3 problems

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Ekstrand–Heluani–Källén–Zabzine's Shatashvili–Vafa algebra conjecture for $G_{2}$ -manifolds
Shatashvili–Vafa algebra conjecture. The section pairs $\{\Phi_{+},K_{+}\}$ and $\{\Phi_{-},K_{-}\}$ generate two commuting copies of the Shatashvili–Vafa $G_{2}$ superconformal al…
Conjectureopenchiral-de-rham-complex g2-holonomy superconformal-algebrasarXiv posted 2 days ago
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Uniqueness of inhomogeneous complete cohomogeneity-one nearly Kähler six-manifolds
Uniqueness conjecture. These are the only inhomogeneous complete cohomogeneity-one nearly Kähler structures in six dimensions.
Conjectureopencohomogeneity-one g2-holonomy nearly-kahler-geometryarXiv posted 2 days ago
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The QR-realisation conjecture for manifolds with $G_2$ holonomy
QR-realisation conjecture. Any $G_2$ -holonomy manifold is a QR-submanifold of a certain hyper-Kähler manifold satisfying these conditions.
Conjectureopeng2-holonomy hyperkahler-geometry qr-submanifoldsarXiv posted 2 days ago

Ekstrand–Heluani–Källén–Zabzine's Shatashvili–Vafa algebra conjecture for G2G_{2}G2​-manifolds