Danijela Damjanovic, Global hypoellipticity and connections to cohomological and local rigidity of abelian actions

Abstract. Given a smooth abelian continuous-time action one can assign to it a second order operator- the (orbit) leafwise Laplacian. It turns out that global hypoellipticity of this differential operator often implies special properties of the cohomology over the given action and this in turn in some cases allows for certain classification of small perturbations of the action. The specific examples I will discuss are actions generated by Diophantine vector fields on tori, and on nilmanifolds.