8 problems

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…

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

Thompson-group conjecture. For every prime $p$,

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

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…