7 problems

Let $n$, $d$, and $K$ be positive integers with $d\geq K$, and let $\Delta_*$ denote the separation parameter for the Gaussian-mixture clustering model. Write $a\gtrsim_{\log} b$ w…

Galois-width conjecture.

Sturmfels's conjecture. For all integers $d,k\geq 1$, the maximum number of modes is

Let $\mathcal{G}_{n,d}$ be the Gaussian moment variety of order $d$ in $n$ variables, and let $\operatorname{Sec}_k(\mathcal{G}_{n,d})$ denote its $k$-th secant variety. Fix $k$ an…

Let $\mathcal{G}_{n,4}$ be the Gaussian moment variety of order $4$ in $n$ variables, and let $\delta_j$ denote the defect of its $j$-th secant variety. The model-parameter count i…

Let $\mathcal{G}_{n,3}$ be the Gaussian moment variety of order $3$ in $n$ variables, and let $\operatorname{Sec}_k(\mathcal{G}_{n,3})$ denote its $k$-th secant variety. For $K$ de…

Let $\mathcal{G}_{n,d}$ denote the Gaussian moment variety of order $d$ in $n$ variables, and let $\operatorname{Sec}_k(\mathcal{G}_{n,d})$ be its $k$-th secant variety. Algebraic…