8 problems

Let $\mathcal M$ be the Monster group, let $g\in\mathcal M$, and let $T_g(q)$ be the McKay–Thompson series associated with $g$. Conway–Norton monstrous moonshine conjecture. The se…

Let $\mathbb M$ be the Monster group and let $V^\natural$ be a graded $\mathbb M$-module. The McKay–Thompson series $T_g$ are the specified modular functions associated with elemen…

Let $W(Y_{555})$ be the Coxeter group associated with the Coxeter diagram $Y_{555}$, whose generators are the reflections corresponding to the nodes of the diagram. Conway's bimons…

Let $V^{\natural}$ be the monster module, the holomorphic vertex operator algebra whose character is $j-744$ and whose symmetry group is the Monster simple group. Monster-module un…

Let $A$ be an indecomposable Majorana algebra. For each $i\in\{2,3,4,5,6\}$, suppose there are Miyamoto involutions $t_1$ and $t_2$ such that the order of $t_1t_2$ is $i$. Straight…

Let $\mathbb{M}$ be the Fischer–Griess monster, and let $j(\tau)$ be the $j$-invariant of a complex elliptic curve, whose Fourier expansion begins … where $q=e^{2\pi i\tau}$. Conwa…

Let $\mathfrak{m}$ be the Monster Lie algebra, and let $\operatorname{Aut}^q(\mathfrak{m})$ denote its group of q-compatible automorphisms. Borcherds's proof of Monstrous Moonshine…

Let $\mathfrak{m}$ be the Monster Lie algebra, and let $G$ be the group of q-compatible automorphisms of $\mathfrak{m}$. The Monster group $\mathbb{M}$ is a subgroup of $G$. The q-…