11 problems

A noetherian connected graded domain is a connected graded domain that is noetherian. Intermediate GK-dimension conjecture. There does not exist a noetherian connected graded domai…

Let $A$ be a graded coherent algebra such that the category $\mathbf{D}^b(\mathsf{qgr}(A))$ admits a classical generator, and let $S$ be the Serre twist functor induced by the grad…

Let $K$ be a field of characteristic zero, let $R=K[t_i\mid i\ge 0]$, and let $L=\operatorname{Lie}(v_1,v_2)\subset\operatorname{Der}R$. Characteristic-zero growth problem. Determi…

Let $W_N$ be the set of standard monomials of length $N$ in the Fibonacci Lie algebra, and regard their multidegrees as points in the plane. Two-line-family conjecture. For every f…

Let $\mathcal L$ be the Fibonacci Lie algebra, let $\gamma_{\mathcal L}(n)$ denote its regular growth function, and let $\lambda=(1+\sqrt 5)/2$. Growth-limit conjecture. The normal…

Bartholdi's conjecture. The growth of this associated graded algebra is subexponential.

Vershik's conjecture. The growth of this associated graded algebra is subexponential.

Quantitative Kurosh conjecture. Any non-linear function that occurs as the growth rate of an algebra is realizable as the growth of a nil algebra.

Let $R$ be a finitely presented associative algebra, and measure its growth through the growth of the dimensions of its graded components or, more generally, its associated growth…

Small's primitivity-or-PI conjecture. The algebra $A$ is either primitive or PI.

Growth-constant bound conjecture. There exists a function $F:(0,\infty)\rightarrow(0,\infty)$ such that $A$ has at most $F({\rm GC}(A))$ prime ideals $P$ satisfying…