Minicourse by Matias del Hoyo during his visit at the CRM with the Call “Lluís Santaló” financed by “Institut d’Estudis Catalans”

Speaker: Matias del Hoyo (Universidade Federal Fluminense)

Abstract: Lie groupoids and Lie algebroids provide a unifying framework to classical problems and constructions in differential geometry. Their theory has developed rapidly, motivated by its deep ties with symplectic geometry, foliation theory, equivariant geometry and mathematical physics. Poisson and Dirac structures can be seen as singular versions of symplectic structures, they serve to model mechanical systems subject to symmetries and constrains, and they admit a neat description in terms of Lie algebroids. In this minicourse we will overview the rudiments of Lie groupoids and Lie algebroids, explain the examples arising from Poisson structures and their integrations, and introduce a novel approach to Dirac geometry from a homotopy viewpoint.