An old question is whether the monodromy group of a Fuchsian system is determined by or determines uniquely the behavior of its solutions near the singularities. The answer is positive for a class of equations that are called rigid systems. We have recently discovered that these rigid systems describe a class of fundamental equations that lie in the heart of the Virasoro and W theories. We used a procedure developed in the last decades for the solutions of rigid systems to provide new results in CFTs.

In this talk, I will introduce the Kats theory for rigid systems and I will explain how these systems are related to the conformal algebras mentioned above.