11 problems

Let $K$ be a field of characteristic zero, ${\mathcal A}$ a commutative $K$-algebra, and let $\delta$ be a locally nilpotent (LN) $K$-derivation or a locally nilpotent $K$-…

Typical finite ring conjecture. The fraction of isomorphism classes of commutative rings $A$ of order at most $N$ satisfying all of the following conditions tends to $1$:

Use the notation of the first determinant conjecture, and for $i<L$ let ${\cal G}_{\rm trunc}(i,p,q)$ be the graph obtained by dropping layers $j<i$, retaining only the nodes $p,q$…

Let ${\cal A}_1\rightarrow\cdots\rightarrow{\cal A}_L$ be the sequence of commutative semisimple algebras above, with ${D_i}$ projectors at layer $i$, and let $B_a^{(i)}$ be the bl…

Monomial Basis Conjecture. A basis of ${\cal A}_L$ is the disjoint union

Halperin's conjecture. The connected component of the automorphism group of the finite-dimensional algebra $A$ is solvable.

Let $H^{-3}(\mathsf{GC}_3)$ be the degree $-3$ cohomology of the Kontsevich graph complex, viewed as a unital commutative algebra, and let $\Theta$ denote its one-dimensional unit…

Let $G(4k+9)$ be the Grassmann algebra, let $G_0$ denote its even component, and let $M_{\mathcal{C}}$ be the subspace associated with the constructed maximal commutative algebraic…

Converse conjecture. The algebras ${\mathcal B}_{G_1}^T$ and ${\mathcal B}_{G_2}^T$ are isomorphic if and only if the bridge-free matroids of $G_1$ and $G_2$ are isomorphic.

Let $E$ be the Grassmann algebra and let $A_1,A_2\subseteq E$ be maximal-dimensional commutative subalgebras. Uniqueness conjecture. If $n=4k+3$, then $A_1\cong A_2$. This asks whe…

Milovanov's conjecture. There exists a complete Poisson commutative subalgebra $M$ of $S(\mathfrak{g})$ generated by elements of degree at most two.