6 problems

Let ${{\normalfont\textsc{Poly}}}_d^{mt}$ be the space of all monic degree-$d$ complex polynomials up to translation with its stratified Euclidean metric, and let $K_d$ be the dual…

Let ${{\normalfont\textsc{Poly}}}_d^{mt}$ be the space of all monic degree-$d$ complex polynomials up to translation, equipped with its stratified Euclidean metric. CAT(0) conjectu…

Pattern-preserving weak equivalence conjecture. The embedding $\mathcal I$ is a weak homotopy equivalence.

Let $\Theta$ be a closed constraint, and let $\mathcal B_d^\Theta$ denote the corresponding space of degree-$d$ polynomials satisfying the constraint. Let…

Let $V\in\operatorname{Gr}_{k,n}(\mathbb{R})$. Suppose that all complex zeros of the Wronskian $\operatorname{Wr}(V)$ are real, and let $I\subseteq\mathbb{R}$ be any interval on wh…

Reduction to $k+1$ variables conjecture. For a generic linear form $lin A_1$, either $bar W$ contains no power of a linear form, or