algebra and Tropical Differential Algebraic Geometry [PDF]
, 2021 This paper presents the relationship between differential algebra and tropical differential algebraic geometry, mostly focusing on the existence problem of formal power series solutions for systems of polynomial ODE and PDE. Moreover, it improves an approximation theorem involved in the proof of the fundamental theorem of tropical differential ...
Boulier, François +3 more
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Trends in Differential Geometry and Algebraic Topology
AxiomsWith this Editorial, we present a Special Issue of Axioms entitled “Trends in Differential Geometry and Algebraic Topology [...]
Byungdo Park
doaj +2 more sources
Completeness in partial differential algebraic geometry
Journal of Algebra, 2014 This paper studies various aspects of complete differential algebraic varieties. The setting is the following, introduced by Kolchin. If \(F\) is a field of characteristic \(0\) equipped with \(m\) commuting derivations, then one has the notion of \textit{differential algebraic varieties} over \(F\). For simplicity, we fix a \textit{universal domain} \(
James Freitag
exaly +2 more sources
Algebraic geometry and local differential geometry [PDF]
Annales Scientifiques De L'Ecole Normale Superieure, 1979 Griffiths, Phillip, Harris, Joseph
exaly +2 more sources
Differential Bundles in Commutative Algebra and Algebraic Geometry
Theory and Applications of Categories, 2023 In this paper, we explain how the abstract notion of a differential bundle in a tangent category provides a new way of thinking about the category of modules over a commutative ring and its opposite category. MacAdam previously showed that differential bundles in the tangent category of smooth manifolds are precisely smooth vector bundles.
Cruttwell, G. S. H. +1 more
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Algebraic branch points at all loop orders from positive kinematics and wall crossing
Journal of High Energy Physics, 2021 There is a remarkable connection between the boundary structure of the positive kinematic region and branch points of integrated amplitudes in planar N $$ \mathcal{N} $$ = 4 SYM.
Aidan Herderschee
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Cyclic spacetimes through singularity scattering maps. The laws of quiescent bounces
Journal of High Energy Physics, 2022 For spacetimes containing quiescent singularity hypersurfaces we propose a general notion of junction conditions based on a prescribed singularity scattering map, as we call it, and we introduce the notion of a cyclic spacetime (also called a multiverse)
Bruno Le Floch +2 more
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Differential algebras in non-commutative geometry [PDF]
Journal of Geometry and Physics, 1995 We discuss the differential algebras used in Connes' approach to Yang-Mills theories with spontaneous symmetry breaking. These differential algebras generated by algebras of the form functions $\otimes$ matrix are shown to be skew tensorproducts of differential forms with a specific matrix algebra.
Kalau, W. +3 more
openaire +2 more sources
Tropical fans, scattering equations and amplitudes
Journal of High Energy Physics, 2021 We describe a family of tropical fans related to Grassmannian cluster algebras. These fans are related to the kinematic space of massless scattering processes in a number of ways.
James Drummond +3 more
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Generalising G2 geometry: involutivity, moment maps and moduli
Journal of High Energy Physics, 2021 We analyse the geometry of generic Minkowski N $$ \mathcal{N} $$ = 1, D = 4 flux compactifications in string theory, the default backgrounds for string model building. In M-theory they are the natural string theoretic extensions of G2 holonomy manifolds.
Anthony Ashmore +3 more
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