10 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…

Parton decomposition conjecture. Every such polynomial can be written as

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

Weak equivalence conjecture. The map $\mathcal I_d$ 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…

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

Let $\mathcal{P}_d$ be the space of polynomials of degree at most $d$, and let a minimal projection onto $\mathcal{P}_d$ mean a projection whose operator norm equals the projection…

Let $S=\{P_i:1\le i\le d\}$ be a set of $d$ generic points in $\mathbf{P}^n$ over a field $\mathbb{F}$ of characteristic zero. A cone polynomial is a homogeneous polynomial of degr…

Dineen's conjecture. The space $P(^m E)$ has an unconditional basis if and only if $E$ is finite-dimensional.