Adalberto P. Bergamasco

Remarks about global analytic hypoellipticity

We present a characterization of the operators L = 8/Ot + (a(t) + ib(t))&/&x which are globally analytic hypoelliptic on the torus. We give information about the global analytic hypoellipticity of certain overdetermined systems and of sums of squares.

On the global solvability for overdetermined systems

We consider a class of systems of two smooth vector fields on the 3-torus associated to a closed 1-form. The global solvability of such systems is completely determined by the connectedness of the sublevel and superlevel sets of a primitive of this 1-form in the minimal covering. The main point of this talk is addressing the case when the 1-form is non-exact and its periods are rationally dependent. This is a work in collaboration with A. Bergamasco, A. Kirilov, and W. Nunes.