8 problems

Let $Q$ be a finite quiver, let $W$ be a polynomial potential on $Q$, and let $\operatorname{\mathsf{nil}}(\mathcal P(Q,W))$ be the category of finite-dimensional right modules ove…

Let $Q$ be the quiver with two vertices $0,1$, no loops, and $k\in\mathbb{Z}_{\geq 1}$ arrows from $0$ to $1$. For $n\in\mathbb{Z}_{\geq 1}$, define the signed quantum numbers … Us…

Let refined BPS invariants and motivic Donaldson–Thomas invariants be the two types of invariants discussed in the source, with the latter introduced by Kontsevich and Soibelman. D…

Let $Q$ be a quiver, and consider all maximal green sequences for $Q$. Their lengths are integers. No Gap Conjecture. The set of lengths of all possible maximal green sequences for…

Nonnegative-power conjecture. The series $S(q)$ and $\overline{S}(q)$ can be expanded as Taylor series in $q$, with no negative powers of $q$.

Let $q=e^{-i\gamma}$ with $\gamma>0$, and let $\lambda$, $\mu$, $\nu$, and $z$ be parameters. Write…

A quiver with a polynomial potential determines a Jacobian algebra via the cyclic derivatives of the potential. For a Dynkin quiver with a discrete stability structure, Keller's qu…

Let $q=\exp(2\pi i\tau)$, where $\tau$ is the variable appearing in the quantum dilogarithm and in the quasimodular form associated with the quintic periods. An $\Omega$-background…