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Differential Graded Models for Local Rings (Commutative Algebra and Algebraic Geometry)

Differential Graded Models for Local Rings (Commutative Algebra and Algebraic Geometry)
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Differential geometry of Hom-Lie algebras and Hom-Lie algebroids

Quaestiones Mathematicae, 2023
In this paper, the geometry of Hom-Lie algebras and Hom-Lie algebroids are studied. In this direction, the effects of connections on Hom-Lie algebras and Hom-Lie algebroids are first investigated. By finding the relations among hom-curvature operator, torsion and  connection on Hom-Lie algebras, Bianchi-like identities for hom-curvature operator ...
Şahin, B., Şahin, F.
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Numerical Algebraic Geometry and Differential Equations

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, Andrew J. Sommese
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Topological algebras and abstract differential geometry

Journal of Mathematical Sciences, 1999
The notions of connection and curvature on principal sheaves, with structural sheaf the sheaf of groups \({\mathcal G}{\mathcal L}(n, {\mathcal A})\), are studied where \({\mathcal A}\) is a sheaf of unital, commutative and associative algebras. Suitable topological algebras provide concrete models of principal sheaves for which an abstract Frobenius ...
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Current Algebras, the Sugawara Model, and Differential Geometry

Journal of Mathematical Physics, 1970
The Lie algebra defined by the currents in the Sugawara model is defined in a way that is natural from the point of view of Lie transformation theory and differential geometry. Previous remarks that the Sugawara model is associated with a field-theoretical dynamical system on a Lie group manifold are made more precise and presented in a differential ...
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Complex Geometry: Interactions between Algebraic, Differential, and Symplectic Geometry

2001
[no abstract available]
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Algebraic and Differential Geometry in Modern Optimization

2023
Stochastic optimization algorithms have become indispensable in modern machine learning. The developments of theories and algorithms of modern optimization also requires the application of tools from different methematical branches, such as algebraic and differential geometry.
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Homology, Cohomology, and Sheaf Cohomology for Algebraic Topology, Algebraic Geometry, and Differential Geometry

2021
Jean Gallier, Jocelyn Quaintance
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