Poisson manifolds of compact types

I will give an overview on the recent (and ongoing) joint work with R.L. Fernandes and D. Martinez on Poisson manifolds of compact types. These are the analogues in Poisson Geometry of the compact Lie groups from Lie theory. However, within this Poisson geometric context, one finds various parts of geometry coming in and interacting with each together (symplectic, foliations, integrable systems, gerbes). My plan is to exhibit these by concentrating on Duistermaat-Heckmann-types of formulas.Non UBCUnreviewedAuthor affiliation: UtrechtFacult