7 problems

Let $\mathcal C$ be a modular tensor category, and let $\operatorname{FPdim}(\mathcal C)$ denote its Frobenius–Perron dimension. Solvability conjecture. If…

Let $\mathcal C$ be a modular tensor category, and let $\operatorname{FPdim}(\mathcal C)$ denote its Frobenius–Perron dimension. Solvability conjecture. If…

Solvability conjecture. Every fusion category $\mathcal{C}$ whose Frobenius–Perron dimension $\operatorname{FPdim}(\mathcal{C})$ is odd is solvable.

Magaard and Tong-Viet's conjecture. If $\operatorname{acd}(G)\leq 3$, then $G$ is solvable.

Let $n$ be the dimension parameter, let $G$ be the group indexing the choices of $\sigma$, and let $\mathrm{KW}_{b,\sigma}^{\mathscr{A}}(\xi)$ denote the corresponding arithmetic K…

3'-degree average character solvability conjecture. If

For a finite group $G$, let $\operatorname{Irr}(G)$ denote the set of irreducible complex characters of $G$, and define the average character degree by … The alternating group…