13 problems

Representability conjecture for coordinate q-matroids. If the corresponding matroid of a coordinate $q$-matroid is representable, then the $q$-matroid is representable.

Finite-dimensional representability conjecture. There exists a finite-dimensional $W$-(super)algebra $B$ such that

Representability conjecture for K(r,t). Every matroid obtained from $K(r,t)$ by relaxing a circuit-hyperplane into a basis is representable.

Let $d$ be a nonnegative integer, and let $\mathsf{K}$ be a simplicial complex. A simplicial complex is $d$-Matoušek and $d$-Leray as defined in the source paper. The d-Matoušek-to…

Affine-plane representability problem. Determine whether

Representability bound conjecture. If $h(X)\leq d$ for $d\geq 1$, then

Let $A$ be a finite integral relation algebra (RA), and suppose that $A$ has a flexible atom. A relation algebra is representable over a finite cyclic group if it embeds into a Com…

For a prime power $q$, let $\mathcal{AC}_q$, $\mathcal{SL}_q$, and $\mathcal{AF}_q$ be the corresponding classes of matroids, with extremal functions $h_{\mathcal{AC}_q}(r)$,…

Let $M_1$ be a matroid with a circuit-hyperplane $H$, and let $M_2$ be obtained from $M_1$ by relaxing $H$. If both $M_1$ and $M_2$ are representable over a finite field…

Let $S\subseteq\mathbb{R}^n$ be MICP representable, so that … where $C\subseteq\mathbb{R}^d$ and each $A_{\bm{z}}\subseteq\mathbb{R}^d$ is a projection of a closed convex set. A fi…

Nonrepresentability conjecture. Asymptotically almost every matroid is not representable over any field.

Structural conjecture. Either $M$ is ternary, for some $e\in L$ the deletion $M\backslash e$ is binary, or $M$ has an $F_7$-minor and either an $F_7^-$- or $(F_7^-)^*$-minor.

Let a finite matroid be a finite set $E^{\mathcal{M}}$ equipped with a rank function … Let MSOL denote monadic second-order logic for matroids, whose structures use finite ground s…