4 problems

Herzog's minimality conjecture. For $1\leq i\leq n$ and $j\geq 0$,

Let $\mathbb{V}$ be a finite-dimensional real vector space with a euclidean or lorentzian inner product, let $p\geq 2$, and let $F\in\Lambda^p\mathbb{V}^*$. For…

Odd-degree annihilator correction conjecture. For odd $d>3$,

Fix vectors $v_1,\dots,v_m\in\mathbb{R}^d$ with $1\le d\le m$. For integers $k$ satisfying $2\le k\le d$, let $|v_{i_1}\wedge\cdots\wedge v_{i_k}|$ denote the Euclidean norm of the…