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We will go through an overview of some more or less recent constructions from geometry: generalized (algebroids and Dirac structures) and graded (Q-manifolds and equivariant cohomology). We will see how they are related to each other and to classical concepts (symplectic and Poisson structures). We will also consider some “applications” for physics (sigma models) and mechanics (geometric formulation and discretization problems).

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Generalized Geometry in Relation to Physics and Mechanics

  • 会议论文

  • 发表日期：

    2025年

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  • Vladimir Salnikov

摘要

We will go through an overview of some more or less recent constructions from geometry: generalized (algebroids and Dirac structures) and graded (Q-manifolds and equivariant cohomology). We will see how they are related to each other and to classical concepts (symplectic and Poisson structures). We will also consider some “applications” for physics (sigma models) and mechanics (geometric formulation and discretization problems).