Sven Sandfeldt: The Greenleaf-Wallach conjecture on nilmanifolds

Abstract: A differential operator $L$ is globally hypoelliptic (GH) if every distributional solution to the equation $L(D) = f$, with $f$ a smooth function, is represented by a smooth function $u = D$. The Greenleaf-Wallach conjecture states that a vector field on a closed smooth manifold is GH if and only if the vector field is (up to a smooth coordinate change) a constant vector field on a torus. In this talk, I will discuss some recent progress toward answering this conjecture and a generalization of the conjecture to multiple commuting vector fields.