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 …

Starting with a gentle approach to the Alday–Gaiotto–Tachikawa (AGT) correspondence
from its 6d origin, these notes provide a wide (albeit shallow) survey of the literature on …

The statistical model of crystal melting represents BPS configurations of D-branes on a toric
Calabi–Yau three-fold. Recently it has been noticed that an infinite-dimensional algebra, the …

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 …

We follow the general recipe for constructing commutative families of W-operators, which
provides Hurwitz-like expansions in symmetric functions (Macdonald polynomials), in order …

A bstract We associate vertex operator algebras to (p, q)-webs of interfaces in the
topologically twisted\(\mathcal {N}= 4\) super Yang-Mills theory. Y-algebras associated to …

A bstract We study the structure of modules of corner vertex operator algebras arrising at
junctions of interfaces in\(\mathcal {N}= 4\) SYM. In most of the paper, we concentrate on …

A bstract Instanton partition functions of\(\mathcal {N}= 1\) 5d Super Yang-Mills reduced on S
1 can be engineered in type IIB string theory from the (p, q)-branes web diagram. To this …

A bstract We describe the general strategy for lifting the Wess-Zumino-Witten model from the
level of one-loop Kac-Moody\({U} _q {\left (\widehat {\mathfrak {g}}\right)} _k\) to generic …

We study the relation between $\mathcal {W} _ {1+\infty} $ algebra and Arbesfeld-
Schiffmann-Tsymbaliuk Yangian using the Maulik-Okounkov R-matrix. The central object …