GENTLE+DÉCOLLAGE

Category: rubio

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

    —

    in , ,

    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…

  • Symmetric Poisson geometry

    —

    in ,

    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…

  • Beyond generalized complex geometry

    —

    in ,

    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

    —

    in ,

    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

    —

    in ,

    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

    —

    in , ,

    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

    —

    in ,

    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

    —

    in ,

    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

    —

    in , ,

    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

    —

    in ,

    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…