12 problems

Let $Q$ be a symmetric quiver with potential $\mathsf{W}$. Let $\mathfrak{g}_{Q,\mathsf{W}}$ be the Lie superalgebra defined from the classical $R$-matrix, and write … The positive…

Consider elliptic quiver BPS algebras and a higgsing operation relating a parent theory to a higgsed theory. The source expects the induced map, when it exists, to preserve the cen…

Consider quiver BPS algebras associated with toric Calabi–Yau threefolds, and suppose that a higgsing operation relates a parent theory to a higgsed theory. In the rational and tor…

Let a toric Calabi–Yau threefold be described by a quiver, and let the quiver determine its associated quiver BPS algebra. Seiberg or toric duality produces a dual quiver and its a…

Let $\mathtt{Y}$ be a quiver Yangian, with positive part $\mathtt{Y}^+$ and dual $\mathtt{Y}^{+*}=\hom_\mathbb{C}(\mathtt{Y}^+,\mathbb{C})$. The Drinfeld double conjecture. The Dri…

Let $A$ be any configuration of non-compactly-supported branes, and let bound states with $n$ D0-branes be denoted by $A\rightarrow n\ \text{D0}$. The weight of such a configuratio…

Costello's conjecture. The Lie bracket does not vanish on the fermionic part of the doubled BPS Lie algebra.

Let $\mathscr{C}$ be one of the four types of categories considered in the paper, and let $\mathfrak{cu}(\mathscr{C})$ denote its cuspidal cohomology. The simple-root conjecture. I…

Let $\mathscr{C}$ be one of the four types of categories considered in the paper. Let $L$ be its grading lattice, let $\mathfrak{cu}(\mathscr{C})$ be the cuspidal cohomology, and l…

Let $\mathscr{C}$ be one of the four types of categories considered in the paper, and let $\operatorname{\mathcal{A}}_{\mathscr{C}}$ be its CoHA. Let $\mathfrak{g}$ be the associat…

Let $\mathscr{C}$ be a 2-Calabi–Yau category, and let $\mathfrak{g}$ denote its BPS Lie algebra. Let $\mathfrak{cu}(\mathscr{C})$ denote the cuspidal cohomology, namely the cohomol…

Let $(Q,W)$ be a quiver with potential and assume that $Q$ is symmetric. Let $\chi_R|_{\Gamma_l}$ be the associated symmetric quadratic form, let $\mathbb{T}$ denote the torus appe…