Antonio Kumpera - On Singular Pfaffian Systems

Abstract. We discuss a recurrent geometrical method due to Élie Cartan  and enabling us to determine, step by step, the integral manifolds of a not necessarily regular Pfaffian system. When the system is regular and integrable then, of course, we shall obtain the maximal integral manifolds. Attention is also given to those integrable systems that can be integrated by quadratures which was, in the 19th century, the dream of many.

Maria Amélia Salazar - Pfaffian groupoids and Spencer operators.

Abstract: The definition of a Pfaffian groupoid came as a result of extracting the structure that matters when dealing with pseudogroups. As a motivation I will start by talking about pseudogroups and give a generalized notion of pseudogroups supported on a Lie groupoid. I will then define prolongations of Pfaffian groupoids, and show their relation to Maurer-Cartan equation, as well as giving the analogous notions of their infinitesimal counterpart. I will briefly explain how in this context we also have linear and non-linear Spencer complexes.

Cristián Ortiz - Morita equivalence of vector bundles

Abstract: Lie groupoids include as particular instances Lie groups, manifolds, Lie group actions, fibrations, among others. The notion of vector bundle over a Lie groupoid arises naturally when dealing with geometric structures on a Lie groupoid, having as important examples both the tangent and cotangent bundles of a Lie groupoid. 

In this talk I will explain the notion of Morita equivalence of vector bundles over a Lie groupoid. Applications to representations theory will be discussed as well as connections with the deformation complex of a Lie groupoid. This talk is based on work in progress joint with M. del Hoyo (IMPA).

Elisha Falbel - Estruturas de contato localmente homogêneas.

Abstract: Estruturas de contacto (essencialmente uma distribuição de planos tangentes não integrável) em variedades de dimensão 3 sempre existem.  Nesta palestra apresentaremos exemplos de variedades com estrutura de contacto localmente homogênea, isto é, com um atlas de cartas à valores numa variedade de contacto homogênea.  

Alexandre Rodrigues - Relação de Equivalência de Cartan para Lie Pseudogrupos

Abstract: TBA

José Miguel Veloso - Nonlinear Spencer operators on differentiable Groupoids

Abstract: We generalize the construction of nonlinear Spencer operators done by Kumpera-Spencer and Malgrange to groupoids of k-jets of bisections of general differentiable groupoids.

Franciso Rui Tavares de Almeida - The Poincaré Conjecture

We display a counter-example to this conjecture which, by the way, has been accepted, as proved, by all mathematical community. It is known that $S^3$ is the universal covering of $RP^3$ which cannot contain a Klein bottle. Our argument relies on the construction of a 3-manifold, with fundamental group $Z_2$ and containing a Klein bottle. Its universal covering space is a homotopy 3-sphere that, perforce, cannot be homeomorphic to $S^3$.

Rui Loja Fernandes - Classifying Algebroids of G-structures

Abstract: We discuss the existence, equivalence and classification problems for classes of geometric structures in the context of G-structures, using the language of Lie algebroids. We explain the role of Lie's Third Theorem for Lie algebroids/groupoids in solving these problems. Joint work with Ivan Struchiner.