TOWARDS A PROOF OF AGT CONJECTURE BY METHODS OF MATRIX MODELS

A matrix model approach to proof of the AGT relation is briefly reviewed. It starts from the substitution of conformal blocks by the Dotsenko-Fateev beta-ensemble averages and Nekrasov functions by a double deformation of the exponentiated Seiberg-Witten prepotential in beta not equal 1 and g(s) not equal 0 directions. Establishing the equality of these two quantities is a typical matrix model problem.