18 problems

A 13-dimensional complex ball quotient is obtained from the Allcock lattice construction, with $X$ denoting the corresponding ball quotient and $X^{\rm sg}$ its singular or special…

Let $V^{f\natural}$ be the super vertex operator algebra constructed from the Leech lattice, and let $\operatorname{Aut}(V^{f\natural})$ denote its automorphism group. Conway group…

Let $V\!B^{\natural}$ denote the shorter moonshine module, also called the Baby Monster SVOA. A self-dual unitary rational SVOA is called “very nice” in the sense used in the sourc…

Let $(U,Y,{\bf 1},\Omega)$ be a nice rational enhanced VOA with local algebra $\mathcal{A}(\Omega)\cong\mathcal{A}(\Omega_{\operatorname{\textsl{Ru}}})$. Assume that $U$ has rank…

Let $A_{{\operatorname{\textsl{Ru}}}}$ be the self-dual enhanced $\operatorname{\textsl{U}}(1)$--VOA of rank $28$ whose full automorphism group is the direct product of a cyclic gr…

Yural'ev–Ryba–Ries conjecture. The following inequality holds:

Neutsch and Meyer's conjecture. The group $G$ is the Lyons group itself.

Meyer and Neutsch's conjecture. The third candidate should be the unique irreducible Brauer character of $Ly$ of degree $111$.

Let $G_\ell$ be the sporadic group associated by generalized moonshine to each supersingular prime $\ell<12$, and let $s_{p,\ell}^+$ be the supersingular polynomial of level $\ell$…

Let $V^{f\natural}$ be the holomorphic SCFT with automorphism group $\mathrm{Co}_1$, and let $\overline{\operatorname{Fer}(3)}$ be the antiholomorphic three-fermion theory. Set … T…

Sporadic-group linear-factor conjecture. For every prime $p$,

Let $J_1$ denote the first Janko sporadic simple group, and let $L_2(11)$ denote the group $\operatorname{PSL}_2(11)$. Existence conjecture. It was conjectured that $J_1$ contains…

FSZ Sylow conjecture. $G$ is FSZ if and only if all of its Sylow subgroups are FSZ.

Let ${\rm Th}$ be the Thompson sporadic group, let ${\cal F}_3$ be the relevant weight one-half weakly holomorphic modular form, and let $W_m$ be the representation attached to the…

Let ${\rm Th}$ be the Thompson sporadic group, let ${\cal F}_3$ be the relevant weight one-half weakly holomorphic modular form, and let $W_m$ be the representation attached to the…

Let ${\rm Th}$ be the Thompson sporadic group, and let $W_m$ be supermodules indexed by integers $m\geq -3$ with $m\equiv 0,1\pmod 4$. Write … For $m\geq 0$ with $m\equiv 0\pmod 4$…

Let $G$ be one of the Janko simple groups $J_1$ or $J_2$, and let $\mathcal D$ be a design obtained from $G$ by Method 1, namely from a primitive action of $G$ on a set $\Omega$, a…

The monster is the largest sporadic finite simple group. Let $\mathcal{O}$ be the complex hyperbolic orbifold mentioned in the conjecture. Monster–complex geometry conjecture. The…