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

• Pavel Safranov

What is a Poisson structure on a différentiable stack?

• Camille Laurent-Gengoux

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.

m-shifted symplectic Lie groupoids

• Miquel Cueca

Diffeological groupoids and their Lie algebroids

• Christian Blohmann

Lie groupoid cohomology relative to a Lie subgroupoid

• Maria Amelia Salazar

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

• Pavel Safranov

Lie groupoids and differential equations

• Francis Bischoff

Deformations of symplectic foliations

• Marco Zambon

Dirac reduction and shifted symplectic geometry

• Maxence Mayrand

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 symplectic geometry. This is joint work with Ana Balibanu and Peter Crooks.

Classification of stacky vector bundles

• Matias del Hoyo

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.

Weil algebras for double Lie algebroids

• Eckhard Meinrenken

Differentiation of Lie n-groupoids

• Chenchang Zhu

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 explicit differentiation, and reach the tangent complex with a Lie n-algebroid structure. This is a joint work with Du Li, Rui Fernandes, Leonid Ryvkin and Arne Wessel.

Poisson structures from corners of field theories

• Alberto Cattaneo

Quantization and integrability

• Alejandro Cabrera

The Fukaya category of the log symplectic sphere

• Charlotte Kirchhoff-Lukat

Some remarks on Lagrangian intersections in the algebraic case (Joint talk with Global Poisson Webminar)

• Kai Behrend

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 made on a better understanding of the origin of these structures, and some related conjectures have been proved. We will explain some of these results. This is a joint talk with Global Poisson Webminar

The linear model around Poisson submanifolds.

• Ioan Marcut

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.

Compatibility of Nijenhuis operators with various structures

• Thiago Drummond

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 sense with Courant algebroids leads to a (not fully understood yet) relation with Kähler geometry.

Symplectic gerbes or symplectic foliations

• Marius Crainic