4 problems

Let $V_{3C}$ denote the Modular Moonshine vertex algebra for the Monster conjugacy class $3C$, and let $E_8$ denote the $E_8$-vertex algebra over $\mathbb{F}_3$. Borcherds's 3C con…

Let $\mathbb{M}$ be the Monster group. For each $g\in\mathbb{M}$, seek a $\frac{1}{|g|}\mathbb{Z}$-graded super-module ${}^g\hat V$ over $\mathbb{Z}[e^{2\pi i/|g|}]$, equipped with…

Let $\mathbb{M}$ be the Monster group, let $V^\natural_{\mathbb{Z}}$ be a self-dual integral form of the Moonshine vertex operator algebra, and let $g\in\mathbb{M}$ be a Fricke ele…

Borcherds–Ryba conjecture. Up to a certain rescaling of weights, $^gV$ is isomorphic, as a vertex algebra over ${\mathbb F}_3$, to