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Numerical Algebraic Geometry and Differential Equations [PDF]

, 2014
In this paper we review applications of numerical algebraic geometry to differential equations. The techniques we address are direct solution, bootstrapping by filtering, and continuation and bifurcation. We review differential equations systems with multiple solutions and bifurcations.
Wenrui Hao, Bei Hu, A. Sommese
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Differential forms in algebraic geometry

, 2011
Before considering more general spaces we shall first discuss (1) the r-dimensional projective space Π r . In this space we shall consider a homogeneous coordinate system (Z0, Z1, ... , Z r ). Let U α be that part of Π r in which Z α ≠ 0. In U α we may then introduce non-homogeneous coordinates zαi = Zι/Zα (ι≠α).
W. Hodge
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Geometry of Differential Polynomial Functions, II: Algebraic Curves

American Journal of Mathematics, 1993
Introduction The present paper is a direct continuation of [B5]; we shall freely borrow terminology and notations from that paper which shall be referred to from now on as Part I.
A. Buium
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Noncommutative differential geometry of matrix algebras

Journal of Mathematical Physics, 1990
The noncommutative differential geometry of the algebra Mn (C) of complex n×n matrices is investigated. The role of the algebra of differential forms is played by the graded differential algebra C(sl(n,C),Mn (C))=Mn (C)⊗Λsl(n,C)*,sl(n,C) acting by inner derivations on Mn (C).
Dubois-Violette, Michel, Kerner, Richard, Madore, John   +2 more
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Differential geometry on Grassmann algebras

Letters in Mathematical Physics, 1976
H. C. Lee [1] developed the analogue of Riemannian geometry on a real symplectic manifold — the fundamental skew two-form taking the place of the symmetric tensor. The usual Riemannian concepts do not adapt themselves very well, thus ‘curvature’ is represented by a tensor of the third rank and ‘Killing's equations’ now involve this ‘curvature tensor ...
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Algebraic geometry of Abel differential equation

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2012
A solution $$y(x)$$ of an Abel differential equation $$(1) \ y^{\prime }=p(x)y^2 + q(x) y^3$$ is called “closed” on
Clara Shikhelman, Y. Yomdin, Y. Shelah, Sh. Giat   +3 more
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Differential Geometry of Quantum States, Observables and Evolution

Quantum Physics and Geometry, 2019
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analysed from this perspective, the relevant ...
Florio M. Ciaglia, Alberto Ibort, G. Marmo   +2 more
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Model Theory with Applications to Algebra and Analysis: Model theory and stability theory, with applications in differential algebra and algebraic geometry

, 2008
This article is based around parts of the tutorial given by E. Bouscaren and A. Pillay at the training workshop at the Isaac Newton Institute, March 29 April 8, 2005. The material is treated in an informal and free-ranging manner.
A. Pillay
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Multiview Differential Geometry of Curves

International Journal of Computer Vision, 2016
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.
R. Fabbri, B. Kimia
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ON THE FOUNDATION OF ALGEBRAIC DIFFERENTIAL GEOMETRY

, 2008
By algebraic differential geometry we shall mean one which is so related to the ordinary algebraic geometry just as what the metric, the affine, or the projective differential geometry is related to the metric, the affine, or the projective geometry.
Wu Wen-tsun
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