11 problems

Physicists' conjecture. Fix a connection $\nabla_A\in\mathcal{C}$. Then for every $\nabla_{A'}\in\mathcal{C}$, there exists a unique $g\in\mathcal{G}$ such that…

Let $M$ be a complex curve equipped with two families of cuts satisfying the conditions in the preceding conjecture. For each integer $n\geq0$, let the associated set of $C^n$-poin…

Let $\mathcal{O}$ be a $\operatorname{Diff}_0(M)$-orbit in the explicit shape space $\mathcal{X}$, let $\mathcal{F}_{\mathcal{O}}\coloneqq \Pi^{-1}\mathcal{O}$ be the entire fiber…

Conjecture on ultra-log-concave intrinsic-volume sequences. The sequence $(a_k)_{k\geq 0}$ is the intrinsic-volume sequence of some infinite-dimensional GB-set if and only if

Gao–Vitale conjecture. Either

Geodesic uniqueness conjecture. Given two spacelike Cauchy hypersurfaces $S_0,S_1\in\mathfrak{C}(M,g)$, there is a unique geodesic path $c:[0,1]\to\mathfrak{C}(M,g)$ such that…

Let $K$ be a field, let $n$ be a positive integer, and let $G$ act on the infinite affine space ${\mathbb A}^n_{K,\infty}$. Write $\textnormal{KQ}({\mathbb A}^n_{K,\infty}/G)$ for…

Let $X$ be a Banach space, and let $(M_n)_{\mathbb{N}'}$ and $(P_n)_{\mathbb{N}'}$ be sequences of subspaces of $X$, with $(P_n)_{\mathbb{N}'}$ finite-dimensional. For $\lambda<1$,…

Hilbert-cube four-point conjecture. The set

Let $G^1$ and $G^2$ be smooth, weak Riemannian metrics on an infinte-dimensional Banach manifold $\mathcal H$. Assume that $G^2$ is uniformly stronger than $G^1$, both metrics admi…

Local 1-affineness conjecture. The prestack $\LocSys_\cG(\oD)$ is 1-affine.