Category: rubio
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On higher Dirac structures
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…
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Symmetric Cartan calculus, the Patterson-Walker metric and Killing vector fields
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 derivative…
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New local invariants in generalized complex geometry
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…
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Local invariants in generalized complex geometry
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…
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New geometric structures on 3-manifolds: surgery and generalized geometry
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…
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On the Equivalence of Generalized Ricci Curvatures
Paper by G. Cavalcanti, J. Pedregal and R. Rubio. Proc. Amer. Math. Soc. 153 (2025), no. 6, 2639–2648. 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 also on the arXiv (2406.06695).
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Generalized geometric structures and invariants on 3-manifolds
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…
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New geometric structures on 3-manifolds: surgery and generalized geometry
Paper by J. Porti and R. Rubio. To appear in Advances in Mathematics. 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…
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Generalized metrics: slice theorem and moduli space
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…
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An introduction to generalized geometry, by R. Rubio
1 Feb 2024, 11h CET. Talk by Roberto Rubio. Abstract: We give an introduction to generalized geometry having in mind the several objectives of GENTLE.