Differentiable Stacks, Poisson Geometry and related geometric structures

Contribution List

1. Minicourse on stacks in algebraic geometry vs differential geometry - session 1

Pavel Safranov

07/02/2022, 09:00

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.

3. m-shifted symplectic Lie groupoids

Miquel Cueca

07/02/2022, 11:20

4. Diffeological groupoids and their Lie algebroids

Christian Blohmann

07/02/2022, 17:00

5. Lie groupoid cohomology relative to a Lie subgroupoid

Maria Amelia Salazar

07/02/2022, 17:50

6. Minicourse on stacks in algebraic geometry vs differential geometry - session 2

Pavel Safranov

08/02/2022, 09:00

7. Lie groupoids and differential equations

Francis Bischoff

08/02/2022, 10:00

8. Deformations of symplectic foliations

Marco Zambon

08/02/2022, 11:20

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...

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.

11. Weil algebras for double Lie algebroids

Eckhard Meinrenken

09/02/2022, 09:00

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...

13. Poisson structures from corners of field theories

Alberto Cattaneo

10/02/2022, 09:00

14. Quantization and integrability

Alejandro Cabrera

10/02/2022, 10:00

15. The Fukaya category of the log symplectic sphere

Charlotte Kirchhoff-Lukat

10/02/2022, 11:20

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...

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.

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...

19. Symplectic gerbes or symplectic foliations

Marius Crainic

11/02/2022, 11:20