4 problems

For $n,p\in\mathbb{N}$, define the $p$-homogeneous semi-symmetric polynomial … for $x\in\mathbb{R}^n$ and $\lambda\in\mathbb{R}^p$. Let $\mathbb{I}$ denote the all-ones direction,…

Real-rootedness concavity conjecture. If $\bar f_{\overrightarrow{a}}$ is real-rooted, then $f_{\overrightarrow{a}}$ is $\frac1p$-concave on $\Gamma_n$; equivalently,…

Diagonal concavity conjecture. The function $f_{\overrightarrow{a}}$ is $\frac1p$-concave on $\Gamma_n$ if and only if it is $\frac1p$-concave on $\Delta$, if and only if…

Sanyal's conjecture. All hyperbolicity cones of elementary symmetric polynomials are spectrahedral.