This is a review article on the quantum toroidal algebras, focusing on their roles in various
solvable structures of 2d conformal field theory, supersymmetric gauge theory, and string …

Borisov and Joyce constructed a real virtual cycle on compact moduli spaces of stable
sheaves on Calabi–Yau 4-folds, using derived differential geometry. We construct an …

This is a mini-review about generalized instantons of noncommutative gauge theories in
dimensions 4, 6 and 8, with emphasis on their realizations in type II string theory, their …

A bstract We explore the quantum algebraic formalism of the gauge origami system in ℂ 4,
where D2/D4/D6/D8-branes are present. We demonstrate that the contour integral formulas …

A bstract The quiver Yangian, an infinite-dimensional algebra introduced recently in [1], is
the algebra underlying BPS state counting problems for toric Calabi-Yau three-folds. We …

Higher rank K-theoretic Donaldson-Thomas Theory of points Page 1 Forum of Mathematics,
Sigma (2021), Vol. 9:e15 1–51 doi:10.1017/fms.2021.4 RESEARCH ARTICLE Higher rank K-theoretic …

Recently, Nekrasov discovered a new “genus” for Hilbert schemes of points on C 4. We
extend its definition to Hilbert schemes of curves and moduli spaces of stable pairs, and …

A bstract We study the counting problem of BPS D-branes wrapping holomorphic cycles of a
general toric Calabi-Yau manifold. We evaluate the Jeffrey-Kirwan residues for the flavoured …

A bstract We introduce a class of 4-dimensional crystal melting models that count the BPS
bound state of branes on toric Calabi-Yau 4-folds. The crystalline structure is determined by …

A bstract Solid partitions are the 4D generalization of the plane partitions in 3D and Young
diagrams in 2D, and they can be visualized as stacking of 4D unit-size boxes in the positive …