7 problems

Equal matroids conjecture. The two join varieties have the same algebraic matroid:

Let $E$ be the ground set of matrix entries, and let $\mathcal{B}\subset E$ be a set of size $2n-1$. A symbic tree is a combinatorial object indexing a maximal cone in the tropical…

Let $\operatorname{Gr}(k,n)$ be the Grassmannian, and let $M_{\operatorname{Gr}(k,n)}$ be its algebraic matroid. For a coherent matching field $L$, let $M_L$ be the algebraic matro…

Let $\Gamma$ be a nontrivial finite group, and let $p$ be a prime. Dowling-geometry algebraicity conjecture. The matroid $\operatorname{DG}(3,\Gamma)$ is algebraic over…

Let $\Gamma$ be a nontrivial finite group, and let $p$ be a prime. Lift-geometry algebraicity conjecture. The matroid $\operatorname{LG}^+(3,\Gamma)$ is algebraic over…

The partition characterization of relaxed SLMFs. Suppose $\#\Omega=r(m+n-r)$ and every vertex of $G_\Omega$ has degree at least $r+1$. Then $\Omega$ is a relaxed $(r,r,m)$-SLMF if…

Let $a,b,c,d$ be elements in an algebraic matroid, and let $cr(a,b,c,d)$ denote their cross ratio. Algebraic-group characterization conjecture. … in an algebraic matroid if and onl…