8 problems

Cheng–Duncan conjecture. For each conjugacy class $g$ of $M_{24}$, the product $\Phi_g$ defines a Siegel modular form with some multiplier on the congruence subgroup…

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…

Let $\mathrm{Tcf}^\bullet$ be the spectrum of topological cusp forms, and let $[\overline{V^{f\natural}}]\nu$ denote the $\mathrm M_{24}$-equivariant class refining the nonequivari…

Let $\nu\in\mathrm{TMF}^{-3}(\mathrm{pt})$ be the class corresponding to $[\overline{\operatorname{Fer}(3)}]$, let $\{24\Delta\}\in\mathrm{TMF}^{-24}(\mathrm{pt})$ be the class cor…

Twisted black-hole counting conjecture. For every $g\in M_{24}$ and $h\in C_{M_{24}}(g)$,

Let $g\in M_{23}\subset M_{24}$, let $\alpha$ satisfy the cocycle conditions referred to in the source, and let $C^\alpha_{M_{24}}(g)$ be the corresponding central extension, with…

Let $K=\bigoplus_{n=-1}^{\infty}K_n q^{n/8}$ be the virtual graded $M_{24}$-module determined by the McKay–Thompson series, with $K_n$ the representation whose character is given b…

Twisted elliptic-genus module conjecture. For $k\equiv0,3\pmod4$ and $k\geq-1$, one has