7 problems

Consider a six-dimensional F-theory compactification with a frozen $7$-brane localized along a divisor $D$ and residual discriminant $\widetilde{\Delta}$. Neutral-hypermultiplet co…

Rank-$n$ $E_8$ compact duality conjecture. The following theories are equivalent:

Compact TCS $G_2$ duality conjecture. The following theories are equivalent:

M-theory–F-theory duality conjecture. The following physical theories are equivalent:

Harmonic intersection-cohomology conjecture. The vector space of $\mathbb{V}$-valued $i$-forms that are harmonic and $L^2$ with respect to the Kähler metric is isomorphic to

Let $W_{4}'$ and $B_{3}'$ be the indicated models, let $\tilde{\tilde{\theta}}$ be the rational map in the commutative diagram, and consider the fiber product…

Let a compact singular elliptically fibered Calabi–Yau $3$-fold have singular fibers associated to ${\mathcal G}$-symmetry in codimension $1$ over the base, admit a crepant resolut…