International conference
Combinatorial Methods in Physics and Knot Theory

It was found recently that the so-called multicut solutions to matrix models (solutions for which the limiting eigenvalue distribution spans several intervals on real axis or even in complex plane while the ``occupation numbers'' S_i are the new parameters) are essential for description of vacua of supersymmatric Yang--Mills theories. They also manifest rich mathematic structures. We prove that such a solution, already in the leading order of 1/N-expansion, is the Whitham--Krichever tau function. It satisfies the set of WDVV (associativity) equations in canonical variables. The geometric/integrable content of corrections in 1/N is an important, still unresolved, problem. The only way to construct systematically these corrections is to solve the set of loop equations. We find the subleading correction (the torus approximation) and discuss its possible singularities of the answer in the set of new parameters S_i.