16 problems

Let $I$ be a chiral ring, and let $X=\operatorname{Spec}(I)$ be its associated variety. The variety $X$ is K-stable when the Futaki invariant $F$ is nonnegative for every test symm…

Consider the ${\cal N}=2$ theories described in the source as Lagrangian realizations of the relevant three-dimensional theories. Supersymmetry-enhancement conjecture. There is non…

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

Transverse-distance conjecture. The transverse distance between the D3-brane probe and the $E_n$ 7-branes is proportional to $\operatorname{vol}(V_2)$ in the local Calabi–Yau three…

Let an $n$-dimensional toric Gorenstein singularity be associated with a polytope $\Delta_{n-1}$, either reflexive or non-reflexive. Let $Y$ be the associated Sasaki–Einstein base…

A three-dimensional canonical singularity is a canonical singularity of complex dimension three, and a 5d SCFT is a five-dimensional superconformal field theory with eight supercha…

A marginality crossing is a situation in which an operator changes between marginal and non-marginal status along the relevant deformation or renormalization-group flow under discu…

Let $S=(\lambda,m,u_r)$ denote the deformation and expectation-value parameters of a four-dimensional $4d \mathcal{N}=2$ superconformal field theory, and let $X$ be a threefold sin…

Singularity–SCFT conjecture. In the limit $g_s\rightarrow 0$ and in the infrared limit, this construction defines a four-dimensional $4d \mathcal{N}=2$ superconformal field theory.…

Let $\mathcal{R}$ be an $\mathcal{N}=1$ chiral ring, equipped with the stability notion defined using test chiral rings and polarized $U(1)_R$ symmetries. Chiral-ring stability con…

Let $\mathcal{R}$ be a chiral ring equipped with a polarization $\zeta$, so that $({\mathcal{R}},\zeta)$ is a polarized chiral ring. A polarized chiral ring is stable if it has no…

The positivity criterion conjecture. The condition $\sum_i w_i>1+d$ is necessary and sufficient for the singularity to define a four-dimensional $\mathcal{N}=2$ superconformal fiel…

A three-dimensional rational Gorenstein graded isolated singularity is a three-dimensional isolated singularity that is rational, Gorenstein, and graded. The rational Gorenstein si…

Rational graded Gorenstein singularity conjecture. The most general type of isolated singularity that gives a four-dimensional $\mathcal{N}=2$ superconformal field theory is a rati…

Vanishing-cycle/BPS-quiver conjecture. The intersection form of the vanishing cycles might be identified with the BPS quiver.

Shapere–Vafa conjecture. These are necessary and sufficient conditions for the isolated hypersurface singularity to define a four-dimensional $\mathcal{N}=2$ superconformal field t…