9 problems

Gupta's three-set polynomial Sylvester–Gallai conjecture. There is a function $\lambda(r)$ such that

Beecken–Michałek–Saxena bounded-rank conjecture. The algebraic rank of such circuits is $O_k(\log d)$.

Gupta's bounded transcendence-degree conjecture. There is a function $\lambda$ such that

Valiant's $\mathbf{VP}_s \neq \mathbf{VNP}$ conjecture. There is no polynomially bounded function $n(m)$ such that $\mathrm{perm}_m$ is a specialization of $\mathrm{IMM}^m_{n(m)}$…

Let $\mathcal{G}$ be the generator for depth-2 circuits, equivalently sparse polynomials, referred to in the statement. Agrawal's generator conjecture. This generator should suffic…

Let $\mathcal{R}$ be a finite ring, and let its Jacobson radical be the ideal governing the factor ring $\mathcal{R}/J(\mathcal{R})$. The sigma equivalence problem concerns equival…

Let $R$ be a matrix algebra over a field $\mathbb{F}$, and let $D$ be an algebraic branching program over $R[x_1,\ldots,x_n]$. A shift is a substitution of the variables by shifted…

Let $K[V]^G$ denote the invariant ring of a representation $V$ of a group $G$, and consider rings of invariants under simultaneous conjugation and coordinate rings of explicit vari…

Let $K$ be a field of characteristic $\operatorname{ch}(K)$, and let $R_{\delta}(k,s)$ strictly upper-bound the rank of any minimal and simple $\Sigma\Pi_{\delta}\Sigma\Pi(k,s,n)$…