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Differentiable Stacks, Poisson Geometry and related geometric structures

6–11 Feb 2022
Europe/Zurich timezone

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Contribution List

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  1. 1. Minicourse on stacks in algebraic geometry vs differential geometry - session 1
    Pavel Safranov
    07/02/2022, 09:00
  2. 2. What is a Poisson structure on a différentiable stack?
    Camille Laurent-Gengoux
    07/02/2022, 10:00

    We will define what a Poisson structure on a differentiable stack is, the latter being seen as an equivalence class of Lie groupoids up to Morita equivalence, and explain why the notion makes sense, as well as those of vector fields and poly vector fields over a differentiable stack. Joint work with Bonechi, Ciccoli and Xu.

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  3. 3. m-shifted symplectic Lie groupoids
    Miquel Cueca
    07/02/2022, 11:20
  4. 4. Diffeological groupoids and their Lie algebroids
    Christian Blohmann
    07/02/2022, 17:00
  5. 5. Lie groupoid cohomology relative to a Lie subgroupoid
    Maria Amelia Salazar
    07/02/2022, 17:50
  6. 6. Minicourse on stacks in algebraic geometry vs differential geometry - session 2
    Pavel Safranov
    08/02/2022, 09:00
  7. 7. Lie groupoids and differential equations
    Francis Bischoff
    08/02/2022, 10:00
  8. 8. Deformations of symplectic foliations
    Marco Zambon
    08/02/2022, 11:20
  9. 9. Dirac reduction and shifted symplectic geometry
    Maxence Mayrand
    08/02/2022, 17:00

    We introduce a notion of reduction of Dirac realizations induced by a submanifold of the base and give an interpretation in shifted symplectic geometry. It yields, in particular, to a notion of symplectic (resp. quasi-Hamiltonian) reduction where the level can be a submanifold of the dual of the Lie algebra (resp. the group) rather than a point, and explains some disparate constructions in...

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  10. 10. Classification of stacky vector bundles
    Matias del Hoyo
    08/02/2022, 18:00

    This is report on a joint project with my student J. Desimoni, where we classify stacky vector bundles by the categorified Grassmanian, the differentiable 2-stack represented by the general linear 2-groupoid.

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  11. 11. Weil algebras for double Lie algebroids
    Eckhard Meinrenken
    09/02/2022, 09:00
  12. 12. Differentiation of Lie n-groupoids
    Chenchang Zhu
    09/02/2022, 10:00

    As a Lie n-groupoid is an atlas for an n-stack in differential geometry, one expects that their differentiation should be the tangent complex of the n-stack carrying a Lie n-algebroid structure. However, an explicit differentiation, like that for Lie groupoid, seems to be missing. Inspired by Severa's idea of an infinitesimal object, we perform (spending a lot of years fixing holes :) an...

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  13. 13. Poisson structures from corners of field theories
    Alberto Cattaneo
    10/02/2022, 09:00
  14. 14. Quantization and integrability
    Alejandro Cabrera
    10/02/2022, 10:00
  15. 15. The Fukaya category of the log symplectic sphere
    Charlotte Kirchhoff-Lukat
    10/02/2022, 11:20
  16. 16. Some remarks on Lagrangian intersections in the algebraic case (Joint talk with Global Poisson Webminar)
    Kai Behrend
    10/02/2022, 17:00

    Some years ago, in joint work with B. Fantechi, we constructed brackets on the higher structure sheaves of Lagrangian intersections, and compatible Batalin-Vilkovisky operators, when certain orientations are chosen (see our contribution to Manin’s 70th birthday festschrift). This lead to a de-Rham type cohomology theory for Lagrangian intersections. In the interim, much progress has been...

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  17. 17. The linear model around Poisson submanifolds.
    Ioan Marcut
    11/02/2022, 09:00

    We built a local model around Poisson submanifolds, which we have shown to generalize Vorbojev's local model around symplectic leaves. A normal form theorem holds in many situations, e.g., Poisson manifolds integrable by proper groupoids, Hamiltonian quotients, etc. This is joint work with Rui Loja Fernandes.

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  18. 18. Compatibility of Nijenhuis operators with various structures
    Thiago Drummond
    11/02/2022, 10:00

    This is a report on recent results involving the compatibility of Nijenhuis operators with various structures (e.g. Poisson groupoids, Dirac Structures, Courant algebroids) by means of an associated connection-like object. An interesting application is the study of holomorphic structures via their underlying real objects. Also, the investigation of Nijenhuis structures compatible in a suitably...

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  19. 19. Symplectic gerbes or symplectic foliations
    Marius Crainic
    11/02/2022, 11:20