Category: seminar
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Holomorphic divergences, by M. García-Fernández
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in 2023/202421 Mar 2024, 11h CET. Talk by M. García-Fernández. Abstract: A smooth divergence on a Courant algebroid E is a differential operator from sections of E to functions on the base manifold, satisfying a natural Leibniz rule with respect to the anchor map. Divergence operators keep track of the ‘conformal geometry’ of the Courant algebroid…
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Courant cohomology, Cartan calculus, connections, curvature, characteristic classes, by M. Cueca
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in 2023/20247 Mar 2024, 11h CET. Talk by M. Cueca. Abstract: It is known that Courant algebroids are in correspondence with degree 2 symplectic dg-manifolds. The standard cochain complex of a Courant algebroid is, by definition, the complex consisting of functions on the corresponding dg-manifold. This definition has been difficult to work with directly, due to…
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Riemannian geometry on Courant algebroids, by F. Moučka
29 Feb 2024, 11h CET. Talk by Filip Moučka. Abstract: We introduce analogues of well known concepts from Riemannian geometry, such as metric, connection, torsion, Levi-Civita connection and curvature in the framework of a general Courant algebroid. We illustrate the usefulness of this theory in theoretical physics by introducing an analogue of the Palatini action…
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An introduction to generalized geometry, by R. Rubio
1 Feb 2024, 11h CET. Talk by Roberto Rubio. Abstract: We give an introduction to generalized geometry having in mind the several objectives of GENTLE.
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Skew-symmetry in generalized geometry II, by F. Moučka
Generalized diffeomorphisms, ∇-Courant algebroids, symmetric Poisson structures and other brackets.
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The space of Dirac structures and the complement problem, by T. Ariel
Introduction to generalized metrics, Dirac structures and their integrability in terms of orthogonal transformations, the complement problem.
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Connections and holonomy, by J. Pedregal
Introduction to connections, Ambrose-Singer theorem, Riemannian holonomy and Simon’s holonomy theorem.