5 problems

Vanishing-integral conjecture. (i) If $\gamma(t)$ is totally unbalanced, then

Rank-separation conjecture. There exist no functions $f,g,h\colon\mathbb{N}\to\mathbb{N}$ such that, for every $p\in\mathbb{R}[x,y]$, independently of the degree of $p$,

Strassen's decomposition conjecture. If $F=\sum_{i=1}^sF_i\in S$ is a degree $d\geq3$ form such that $F_i\in S^{[i]}$ for all $i=1,\ldots,s$, then any minimal Waring decomposition…

Let $p$ be a general binary form of even degree $2s$, and let $\alpha_j,\beta_j\in\mathbb{C}$ for $1\leq j\leq s+1$. Canonical representation conjecture. The form $p$ can be writte…

Let $\mathbb{K}$ be a field of characteristic $\operatorname{char}(\mathbb{K})$, and let $f$ be a rational function over $\mathbb{K}$ whose degree is not a multiple of…