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Category: moucka

  • Symmetric Cartan calculus, the Patterson-Walker metric and symmetric cohomology

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    Paper by F. Moučka and R. Rubio. Abstract: We develop symmetric Cartan calculus, an analogue of classical Cartan calculus for symmetric differential forms. We first show that the analogue of the exterior derivative, the symmetric derivative, is not unique and its different choices are parametrized by torsion-free affine connections. We use a choice of symmetric…

  • Cn-generalized complex geometry

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    24 Jan 2024. Talk by Filip Moučka at the 45th Winter School Geometry and Physics, Srni (Czech Republic). Abstract: The vector bundle TM+T*M comes equipped with a canonical symmetric pairing, which is a fundamental object when introducing standard generalized geometry. However, there is also an equally canonical skew-symmetric pairing, which motivates the introduction of Cn-generalized…

  • Cn-generalized complex geometry

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    26 Nov 2024. Talk by Filip Moučka at the meeting of the Spanish Network of Geometry and Physics, ICMAT (Madrid). Abstract: The vector bundle TM+T^*M comes equipped with a canonical symmetric pairing, which is a fundamental object when introducing standard generalized geometry. However, there is also an equally canonical skew-symmetric pairing, which motivates the introduction…

  • Generalized geometry with skew-symmetric pairing

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    29 Aug 2024. Talk by Filip Moučka at the Student Colloquium and School on Mathematical Physics, Stará Lesná (Slovakia). Abstract: Generalized geometry is the study of the geometry of T+T* with the canonical symmetric pairing and the Dorfman bracket. If instead of the symmetric pairing one considers the skew-symmetric pairing, the Dorfman bracket is no…

  • Generalized geometry with skew-symmetric pairing, poster

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    8 July 2024. Poster by Filip Moučka at the Poisson conference 2024, Napoli. Abstract: Generalized geometry is the study of the geometry of T+T* with the canonical symmetric pairing and the Dorfman bracket. If instead of symmetric pairing one considers the skew-symmetric pairing, the Dorfman bracket is no longer suitable. We introduce a new bracket…

  • Riemannian geometry on Courant algebroids, by F. Moučka

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    29 Feb 2024, 11h CET. Talk by Filip Moučka. Abstract: We introduce analogues of well known concepts from Riemannian geometry, such as metric, connection, torsion, Levi-Civita connection and curvature in the framework of a general Courant algebroid. We illustrate the usefulness of this theory in theoretical physics by introducing an analogue of the Palatini action…

  • Symmetric Poisson geometry

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    26 Jan 2024. Talk by Filip Moučka at the 32nd Winter School on Mathematical Physics, Jánské Lázně, Czech Republic. Abstract: A Poisson manifold is a generalization of the notion of phase space from Hamiltonian mechanics. It is a manifold endowed with a skew-symmetric bivector field such that the Schouten bracket of the bivector field with itself…

  • Symmetric Poisson geometry

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    18 Jan 2024. Talk by Filip Moučka at the 44th Winter School Geometry and Physics, Srni, Czech Republic. Abstract: A Poisson manifold is a generalization of the notion of phase space from Hamiltonian mechanics. It is a manifold endowed with a skew-symmetric bivector field such that the Schouten bracket of the bivector field with itself vanishes.…

  • Symmetric Cartan calculus, poster

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    2 Nov 2023. Poster by Filip Moučka at the Barcelona Mathematical Days 2023.

  • Symmetric Cartan calculus, symmetric Poisson geometry, and Cn-generalized geometry

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    31 Oct 2023. Talk by Filip Moučka at the Geometry Seminar (LIGAT), UAB. Abstract: We introduce analogues of the exterior derivative, the Lie derivative, and the Lie bracket of vector fields, on the algebra of completely symmetric covariant tensor fields. Then we discuss the basic properties and geometrical interpretation of these objects. Using the correspondence…