7 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…

Let $A$, $B$, and $D$ denote classical matrix algebras, let $g^\vee$ be the dual Coxeter number, and let $r_0$ denote a local endpoint in the ring $B$ at level $g^\vee-1$. The prop…

Let $\mathfrak g$ be a simple Lie algebra, let $B=\wedge\mathfrak g/\langle[X,X]\rangle$, let $A=(B\times B)/\langle[X,Y]\rangle$, and let $A^{\mathfrak g}$ denote the subring of…

Tachikawa's conjecture. All possible relations reduce to

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 Coulomb branch of a four-dimensional $\mathcal{N}=2$ superconformal field theory is parameterized by expectation values of chiral primary operators ${\cal E}_{r,(0,0)}$, where…