Poisson Geometry, Lie Groupoids and Differentiable Stacks (22w5035)


(University of Illinois at Urbana-Champaign)

Henrique Bursztyn (Instituto Nacional de Matemática Pura e Aplicada)

Jiang-Hua Lu (The University of Hong Kong)

(McGill University)


The Banff International Research Station will host the "Poisson Geometry, Lie Groupoids and Differentiable Stacks" workshop in Banff from June 5 - 10, 2022.

Poisson Geometry lies at the intersection of Mathematical Physics and Geometry. It originates in the mathematical formulation of classical mechanics as the semiclassical limit of quantum mechanics. Although the field has a long history, tracing back to the 19th century classics by Poisson, Hamilton, Jacobi and Lie, modern Poisson Geometry was developed in the last 40 years and is anchored on a multitude of connections with a large number of areas in mathematics and mathematical physics, including differential geometry and Lie theory, quantization, noncommutative geometry, representation theory, geometric mechanics and integrable systems. One of the landmarks of the modern era is Kontsevich's formality yielding that every Poisson manifold admits a deformation quantization. The discovery of quantum groups in the 1980s also led to a rich class of examples of Poisson manifolds related to Lie theory.

The theory of Lie groupoids on the other hand was launched in the 1950's, through work of Ehresmann on differential equations. It has since entered many areas of mathematics and physics, such as algebraic geometry, foliation theory, index theory, gauge theory, exterior differential systems and geometric mechanics. Just as Lie groups arise as the symmetries of objects, Lie groupoids arise as the symmetries of continuous families of objects.

The two theories came together in late 80's in the pioneer work of Karasev and Weinstein, who understood that Lie algebroids are special kind of Poisson manifolds and that Poisson manifolds, in general, give rise to symplectic Lie groupoids. In the last 5 years there have been fascinating new applications, such as the work on shifted symplectic geometry and derived stacks which aims at establishing the deformation quantization (after Kontsevich) of derived stacks. This workshop will bring together leading junior and senior researchers working on Poisson Geometry, Lie groupoids and differentiable stacks, to explore and discuss the most recent progress in the fields and to promote cross-fertilization.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).