6 problems

Horn's conjecture. The inequalities arising from the recursively characterized triples $(I,J,K)$ are sufficient to characterize all Horn triples $(\lambda,\mu,\nu)$; equivalently,…

Odd-dimensional Hermitian isotropic Grassmannian conjecture. The function $S\mapsto p_S(L)$ is a valuated $\Delta$-matroid for every maximal isotropic subspace $L$. The even-dimens…

Assume $\operatorname{char} K=2$, let $F$ be the fixed field of the involution on $K$ with $F\ne K$, and write $K=F[\omega]$ where $\omega^2+\omega+\beta=0$ for some $\beta\in F$ a…

Let $H_m^{(n)}$ denote the relevant space of Hermitian matrices, and let a polynomial ensemble on $H_m^{(n)}$ have weights … as in Eq. (pol.H). A random matrix $g$ is drawn from a…

Kippenhahn's conjecture. The algebra generated by $H$ and $K$ cannot be the full algebra $M_{2n}(\mathbb{C})$.

Knutson–Tao conjecture. The direct sum of Hermitian matrices corresponds to an overlay of honeycombs; conversely, Littlewood–Richardson fillings should correspond to Hermitian matr…