11 problems

Let $A$ and $B$ be positive definite matrices, and let $n$ be a positive integer. The BMV conjecture. The polynomial in $t$ … has all positive coefficients. The source presents thi…

Hillar's commuting-minimizers conjecture. Such matrices $A$ and $B$ commute.

Let $A,B\geq 0$. Let $f$ be a nonnegative and nondecreasing function on an interval $\mathcal{J}$ such that $\operatorname{spec}(A)\subseteq\mathcal{J}$. Reverse trace inequality.…

Let $K\colon \mathbb{R}^d\to\mathbb{R}^d$ be homogeneous of order $1-d$ and smooth outside the origin. Let $\nu$ be a measure satisfying … For $f\in C_0^\infty(\mathbb{R}^d)$, cons…

All-order trace derivative positivity conjecture. The function $t\mapsto\operatorname{tr} f(A+tB)$ has non-negative $k$th derivative.

Let $F$ be an $\mathbb{R}^d$-valued charge with $\operatorname*{\div}F=0$, let $u$ be a measure on $\mathbb{R}^d$, and let $K1,K2,\ldots,Kd$ be sufficiently smooth functions on…

Let $\Gamma=\langle\xi_1,\xi_2,\dots,\xi_n\rangle$, and let $\alpha_n$ be as described in the generalized Jørgensen conjecture. For $i\ne1$, define … Let $z_1$ and $z_2$ be the mid…

Henrot's conjecture. One has

Let $\mathsfsl{A},\mathsfsl{B},\mathsfsl{C}\in\mathbb{H}^{d}$ be Hermitian matrices, let $q$ be a positive integer, and let $s>0$. For a Hermitian matrix $\mathsfsl{X}$, write…

Let $A$ and $B$ be positive operators and let $q\in\mathbb{R}$. Complementary McCarthy conjecture. … for $-2<q<0$, while the reversed inequality should hold for $3\leq q$. The disp…

Furuta's conjecture. It was asked whether