Mathematics

I shall discuss recent progress in understanding the duality between supersymmetric gauge theories and integrable systems of Calogero-Moser type. When the number of color degrees of freedom in gauge theories is large they, together with the dual integrable systems admit an effective description which involves moduli space of instantons of a different gauge theory. Alternatively, the large-N description can be understood in terms of a one-dimensional hydrodynamical model which is called intermediate long-wave system.