11 problems

Let $CY_{n-2}$ be a Calabi–Yau space realized as a hypersurface in a weighted projective space, and let its reflexive weight data determine a Berger graph. An n-ary Lie algebra is…

Let $CY_n$ denote a Calabi–Yau space with $SU(n)$ holonomy, and let ternary and n-ary symmetries be higher-arity generalizations of binary Cartan–Killing–Lie symmetries. Dubrovski–…

A Berger graph is the graph associated with the holonomy data of a Calabi–Yau space, while an n-ary algebra is an algebra equipped with an n-ary operation. The Calabi–Yau spaces wi…

The length bound conjecture. Let $\mathcal{N}$ be a $k$-dimensional $(A,C)$-commutative $n$-ary algebra. Then its length is at most

Let ${p\mathcal{A}ss}^n_d$ be the operad for degree-$d$ partially associative $n$-ary algebras, in the non-Koszul parity case $n \not\equiv d \pmod{2}$. A gap in a minimal model me…

Let ${p\mathcal{A}ss}^n_d$ be the operad for degree-$d$ partially associative $n$-ary algebras. The Koszul duality isomorphisms identify ${p\mathcal{A}ss}^n_d$ with the Koszul dual…

Let ${t\mathcal{A}ss}^n_d$ be the operad for degree-$d$ totally associative $n$-algebras. The Koszul property is considered for arbitrary arity $n$ and degree $d$. Koszulity parity…

Finite-generation conjecture. Every polynomial identity satisfied by $n$-ary intermolecular recombination, with no restriction on the degree, is a consequence of complete symmetry…

Degree-$3n-2$ consequence conjecture. Every polynomial identity satisfied by $n$-ary intermolecular recombination in degree $3n-2$ is a consequence of complete symmetry in degree…

Degree-$2n-1$ consequence conjecture. Every polynomial identity satisfied by $n$-ary intermolecular recombination in degree $2n-1$ is a consequence of complete symmetry in degree…

A Calabi–Yau space is a quadruple $(M,J,g,\Omega)$, where $(M,J)$ is a complex compact $n$-dimensional manifold. Berger graphs are constructed from reflexive weight vectors and New…