8 problems

For a finite group $G$, let $\operatorname{ed}(G)$ denote its essential dimension and let $S_n$ be the symmetric group on $n$ letters. The essential-dimension conjecture for symmet…

Hilbert's Sextic Conjecture. For any smooth, irreducible, generically free $A_6$-curve $X$,

Let $G$ be a connected algebraic group over a field $k$. Radical splitting conjecture. One has … This would follow from a positive answer to Tits's question of whether torsors unde…

Hilbert's octic conjecture.

Segre's asymptotic resolvent degree conjecture. The difference between $n$ and the resolvent degree $\operatorname{RD}(n)$ tends to infinity as $n$ tends to infinity.

For each $n$, let $\mathcal{P}_n$ be the parameter space of degree-$n$ polynomials and let $\widetilde{\mathcal{P}}_n\to\mathcal{P}_n$ be the associated cover parametrizing a root.…

For each $n$, let $\mathcal{P}_n$ be the parameter space of degree-$n$ polynomials and let $\widetilde{\mathcal{P}}_n\to\mathcal{P}_n$ be the associated cover parametrizing a root.…

Let $\mathcal{H}_{3,3}$ denote the moduli space of smooth cubic surfaces, and let $\mathcal{H}_{3,3}(r)$ denote the moduli space of smooth cubic surfaces together with $r$ specifie…