Speaker: Nguyen Tien Zung (Institut de Mathématiques de Toulouse)
Title: Normal forms of integrable non-Hamiltonian systems
Abstract: I'll mention briefly about local normal form problems for general integrable finite-dimensional non-hamiltonian systems, and then talk about the case of systems of type (n,0), i.e. n commuting vector fields on n-dimensional manifolds
Speaker: Eva Miranda (Universitat Politècnica de Catalunya)
Title: Revisiting normal forms of Poisson structures (From Weinstein to Crainic-Marcut via Conn, Hamilton and Monnier-Zung)
Abstract: In the Ph.D thesis presentation of Ionut Marcut, we saw very interesting contributions to the study of many problems of normal form theory and stability in Poisson Geometry. In this talk we will present another example of normal form result (joint work with Philippe Monnier and Nguyen Tien Zung on rigidity for Hamiltonian actions) which uses a geometrical analysis approach. The initial motivation was to extend some local equivariant Weinstein's splitting result to the global setting where local normal forms results are replaced by stability results. We also plan to present some applications to generalized complex structures and some projects in the pipeline for Dirac structures.
Speaker: Rui Fernandes (University of Illinois at Urbana-Champaign)
Title: Normal forms for regular proper groupoids and symplectic complete isotropic realizations
Abstract: In this talk I will discuss the following question: When is a groupoid Morita equivalent to a bundle of Lie groups? When this happens, the groupoid takes a special normal form. We will see also that in the case of symplectic groupoids this question is intimately related to the existence of symplectic complete isotropic realizations (i.e., non-commutative integrable systems on symplectic manifolds).
This question arose in discussions on different issues with several groups of people: with M. Crainic and D. Martinez-Torres, on issues related to Poisson manifolds of compact type; with R. Caseiro, C. Laurent-Gengoux and Pol Vanhaecke on the geometry of non-commutative integrable systems, and with D. Sepe on singular integral affine structures.
