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Category: talks

  • 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…

  • Curvature and Holonomy in Generalized Geometry

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    26 Feb 2025. Talk by Jaime Pedregal at the ICMAT Geometry seminar. Abstract: Curvature in generalized geometry has proven to be an elusive concept admitting several different approaches, each one with its own advantages and disadvantages. Furthermore, the concept of holonomy for generalized connections is, so far, missing from the theory, partly because any sensible…

  • A gentle introduction to holonomy and generalized geometry

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    25 Feb 2025. Talk by Jaime Pedregal at the University of Castilla La Mancha. Abstract: The concept of connection in differential geometry is a way to coherently answer questions such as “What is a constant vector field on a manifold?” or “What is the acceleration of a curve on a manifold?” The holonomy group is…

  • 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…

  • Cn-generalized complex geometry

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    24 Jan 2024. Talk by Filip Moučka at the 45th Winter School Geometry and Physics, Srni (Czech Republic). Abstract: The vector bundle TM+T*M comes equipped with a canonical symmetric pairing, which is a fundamental object when introducing standard generalized geometry. However, there is also an equally canonical skew-symmetric pairing, which motivates the introduction of Cn-generalized…

  • A Gentle Introduction to Generalized Riemannian Geometry

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    14 Jan 2025. Talk by Jaime Pedregal at the RSME’s 7th Congress of Young Researchers, Bilbao. Abstract: Generalized geometry has proven to be a powerful unifying framework for different geometries such as complex, symplectic, Poisson and the like. The theory of generalized metrics has led to further links to other geometries, e.g. bihermitian geometry, which…

  • 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…

  • Cn-generalized complex geometry

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    26 Nov 2024. Talk by Filip Moučka at the meeting of the Spanish Network of Geometry and Physics, ICMAT (Madrid). Abstract: The vector bundle TM+T^*M comes equipped with a canonical symmetric pairing, which is a fundamental object when introducing standard generalized geometry. However, there is also an equally canonical skew-symmetric pairing, which motivates the introduction…

  • 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…