GENTLE+DÉCOLLAGE

Category: moucka

  • Symmetric Poisson geometry, totally geodesic foliations and Jacobi-Jordan algebras

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    Paper by F. Moučka and R. Rubio. Abstract: We introduce symmetric Poisson structures as pairs consisting of a symmetric bivector field and a torsion-free connection satisfying an integrability condition analogous to that in usual Poisson geometry. Equivalent conditions in Poisson geometry have inequivalent analogues in symmetric Poisson geometry and we distinguish between symmetric and strong…

  • Beyond Poisson geometry: when a bivector field is symmetric

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    8-12 September. Talk by Filip Moučka at Differential Geometry and its Applications, Brno (Czech Republic). Abstract: Poisson geometry is a well-established field of mathematics concerned with skew-symmetric bivector fields obeying a specific integrability condition, however, much less is known about their symmetric counterparts. In this talk, I will introduce symmetric Poisson structures: symmetric bivector fields…

  • Symmetric Poisson structures and where to find them

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    24-30 August. Talk by Filip Moučka at the Student Colloquium and School on Mathematical Physics, Stará Lesná (Slovakia). Abstract: I will introduce symmetric Poisson structures: symmetric bivector fields satisfying a specific integrability condition. I will explain how this new framework extends (pseudo-)Riemannian geometry and show the geometric interpretation of symmetric Poisson structures. I will illustrate…

  • Symmetric Poisson geometry, poster

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    30 Jun 2025. Poster by Filip Moučka at the conference Interactions of Poisson Geometry, Lie Theory and Symmetry.

  • 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…