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Algebraic and Differential Geometry in Modern Optimization
2023Stochastic 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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Noncommutative geometry with graded differential Lie algebras
Journal of Mathematical Physics, 1997Starting with a Hilbert space endowed with a representation of a unitary Lie algebra and an action of a generalized Dirac operator, we develop a mathematical concept towards gauge field theories. This concept shares common features with the Connes–Lott prescription of noncommutative geometry, differs from that, however, by the implementation of unitary
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Preliminaries on linear algebra and differential geometry
2023Jean-Michel Bismut +2 more
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Fourteen Papers on Algebra, Topology, Algebraic and Differential Geometry
1968V. Kompaniec +14 more
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Finiteness results in differential algebraic geometry and Diophantine geometry
2005openaire +1 more source