7 problems

Let $G$ be a solvable Lie group. A complete left-invariant affine structure on $G$ is a left-invariant flat and torsion-free affine connection whose associated affine structure is…

A Lie algebra is characteristically nilpotent when every derivation of it is nilpotent. Kharitonov's conjecture. Every nilpotent Lie algebra which does not admit an affine structur…

Affine-structure conjecture. For $n\ge 13$, these algebras do not admit any affine structure.

Let $(Y_t,D_t)$, $t\in (0,1]$, be a $1$-parameter family of pairs of del Pezzo surfaces $Y_t$ of degree $d$ with smooth anti-canonical divisors $D_t$. Assume that…

Existence conjecture. Every nilpotent Lie algebra over $\mathbb{C}$ admits an LSA structure.

A representation is strictly affine when it is nonabelian, is not unitary, and has linear-part angles generating an infinite subgroup of $\mathbb{R}/\mathbb{Z}$. A branched affine…

Consider a large complex degeneration of Calabi–Yau manifolds, and rescale the Ricci-flat metrics so that the diameter remains fixed. Gross–Wilson–Kontsevich–Soibelman conjecture.…