5 problems

Chiral de Rham realization conjecture. The vertex algebra $V$ is isomorphic to

Embedding conjecture. The chiral de Rham complex of $M$ admits an embedding of the SUSY vertex algebra $\mathrm{SV}_a$, where the value of $a$ is determined by the eigenvalue…

Let $M$ be an $8$-dimensional Riemannian manifold with holonomy $Spin_7$, and let $\Omega^{ch}_M$ denote its chiral de Rham complex. Write $C^\infty(M,\Omega^{ch}_M)$ for the assoc…

Shatashvili–Vafa algebra conjecture. The section pairs $\{\Phi_{+},K_{+}\}$ and $\{\Phi_{-},K_{-}\}$ generate two commuting copies of the Shatashvili–Vafa $G_{2}$ superconformal al…

Let $W$ be the canonical bundle over ${\mathbb P}^4$, let $\Sigma$ be the generalized fan described by the cones generated by $\deg^{\vee}$, $-\deg^{\vee}$, and four of the five ve…