10 problems

Regularity conjecture. The CW-complex formed by the cells $S_\mathcal{M}^\mathrm{tnn}$ is regular. The closure of each cell is homeomorphic to a closed ball of appropriate dimensio…

Cube conjecture. The cell-decomposed space $Y_{ge 0}$ is homeomorphic to an $(n-1)$-dimensional cube.

Let $n$ be a positive integer, let $K\subseteq J\subseteq [n-1]$, and let $E_{K,J}$ be the face of the standard cube $[0,1]^{n-1}$ defined by … Write $\operatorname{Int}(E_{K,J})$…

Let $\mathcal{M}_{n,k}$ be the momentum amplituhedron, and let $\mathcal{S}_{n,k}$ consist of the decorated permutations whose strata are boundary strata, together with the decorat…

Exponent-one locally modularity conjecture. Every distal locally modular geometric structure admits distal cell decompositions of exponent $1$.

Let $n$ be a positive integer, and consider the space of complex monic degree-$n$ polynomials with distinct roots, identified with … A Gauss-skizze is the set of curves in the comp…

Let $\operatorname{OG}_{\ge0}(n,2n)$ be the positive orthogonal Grassmannian, with cell decomposition … where the cells are indexed by matchings $\tau$ on $[2n]$, and the cell inde…

Cell-dimension torus-action conjecture. There exists a torus action on $\operatorname{Gr}_{\mathbf e}(P_{m+1}^V)$ such that the dimension of the cell labeled by $(S_H,S_V)$ is…

Cell decomposition conjecture. Every quiver Grassmannian attached to an exceptional representation of any quiver admits a cell decomposition; in particular, this should hold for qu…

Let $Q$ be a quiver with stability parameter $\Theta$, and let $d$ be a dimension vector that is coprime for $\Theta$. Consider the moduli space $M_d^{\rm st}(Q)$ of stable represe…