Knizhnik-Zamolodchikov equation for quantum toroidal algebras

Quantum toroidal algebras are two-loop generalizations of quantum affine algebras. They depend on two independent quantum deformation parameters, admit two gradings and include two central elements. In this talk I will show how to construct an analogue of quantum Knizhnik-Zamolodchikov equation for quantum toroidal algebras of type gl_n (n=1 and n>2). I will also demonstrate that the solutions of the equation are given by certain refined topological string amplitudes and Nekrasov partition functions of five-dimensional gauge theories. The talk is based on the papers 1703.06084 and 1712.08016.