14 problems

Let $\mathcal{H}_n$ be the set of $n\times n$ positive semidefinite Hermitian matrices. For matrices $A=[a_{i,j}]$ and $B=[b_{i,j}]$ in $\mathcal{H}_n$, define the Hadamard product…

Let $\mathcal{H}_{2g+1}$ be the set of monic square-free polynomials of degree $2g+1$ over $\mathbb{F}_q[x]$, and define … Let $P_X(\chi_D)=P_X(\tfrac12,\chi_D)$ and…

For each $n\in\mathbb{N}$, let $X_n^\star$ be the idealizer associated with quasi-stable polynomials, and let $Y_n^\star$ be the corresponding family defined by $Y_n^\star=Y_n$ for…

For each $n\in\mathbb{N}$, let $X_n\subset\mathbb{R}_n^+$ be the largest subsemigroup containing $\mathcal{H}_n$ and $\mathbb{I}_n$ such that, for every $m\leq n$, Hadamard multipl…

Let $A,B e 0$ be Hermitian positive semidefinite matrices of the same size, and let $A\circ B$ denote their Hadamard product. Chollet's conjecture. … The conjecture is a permanent…

For positive integers $k_1,k_2$, set $n=k_1+k_2-1$. Let $h_{k_1,k_2}(p)$ denote the number of pairs of matroids of ranks $k_1$ and $k_2$ on the ground set $[n]$, counted up to perm…

Let $\lambda=(\lambda_1,\dots,\lambda_n)$ and $\mu=(\mu_1,\dots,\mu_n)$ be partitions with at most $n$ parts satisfying $\mu\subseteq\lambda$. Let $k$ and $r$ be integers with…

Let $SV_{\mathbf{d},\mathbf{n}}$ be a Segre-Veronese variety, let $\sigma_{\mathbf{r}}(SV_{\mathbf{d},\mathbf{n}})$ denote its secant variety, and let a Hadamard product mean the c…

Let $L_1, \ldots, L_d \subset \mathbb{C}^m$ be linear spaces not contained in any coordinate hyperplane, and let $r_1, \ldots, r_d$ be the rank functions of the corresponding linea…

Let $p$ be a polynomial with nonnegative coefficients, and let $\mathscr{W}(p)$ denote the polynomial obtained by the operator $\mathscr{W}$. Fischer–Kubitzke conjecture. For all s…

Let ${\cal H}_n$ be the cone of positive-semidefinite Hermitian matrices, and let $A\circ B$ denote the Hadamard (entrywise) product. Chollet's conjecture. For $A,B\in{\cal H}_n$,…

Let $L_1,\dots,L_d \subseteq \mathbb{R}^E$ be finite-dimensional linear spaces, and let $M_1,\dots,M_d$ be their algebraic matroids. Write $r_{M_i}$ for the rank function of $M_i$,…

Hadamard-product convexity conjecture. For any $f_1,f_2\in\Omega$, one has

Let $\mathcal{H}_{2g+1}$ be the set of monic square-free polynomials of degree $2g+1$ over $\mathbb{F}_q[x]$, and write … For the partial Hadamard product, set…