Geometric Structures on Lie Groupoids (17w5023)


Rui Loja Fernandes (University of Illinois Urbana Champaign)

Henrique Bursztyn (IMPA)

Eckhard Meinrenken (University of Toronto)


The Banff International Research Station will host the "Geometric Structures on Lie Groupoids" workshop from April 16th to April 21st, 2017.

The theory of Lie groupoids 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 foliation theory, gauge theory, and geometric mechanics. Just as Lie groups arise as the symmetries of objects, Lie groupoids arise as the symmetries of continuous families of objects. A central question in the theory is the integration of infinitesimal symmetries (described by Lie algebroids) to global symmetries (described by Lie groupoids). In recent years, there have been fascinating new applications of the theory of Lie groupoids and Lie algebroids in a variety of contexts, such as Poisson geometry, generalized complex geometry, index theory, the theory of exterior differential systems, Stokes phenomena in complex analysis, and more. Typically, these applications involve additional structures on Lie groupoids, and require a detailed understanding of their relation with the corresponding infinitesimal structures.

This workshop will bring together researchers using Lie groupoids and Lie algebroids as tools in their work, with leading experts on their properties and structural theory. Among the themes to be explored in this meeting are multiplicative differential forms on groupoids, compatible measures and metrics on groupoids, as well as symplectic and complex structures on groupoids. Throughout, there will be an emphasis on concrete applications.

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 disc
iplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineeri
ng 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).