  The prepotential of the effective N=2 super-Yang-Mills theory perturbed in
the ultraviolet by the descendents of the single-trace chiral operators is
shown to be a particular tau-function of the quasiclassical Toda hierarchy. In
the case of noncommutative U(1) theory (or U(N) theory with 2N-2 fundamental
hypermultiplets at the appropriate locus of the moduli space of vacua) or a
theory on a single fractional D3 brane at the ADE singularity the hierarchy is
the dispersionless Toda chain. We present its explicit solutions. Our results
generalize the limit shape analysis of Logan-Schepp and Vershik-Kerov, support
the prior work hep-th/0302191 which established the equivalence of these N=2
theories with the topological A string on CP^1 and clarify the origin of the
Eguchi-Yang matrix integral. In the higher rank case we find an appropriate
variant of the quasiclassical tau-function, show how the Seiberg-Witten curve
is deformed by Toda flows, and fix the contact term ambiguity.
