13 problems

ADE hypersurface conjecture. The dual geometry should be the hypersurface singularity

Quiver Hilbert-series conjecture. The series $H_{00}(Q,t)$ should be identified with the Hilbert series of the dual geometry, allowing the dual geometry to be guessed from it.

Star-shaped quiver Coulomb-branch conjecture. The Coulomb branches of star-shaped quiver gauge theories are conjectured to be equivalent to the Higgs branches of 3D Sicilian theori…

Let $\mathcal M(\lambda,\mu)$ be the Coulomb branch associated with a quiver gauge theory, let $\chi\colon\mathbb C^\times\to\pi_1(\mathbf G)^\wedge$ be the one-parameter subgroup…

Consider Seiberg-dual dimer models, with the canonical weight choice, and let $R(x,y)$ be the Ronkin function associated with their Newton polynomial. Ronkin Seiberg-duality conjec…

Consider Seiberg-dual dimer models with canonical edge weights, and let $P_1(z,w)$ and $P_2(z,w)$ be their Newton polynomials. Let $n_i$ be the number of edges, equivalently multip…

Consider a quiver gauge theory based on a quiver of $ADE$ type or of affine type ${\hat A}$, ${\hat D}$, or ${\hat E}$, with a suitable arrangement of surface defects. In the rank-…

Consider the $\mathbb{Z}_2$ orbifold of $\mathcal{N}=4$ super-Yang–Mills theory with gauge group $\mathrm{SU}(N)\times\mathrm{SU}(N)$, and let $\mathfrak{h}_{qu}$ denote the quantu…

Let $Q$ be a quiver of type $ADE$, with dimension vectors $\mathbf v$ and $\mathbf w$, and let $G_{ADE,c}$ be the corresponding group. The coweights…

Let $Q$ be a quiver of finite type with vertex set $Q_0$, and let $V_i$ and $W_i$ be the corresponding gauge and framing vector spaces. Write $\mathop{\text{\rm dim}}\nolimits V_j$…

The Seiberg–Witten spectral curve defines an integrable system whose phase space is denoted by ${\mathfrak P}$; let ${\mathcal A}_{\mathfrak m}$ be the subalgebra associated with t…

For a generalized quiver, let $f^\alpha(\mathbf{a})$ be functions of the flavor fugacities that diagonalize the structure constants of the associated index. Let…

Coherent-component invariance conjecture. Quivers which are toric (Seiberg) duals have the same coherent component of the master space.