5 problems

Let $A$ be an abelian variety over a field $L$ of characteristic zero, and let $[p]:A\to A$ denote multiplication by a prime $p$. Brosnan's conjecture. For every prime $p$, the map…

Let $p$ be a prime, $D$ a Hermitian symmetric domain, $G=\operatorname{Aut}^0(D)$, and let $\Gamma$ be an arithmetic subgroup of $G$ as in the source. For a subgroup…

Incompressibility conjecture. The lower bound for the ground-state energy should satisfy

Full-kernel optimality conjecture. The restriction to states built on $\mathcal{V}_2^D$ is unnecessary: the same asymptotic optimality result holds when the full variational set…

Let $\varphi$ be a nondegenerate quadratic form on a vector space over a field $F$, and for a positive integer $d$ let $X_d$ be the variety of $d$-dimensional totally isotropic sub…