6 problems

Let $J^k(\mathbb{R},\mathbb{R})$ be the space of $k$-jets of real functions of one real variable, equipped with its sub-Riemannian distance. A geodesic…

Let $X$ be a quasi-compact complex manifold, let $\mathcal{F}$ be a codimension-$1$ foliation on $X$, let $\mathfrak{V}(\mathcal{F})$ denote the set of hypersurfaces that are smoot…

Finite generation conjecture. The ring of invariant polynomials

Let $\pi:\mathbb{H}\rightarrow S$ be the uniformizing maps of a Shimura variety $S$ corresponding to a semisimple group $G$. Let $k\geq 2$ and let…

Fiber-structure conjecture. For $n\gg0$, the fiber of $p_n$ over the image of $\gamma$ is homeomorphic to a quotient of

Let $\mathcal{X}$ be a Deligne–Mumford stack of finite type over $D$, and let $\mathcal{J}_{\infty}\mathcal{X}$ be its moduli space of twisted arcs. For $n\in\mathbb{Z}_{\ge0}$, a…