Mikhail Bershtein

Instantons and 2d superconformal field theory

A recently proposed correspondence between 4-dimensional

Bases in coset conformal field theory from AGT correspondence and Macdonald polynomials at the roots of unity

\mathcal{N} = 2

Quadratic Algebras Related to the Bi-Hamiltonian Operad

SUSY SU(k) gauge theories on

AGT, Burge pairs and minimal models

{{{{\mathbb{R}^4}}} \left/ {{{\mathbb{Z}_m}}} \right.}

Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory

and SU(k) Toda-like theories with Zm parafermionic symmetry is used to construct four-point

Homomorphisms between different quantum toroidal and affine Yangian algebras

\mathcal{N} = 1

Exact results for

super Liouville conformal block, which corresponds to the particular case k = m = 2.The construction is based on the conjectural relation between moduli spaces of SU(2) instantons on

\mathcal{N}

{{{{\mathbb{R}^4}}} \left/ {{{\mathbb{Z}_2}}} \right.}

= 2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants

and algebras like

Coupling of two conformal field theories and Nakajima-Yoshioka blow-up equations

\widehat{\text{gl}} {(2)_2} \times \mathcal{N}\mathcal{S}\mathcal{R}