6 problems

Let $V_i$ and $V_j$ be finite-dimensional vector spaces, and let $\operatorname{GL}(V_i)$ and $\operatorname{GL}(V_j)$ act on the Hamiltonian spaces $\mathbf M_{\medcirc}(V_i,V_j)$…

Let $n,m$ be positive integers and let $e\in\mathbb{Z}^n$ and $f\in\mathbb{Z}^m$ be arbitrary. Write $Z_{\mathrm{quotient}}^c(q,t)$ for the quotient generating series, and interpre…

For $e\in \mathbb{Z}^n$ and $f\in \mathbb{Z}^m$, let … Here $P_s(t)$ is a polynomial, and $N_s$ is a sequence of integers with $N_s\to\infty$. Stabilization conjecture. The polynom…

Let $\DD$ be a brane diagram and let $f\in\Ch(\DD)^{\T}$ be a fixed point. For each tangent-weight term $\alpha_{x,y,k}\frac{x}{y}\mathbf h^k$, call it $f$-small when its restricti…

Let $V_{i-1}$ and $V_i$ be the vector spaces associated with adjacent vertices in a bow, and let $A_{i-1}$, $B_{i-1}$, $B'_i$, $a_i$, and $b_{i-1}$ satisfy conditions (i), (a), (S1…

Let a bow variety be described as a Hamiltonian reduction of a finite-dimensional symplectic manifold, and assume that the associated dimension data satisfy the balanced condition,…