4 problems

Bapat's conjecture. The minimum over doubly stochastic tuples is

Let ${\bf A}=(A_1,\ldots,A_n)$ be an $n$-tuple of complex $n\times n$ matrices. Let $D({\bf A})$ be their mixed discriminant, and let $D_n$ be the set of tuples satisfying … and ……

Bapat's conjecture. For all $\mathbf{A}\in\Omega(m)$,

Let $D_n$ be the set of $n$-tuples ${\bf A}=(A_1,\ldots,A_n)$ of positive semidefinite $n\times n$ matrices satisfying $\operatorname{tr}A_i=1$ for every $i$ and…