9 problems

De Sitter swampland conjecture. There is an order-one constant $\gamma$ such that

Large complex structure suppression conjecture. In this limit, $R_\perp(\hat{Y})$ becomes a small perturbation, with a mass scale much smaller than the Kaluza--Klein scale set by t…

Let $\cM_{\rm cs}$ be the complex-structure moduli space of a Calabi–Yau manifold, and let its period integrals be the functions obtained by integrating the relevant Calabi–Yau for…

Consider fluxes that stabilize moduli in a flux compactification, and let the tadpole charge be the charge induced by those fluxes. Tadpole conjecture. The tadpole charge induced b…

Consider exponential corrections to the prepotential determining periods on a Calabi–Yau threefold. Enhanced-supersymmetry conjecture. The absence of these corrections is linked to…

Let $\mathcal M$ be the moduli space of a compactification manifold, and let a Hodge locus in $\mathcal M$ be a locus on which a higher Hodge tensor exists. Higher Hodge tensor–sym…

The discussion concerns compact elliptic Calabi–Yau manifolds and records for the numbers of tensor multiplets and the rank of the gauge group in associated F-theory compactificati…

Fix $(M,g_0,T_{\text{st}}^{g_0})$ and let $(\varphi,\mathcal{F})$ depend smoothly on a real parameter $t$. Assume that at $t=0$ the data satisfy one of the situations governed by t…

Let $M$ be a compact $n$-dimensional manifold, let $g=e^{2\varphi}g_0$ range over a conformal class of metrics, let $v$ be a positive warp factor, and let $F^{(p)}$ be the field st…