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 …

We demonstrate that commutativity of numerous one-dimensional subalgebras in W 1+∞
algebra, ie the existence of many non-trivial integrable systems described in recent arXiv …

We review the holomorphic block factorisation of partition functions of supersymmetric
theories on compact manifolds in various dimensions. We then show how to interpret 3d and …

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 extend our consideration of commutative subalgebras (rays) in different
representations of the W 1+∞ algebra to the elliptic Hall algebra (or, equivalently, to the …

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 We consider T [SU (N)] and its mirror, and we argue that there are two more dual
frames, which are obtained by adding flipping fields for the moment map on the Higgs and …