5 problems

Let $P$ be a $d$-dimensional smooth Fano polytope, and let $n$ denote the parameter appearing in the conjectured bound. Sharp volume bound conjecture. The following upper bound is…

Let $P$ be a Fano polygon, that is, a two-dimensional Fano polytope. Call $P$ symmetric when its symmetry group is nontrivial. Hacking–Kim conjecture. If $P$ is a Kähler–Einstein F…

Let $P$ be a smooth Fano polytope, and let $B(P)$ denote its barycentric transformation. A Fano polytope is of type $B_\infty$ when the barycentric transformation can be applied in…

Conjecture A. There exists a bijective correspondence between the set of mutation-equivalence classes of Fano polygons and the set of qG-deformation equivalence classes of locally…

Sato's conjecture. Every smooth Fano $n$-polytope is either F-equivalent to $T^n$ or pseudo-symmetric.