GENTLE

Category: seminar

  • What is the h-principle and how may it be relevant to generalized geometry?, by Á. del Pino

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    17 Dec 2024. 14:00 CET. Talk by Álvaro del Pino. Abstract: The h-principle is the subfield of Differential Topology dedicated to the classification problem for geometric structures on manifolds, up to homotopy. Statements in h-principle are often of the form: “The space of structures of type X is weakly homotopy equivalent to some other space…

  • Graded geometry and generalized geometry, by R. Mehta

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    19 Nov 2024, 14:30 CET (note the time change). Talk by Rajan Mehta. Abstract: I’ll give an overview of graded geometry and explain how various structures that fall under the umbrella of “generalized geometry” (such as Lie algebroids, Poisson manifolds, Jacobi manifolds, Courant algebroids, and generalized complex manifolds) can be viewed as graded geometric objects.…

  • 25 years since the letters to Weinstein, by P. Ševera

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    22 Oct 2024, 14:00 CET. Talk by Pavol Ševera. Abstract: I will talk about the original motivations and dreams that lead to these infamous letters (which are known mainly for the introduction and classification of exact Courant algebroids) and about some of the related developments in generalized geometry, higher structures and physics that happened at…

  • Some aspects of L-infinity algebras in geometry, by K. Singh

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    18 Jul 2024, 11:00 CET. Talk by Karandeep Singh. Abstract: L-infinity algebras were introduced by Lada and Stasheff in the 90s as strongly homotopy Lie algebras, and are a generalization of Lie algebras, where the structure equations are only required to hold up to coherent homotopy. After giving the relevant definitions, I will give some…

  • Geodesic invariance and the symmetric product: mechanics, control theory, and geometry, by A. Lewis

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    18 Jun 2024 (Tuesday). 14:00 CET. Talk by A. Lewis. Note the unusual day and time. Abstract: The property of geodesic invariance of a distribution on a manifold with an affine connection is that for which geodesics with initial tangent vectors in the distribution are such that all subsequent tangent vectors are in the distribution.…

  • Generalized connections, spinors, and integrability of generalized structures on Courant algebroids, by V. Cortés

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    8 May 2024 (Wednesday), 12:30 CET. Talk by V. Cortés. Note the unusual day and time. Abstract: I will discuss various geometric structures on Courant algebroids in terms of generalized connections, spinors and Dirac generating operators. The talk is based on joint work with Liana David.

  • What is… the torsion of a connection? And why we should care, by I. Agricola

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    11 Apr 2024, 11h CET. Talk by I. Agricola. Abstract: Following the seminal work of Elie Cartan, I will summarise the concept of torsion of a metric connection and the most important properties; in particular, we will meet the three basic types of metric connections with torsion and what singles out the skew symmetric case.…

  • Holomorphic divergences, by M. García-Fernández

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    21 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…

  • Courant cohomology, Cartan calculus, connections, curvature, characteristic classes, by M. Cueca

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    7 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…

  • Riemannian geometry on Courant algebroids, by F. Moučka

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    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…