5 problems

Let $\mathbb{K}$ be a non-archimedean local field with ring of integers $\mathscr{O}_\mathbb{K}$, prime ideal $\mathfrak{p}=\textbf{p}\mathscr{O}_\mathbb{K}$, and residue field…

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…

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 $M$ be a closed, connected, orientable manifold, and let $X$ be a vector field on $M$. The vector field $X$ is globally hypoelliptic when every distributional solution of…

Let $N$ be a nilpotent Lie group of step $r$ with Lie algebra $\mathfrak N$, let $\mathfrak N_j=[\mathfrak N,\mathfrak N_{j-1}]$ for $j=1,\dots,r$, let $\Gamma\setminus N$ be a com…