GENTLE+DÉCOLLAGE

Category: rubio

  • 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…

  • Flat Generalized Connections on Courant Algebroids

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    Paper by G. Cavalcanti, J. Pedregal and R. Rubio. To appear in Selecta Math. New Ser. Abstract: We consider a family of metric generalized connections on transitive Courant algebroids, which includes the canonical Levi-Civita connection, and study the flatness condition. We find that the building blocks for such flat transitive Courant algebroids are compact simple…

  • 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…

  • 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…

  • New local invariants in generalized complex geometry

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    31 Jan 2025. Talk by Roberto Rubio at the conference BCN-Face(t)s in SG, UPC, Barcelona. Abstract: After recalling some classical geometric structures, I will review generalized complex geometry for even-dimensional manifolds and introduce its extension to manifolds of any dimension, known as Bn-generalized complex geometry. Then, I will focus on the case of 3-manifolds and…

  • Local invariants in generalized complex geometry

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    26 Nov 2024. Talk by Roberto Rubio at the meeting of the Spanish Network of Geometry and Physics, ICMAT (Madrid). Abstract: I will first review generalized complex geometry for even-dimensional manifolds and introduce its extension to manifolds of any dimension, known as Bn-generalized complex geometry. Then, I will focus on the case of 3-manifolds and…

  • New geometric structures on 3-manifolds: surgery and generalized geometry

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    7 Oct 2024. Talk by Roberto Rubio at the LIGAT-UAB Geometry seminar. Abstract: I will first give an introduction to standard generalized complex geometry, which encompasses complex and symplectic structures. I will then describe how a variant of generalized complex geometry can reach odd-dimensional manifolds and finish by describing recent results on 3-manifolds that are…