6 February 2022 - 11 February 2022
Henrique Bursztyn (IMPA), Rui Loja Fernandes (University of Illinois), Marco Gualtieri (University of Toronto), Jiang-Hua Lu (University of Hong-Kong). Event page & registration
Recent days have seen a rapid developments on shifted Poisson and symplectic structures on (derived) differentiable or algebraic stacks. A differentiable stack is, roughly speaking, a Lie groupoid up to Morita equivalence, and the stack represented by a symplectic groupoid of a Poisson manifold naturally has a 1- shifted symplectic structure. There have also been remarkable recent advances in other geometries, such as Dirac geometry and generalized complex geometry, that generalize Poisson geometry and have Lie groupoids and Lie algebroids at their cores. Many basic concepts and constructions in these geometries can be rephrased using the language of differential stacks, and such reformulations put these geometric structures in vastly new perspectives and establish further connections with other fields of mathematics such as algebraic geometry, deformation theory and high category theory.
We propose a workshop with at most 40 participants, centered at Differentiable stacks, Poisson geometry and Lie groupoids, but also covering other related geometrical structures. More concretely, we propose to cover the following specific topics.
- Integrations of Poisson and Dirac structures
- Generalized complex geometry and mirror symmetry
- Multiplicative structures on Lie groupoids and stacks
- Shifted symplectic geometry
- Higher Lie groupoids and higher gauge theory
We plan to organize the workshop around these five different topics, each day devoted to a main theme. Each day will start with a keynote lecture by a top researcher in the field, followed by a problem session run by a junior researcher. The afternoon sessions will be a mix of talks by by senior researchers and some of the most promising young researchers in these fields. Senior speakers will be asked to focus mostly on open problems and to discuss major research directions.
SwissMAP Research Station, Les Diablerets, Switzerland