GENTLE

Category: rubio

  • 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…

  • Local invariants in generalized complex geometry

    —

    in ,

    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

    —

    in ,

    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…

  • On the Equivalence of Generalized Ricci Curvatures

    —

    in , ,

    Paper by G. Cavalcanti, J. Pedregal and R. Rubio. Abstract: We prove the equivalence between the several notions of generalized Ricci curvature found in the literature. As an application, we characterize when the total generalized Ricci tensor is symmetric. Find it on the arXiv (2406.06695). To appear in Proc. Amer. Math. Soc.

  • Generalized geometric structures and invariants on 3-manifolds

    —

    in ,

    16 Jul 2024. Talk by Roberto Rubio at the Poisson Days at Trieste 2024 (SISSA). Abstract: Complex and symplectic manifolds are, in particular, generalized complex manifolds, a class that supersedes them: there exist neither complex nor symplectic manifolds that are generalized complex. This happens very tightly, as generalized complex manifolds must be almost complex (and…

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

    —

    in ,

    Paper by J. Porti and R. Rubio. Abstract: Cosymplectic and normal almost contact structures are analogues of symplectic and complex structures that can be defined on 3-manifolds. Their existence imposes strong topological constraints. Generalized geometry offers a natural common generalization of these two structures: B3-generalized complex structures. We prove that any closed orientable 3-manifold admits…

  • Generalized metrics: slice theorem and moduli space

    —

    in ,

    21 Feb 2024. Talk by Roberto Rubio at Mathematical Supergravity 2024. Abstract: Generalized geometry is a recent approach to geometric structures with the ability of uniting, for instance, complex and symplectic geometry. Many concepts, like diffeomorphism or metric, have their generalized counterpart, and some of them have found applications within mathematics and theoretical physics. In…