GENTLE

Category: talks

  • 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…

  • Generalized metrics: slice theorem and moduli space

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    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…

  • Lie algebroid holonomy

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    5 Feb 2024. Talk by Jaime Pedregal at the LIGAT Geometry Seminar, UAB. Abstract: Lie algebroids can be considered as “adapted tangent bundles” for specific geometric situations. As such, it makes sense to consider Lie algebroid connections and Lie algebroid holonomy. In this talk, after a very brief recap of classical holonomy, we will introduce…

  • Symmetric Poisson geometry

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    26 Jan 2024. Talk by Filip Moučka at the 32nd Winter School on Mathematical Physics, Jánské Lázně, Czech Republic. Abstract: A Poisson manifold is a generalization of the notion of phase space from Hamiltonian mechanics. It is a manifold endowed with a skew-symmetric bivector field such that the Schouten bracket of the bivector field with itself…

  • Generalized geometry through Clifford algebra glasses

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    25 Jan 2024. Talk by Roberto Rubio at the Cable Car Algebra Seminar (Technion-UHaifa), University of Haifa. Abstract: Generalized geometry is a recent approach to geometric structures encompassing symplectic and complex geometry. At its heart lies a Clifford module, which is essentially a global version of the spin representation of the Clifford algebra. In this…

  • Symmetric Poisson geometry

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    18 Jan 2024. Talk by Filip Moučka at the 44th Winter School Geometry and Physics, Srni, Czech Republic. Abstract: A Poisson manifold is a generalization of the notion of phase space from Hamiltonian mechanics. It is a manifold endowed with a skew-symmetric bivector field such that the Schouten bracket of the bivector field with itself vanishes.…

  • Symmetric Cartan calculus, poster

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    2 Nov 2023. Poster by Filip Moučka at the Barcelona Mathematical Days 2023.

  • Symmetric Cartan calculus, symmetric Poisson geometry, and Cn-generalized geometry

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    31 Oct 2023. Talk by Filip Moučka at the Geometry Seminar (LIGAT), UAB. Abstract: We introduce analogues of the exterior derivative, the Lie derivative, and the Lie bracket of vector fields, on the algebra of completely symmetric covariant tensor fields. Then we discuss the basic properties and geometrical interpretation of these objects. Using the correspondence…