Normal forms for smooth Poisson structures by J. Conn, Annals of Math, 121 (1985) (paper available through the link).
Aim: to study some of the various "local form results" in geometry with the final goal of reaching the rather remarkable result of Conn on the linearization of Poisson structure (on linearization of Poisson structures at fixed points of semi-simple compact type) and the recent result on linearization of Zung in the general context of Lie groupoids. These results can be found in:
Normal forms for smooth Poisson structures by J. Conn, Annals of Math, 121 (1985) (paper available through the link).
Zungs's linearization theorem for groupoids by Zung, paper available, through the link.
However, the idea is to build up by reading some standard "normal form results" in differential geometry, such as the slice theorem for group actions, Reeb stability for foliations and the Darboux theorem and other normal form results in symplectic geometry.
Literature: Appart from the previous literature, for the more classical results we will use the following:
Lie groups by Duistermaat and Kolk.
Introduction to foliations and Lie groupoids by Moerdijk and Mrcun.
Introduction to symplectic topology by McDuff and Salamon.
As an overall reference, we will use:
Poisson structures and their normal forms by Dufour and Zung.
Level: The intended level of these lectures is that of Master students/beginning PhD students interested in Geometry.
Person in charge: Ionut Marcut.