I will talk about N=2 Yang-Mills theories with the classical gauge groups. That is, for SU(N), SO(N), and Sp(N) theories with almost all possible matter multiplets. The main goal is to compute the prepotential which describes the leading terms in the low-energy effectif action (up to two derivatives and up to four fermions). The standard approach to compute the prepotential is the Seiberg-Witten theory which establishes the connection between this prepotential and the periods of a meromorphic differential living on an algebraic curve. An alternative approach is the Nekrasov deformation technique, which gives the prepotential as a series on the dynamically generated scale. Therefore, to compare two approaches we need to extract Seiberg-Witten data from the series (it seems to be easier than extract the whole series from the curve). A technique to extract the curve is presented. In some simple cases the exact curve is obtained and it is shown that it coincides with all available results. In all considered cases it is shown that an approximation for this curve, which is sufficient to compute 1-instanton correction, provides the correct answer. It is shown that the deformation technique is consistent.

IHES, Bures sur Yvette