4 problems

Kollár–Villarino conjecture. The following conditions are equivalent:

Becher–Grimm–Van Geel's conjecture. The inequality

Let $\Phi:M_n(\mathbb{R})\rightarrow M_n(\mathbb{R})$ be a completely positive map whose Choi matrix is invariant under partial transposition. Such a map is an IPT map. A map break…

Let $P$ be a real polynomial of degree $n>1$ whose roots are all real. Suppose that $P$ shares a root with each derivative $P^{(k)}$ for $k=1,2,\ldots,n-1$. Real Casas–Alvero conje…