7 problems

Basheer–Moori conjecture. In the Clifford–Fischer construction, the block attached to the nontrivial $\operatorname{Sp}(V_m)$-orbit in $\operatorname{Irr}(V_m)$ can be computed fro…

Character-table conjecture. If $S$ is a normalized ideal Perron similarity and $S$ is totally extremal, then $S$ is the character table of a finite Abelian group.

Average class size conjecture (weak version (b)). The limiting ratio satisfies

Average class size conjecture (strong version). The cumulative ratio satisfies

Circle generator complexity conjecture (weak version). There exists a finite $m\in\mathbb{N}$ such that

Circle generator complexity conjecture (strong version). The average circle generator complexity of class algebras is smaller than the corresponding average for fusion algebras:

Alternating-group supercharacter theory conjecture. For all $n\geqslant 7$, every supercharacter theory of $A_n$ other than $\mathsf{M}(A_n)$ can be constructed from a group of tab…