GENTLE

Category: talks

  • 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…

  • 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…

  • Curvature and Holonomy in Generalized Geometry

    —

    in ,

    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

    —

    in ,

    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

    —

    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…

  • Cn-generalized complex geometry

    —

    in ,

    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

    —

    in ,

    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…