GENTLE

Category: talks

  • 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…

  • Generalized geometry with skew-symmetric pairing

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    29 Aug 2024. Talk by Filip Moučka at the Student Colloquium and School on Mathematical Physics, Stará Lesná (Slovakia). Abstract: Generalized geometry is the study of the geometry of T+T* with the canonical symmetric pairing and the Dorfman bracket. If instead of the symmetric pairing one considers the skew-symmetric pairing, the Dorfman bracket is no…

  • Generalized geometric structures and invariants on 3-manifolds

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    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…

  • Generalized geometry with skew-symmetric pairing, poster

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    8 July 2024. Poster by Filip Moučka at the Poisson conference 2024, Napoli. Abstract: Generalized geometry is the study of the geometry of T+T* with the canonical symmetric pairing and the Dorfman bracket. If instead of symmetric pairing one considers the skew-symmetric pairing, the Dorfman bracket is no longer suitable. We introduce a new bracket…

  • New geometric structures on 3-manifolds from generalized geometry

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    13 May 2024. Talk by Roberto Rubio at the Generalized Geometry meets String Theory conference (BIRS-IMAG). Abstract: Generalized complex structures encompass complex and symplectic ones and go beyond them: there are generalized complex manifolds that are neither complex nor symplectic. However, they are only possible on almost complex manifolds, and hence in even dimensions. In…