Category: talks
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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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Lie algebroid holonomy
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…
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Symmetric Poisson geometry
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…
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Generalized geometry through Clifford algebra glasses
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…
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Symmetric Poisson geometry
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.…
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Symmetric Cartan calculus, poster
2 Nov 2023. Poster by Filip Moučka at the Barcelona Mathematical Days 2023.
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Symmetric Cartan calculus, symmetric Poisson geometry, and Cn-generalized geometry
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…
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Cartan calculus on symmetric algebra.
7 Sep 23. Talk by Filip Moučka at the Training School on Cartan Geometry, Brno. Abstract: Cartan calculus on the space of symmetric tensor fields will be introduced. First, we find a certain analogue of the exterior derivative. Then we will define analogues of the Lie derivative and the Lie bracket of vector fields in…
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New geometric structures on 3-manifolds through generalized geometry
7 Sep 2023. Talk by Roberto Rubio at the Thematic section DGGA Differential Geometry and Geometric Analysis of the Spanish+Polish mathematical meeting. Abstract: https://es-pl.math.uni.lodz.pl/sessions_PDF/DGGA.pdf