3 problems

The 1-trivial-motion conjecture. The set of $1$-trivial motions of size-$k$ psd factorizations of matrices in $\mathcal{M}_{\binom{k+1}{2},k}^{p \times q}$ is equal to…

Let $M$ be a finite-volume hyperbolic manifold of dimension at least $4$. Let $f\colon M\to S^1$ be a non-homotopically trivial smooth map such that $\ker(f_*)$ is finitely generat…

Let an abstract triangulated sphere be realized in $\mathbb{R}^3$, and let $\operatorname{D}$ denote its discrete Dirac operator. A triangulated-sphere realization conjecture. Ever…