10 problems

Let $M$ be a manifold and let $X$ be a globally hypoelliptic vector field on $M$. A vector field on a torus is called constant diophantine when it is given by a constant vector sat…

Let $N$ be a connected simply connected nilpotent Lie group of step $r$, let $\Gamma\setminus N$ be a compact nilmanifold, and let $X_1,\dots,X_k$ be constant coefficient vector fi…

Let $M$ be a smooth connected compact manifold, and let a smooth flow be a smooth $\mathbb R$ action on $M$. The flow is globally hypoelliptic if its associated leafwise Laplacian…

Let $X_0,X_1,\ldots,X_r$ be vector fields defining a sum-of-squares operator, and let the associated control system be the system denoted by … is sufficient for global hypoelliptic…

Let a globally hypoelliptic $\mathbb{R}^{k}$-action be an action whose orbitwise Laplacian is globally hypoelliptic, and let the class of actions constructed in the cited forthcomi…

Let $M$ be a compact nilmanifold and let an action of $\mathbb{R}^{k}$ on $M$ be homogeneous when it is induced by translations in the nilmanifold structure. The action is globally…

Let $M$ be a smooth compact manifold and let $\rho$ be a smooth flow. Denote by $H^1_\rho(C^\infty(M))$ the first cohomology of the action with coefficients in smooth functions. A…

Let $\rho$ be a homogeneous $\mathbb R^k$ action on a finite-volume space $G/D$, where $G$ is a connected Lie group and $D$ is a closed subgroup of $G$. An $r$-step nilmanifold is…

A homogeneous $\mathbb R^k$ action is an action by multiplication by group elements on a homogeneous space. A nilmanifold is a compact quotient of a connected simply connected nilp…

Let $G$ be a Lie group, let $\Gamma$ be a cocompact lattice in $G$, and let $\rho$ be an $\mathbb R^k$ homogeneous action on $\Gamma\setminus G$. Its leafwise Laplacian is denoted…