3 problems

Finiteness conjecture. There are only finitely many abelian groups, up to isomorphism, that are not generically closed with respect to at least one representation.

Let $Pr(n)$ and $Ar(n)$ denote uniform prisms and antiprisms, respectively, with $n$-gon bases. Let $N_{Pr(n)}$ and $N_{Ar(n)}$ be the corresponding partition counts, and suppose t…

Let $G\leqslant \operatorname{GL}(d,\mathbb{R})$ be finite and let $P(G,v)$ be a full-dimensional orbit polytope. Orbit-polytope symmetry conjecture. There is a point $v_0$ such th…