GENTLE+DÉCOLLAGE

Category: moucka

  • A symmetric cousin of Poisson geometry

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    23 Mar 2026. Talk by Filip Moučka at Poisson Geometry and its relatives: a thematic day at CRM, Barcelona. Abstract: Poisson geometry is a natural extension of symplectic geometry that encodes Hamiltonian dynamics, Lie algebras, and singular foliations via skew-symmetric bivector fields. In this talk, I will explore a symmetric counterpart of this framework by…

  • The Patterson-Walker metric

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    26 Jan 2026. Talk by Filip Moučka at the 34th Student conference: Winter School on Mathematical Physics in Jánské Lázně, Czech Republic. Abstract: Replacing the minus sign in the canonical Poisson bracket by the plus sign yields a commutative bracket that nevertheless allows one to formulate Newton’s equations for conservative systems in close analogy with…

  • Courant algebroid lifts and curved Courant algebroids

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    19 Jan 2026. Talk by Filip Moučka at the 46th Winter school on geometry and physics, Srní, Czech Republic. Abstract: Given a Courant algebroid on a bundle of the form TM+E, we describe a natural construction of a pairing, an anchor, and a bracket on TE using a vector bundle connection on E. In general,…

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

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    25 Nov 2025. Talk by Filip Moučka at the Quantum Universe Attract.Workshop, Hamburg. 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…

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

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    16 Sep 2024. Poster by Filip Moučka at the meeting of the Spanish Network of Geometry and Physics, Barcelona. 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…

  • 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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    25 Aug 2025. 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…

  • 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…