7 problems

Let $P$) and $Q$ be two colored paths on $m$ vertices with concentration matrices $K_P$ and $K_Q$ satisfying … A reflection of a colored path is the path obtained by reversing its…

Let $C_n$ be the cycle graph on $n$ vertices, and let $\MLdeg(C_n)$ denote the number of critical points of the Gaussian log-likelihood function for generic sample covariance data,…

Gaussoid-axioms sufficiency conjecture. If $a \perp\!\!\!\perp b \mid C$ holds for every covariance matrix $\Sigma \in \mathcal{M}_{\mathcal{G}, i \perp\!\!\!\perp j\mid K}$, then…

Sullivant's saturation conjecture. The vanishing ideal satisfies

Let $G$ be a directed acyclic graph (DAG) with toric vanishing ideal $I_G$. The relevant constructions are safe gluing, gluing at sinks, and adding a sink. Recursive classification…

Let $G$ be a directed acyclic graph (DAG), with vanishing ideal $I_G$ and shortest trek ideal $ST_G$. Shortest-trek characterization conjecture. The vanishing ideal $I_G$ is toric…

Let $\mathcal{C}_{\mathcal{G}}$ denote the cone associated with a graph $\mathcal{G}$. A basic open semialgebraic set is an open semialgebraic set defined by finitely many strict p…