6 problems

3d mirror vertex-function conjecture. The vertex functions of $X$ with vanishing equivariant parameters are given by the Taylor series expansions of

Let $\mathfrak{g}=\mathfrak{h}\oplus\bigoplus_{\alpha\ne 0}\mathfrak{g}_\alpha$ be the Borcherds–Kac–Moody Lie algebra associated with a general Nakajima variety, with finite-dimen…

Hyperplane and monodromy conjectures. The hyperplanes in the quantization-theoretic arrangement should coincide with those in $$ , and the resulting action on $K_\mathsf{T}(X)$ sho…

Bezrukavnikov's monodromy conjecture. The action of $B$ lifts to

Nekrasov–Shatashvili principle. The Baxter subalgebras of $\mathsf{Y}_Q$ corresponding to $g\in\mathfrak{H}$ are the algebras of modified equivariant quantum multiplication for Nak…

Rationality conjecture. For all equivariant symplectic resolutions, and in particular for Nakajima quiver varieties, the series defining quantum multiplication represents a rationa…