8 problems

Quaternionic Haiman conjecture. There is a $(g+1)^n$-dimensional quotient ring of the zero-fiber ring of $W$.

Alesker–Verbitsky conjecture. For every such $f$, the quaternionic Monge–Ampère equation admits a unique smooth solution $\phi$, up to addition of a constant.

Let $(M,I,J,K)$ be an HKT manifold of quaternionic dimension $n$, with HKT form $\Omega$ and operators $\partial$ and $\partial_J=J^{-1}\circ\overline{\partial}\circ J$. A q-positi…

Let $f:S^2\to\textbf{HP}^n$ be a proper minimal immersion, meaning that $f(S^2)$ is not contained in any totally geodesic submanifold of $\textbf{HP}^n$, and suppose that $f$ has c…

Let $t\in\mathbb{N}^*$, let $S^3\subset\mathbb{R}^4$ be the unit $3$-sphere, and let $\nu(5^t)$ denote the integer solutions of … For $x\in\nu(5^t)\cup\nu(5^{t-1})$, write…

Local dimension conjecture. There exists a $12$-point, respectively $13$-point, tight simplex in ${\mathbb H}{\mathbb P}^2$ such that, in a neighborhood of it, the space of tight s…

Existence conjecture. As $d\to\infty$, there exist tight $N$-point simplices in ${\mathbb H}{\mathbb P}^{d-1}$ for every $N$ satisfying

Quaternionic Calabi conjecture. If the necessary condition