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We give a concise summary of the impressive recent development unifying anumber of different fundamental subjects. The quiver Nekrasov functions(generalized hypergeometric series) form a full basis for all conformal blocksof the Virasoro algebra and are sufficient to provide the same for some(special) conformal blocks of W-algebras. They can be described in terms ofSeiberg-Witten theory, with the SW differential given by the 1-point resolventin the DV phase of the quiver (discrete or conformal) matrix model(\beta-ensemble), dS = ydz + O(\epsilon^2) = \sum_p \epsilon^{2p}\rho_\beta^{(p|1)}(z), where \epsilon and \beta are related to the LNSparameters \epsilon_1 and \epsilon_2. This provides explicit formulas forconformal blocks in terms of analytically continued contour integrals andresolves the old puzzle of the free-field description of generic conformalblocks through the Dotsenko-Fateev integrals. Most important, this completesthe GKMMM description of SW theory in terms of integrability theory with thehelp of exact BS integrals, and provides an extended manifestation of the basicprinciple which states that the effective actions are the tau-functions ofintegrable hierarchies.

Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions