GENTLE+DÉCOLLAGE

Category: talks

  • 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

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    11 Aug 2025. Talk by Roberto Rubio at the Workshop on Poisson Geometry and Related Topics, Beijing, China. Abstract: I will introduce symmetric Poisson geometry, the study of symmetric bivector fields on a manifold. I will first discuss the integrability condition, then move to their geometric and dynamical interpretation, and finally discuss some interesting examples. This…

  • Obstructions to the existence of a Dirac complement, poster

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    3 Jul 2025. Poster by Tom Ariel at the conference Interactions of Poisson Geometry, Lie Theory and Symmetry.

  • 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.

  • Beyond generalized complex geometry

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    8 May 2025. Talk by Roberto Rubio at the UIUC Symplectic and Poisson geometry seminar. Abstract: Generalized complex geometry encompasses complex and symplectic structures. I will start by recalling this by using just differential forms. Other geometric structures, such as cosymplectic or almost contact, involve or can be reformulated also in terms of differential forms.…

  • Differential forms as a unifying force for geometric structures

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    24 Apr 2025. Talk by Roberto Rubio at the UB Topology seminar. Abstract: Many geometric structures such as symplectic, complex, cosymplectic, almost contact… involve or can be reformulated using differential forms. First, I will describe how generalized complex geometry uses this fact to encompass complex and symplectic geometry and show how much further it can…

  • Beyond the canonical symmetric pairing in generalized geometry

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    9 Apr 2025. Talk by Roberto Rubio at the IMPA Symplectic geometry seminar. Abstract: The canonical symmetric pairing on TM+T*M is key to Dirac structures and generalized complex geometry. Not only is it used to define lagrangian subbundles, but also is at the core of the Clifford module structure, from which the Dorfman bracket can…

  • Differential forms as a unifying force for geometric structures

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    8 Apr 2025. Talk by Roberto Rubio at the IMPA Differential Geometry seminar. Abstract: Many geometric structures such as symplectic, complex, cosymplectic, almost contact… involve or can be reformulated using differential forms. First, I will describe how generalized complex geometry uses this fact to encompass complex and symplectic geometry and show how much further it…

  • On higher Dirac structures

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    20 Mar 2025. Talk by Roberto Rubio at the Gamma seminar. Abstract: Dirac structures are the least common multiple of (pre)symplectic and Poisson structures. What about an analogous concept for multi(pre)symplectic and higher Poisson structures? The answer should clearly bear the name of higher Dirac, but we will see that its definition is not so…