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Raoul Santachiara : Rigid Fuchsian systems in conformal algebras
E161 (de Hemptinne)
A Fuchsian system is a system of first order ordinary differential equations in the complex plane with only regular singularities.
An important question is whether the global properties of its solutions (its monodromy group) are determined by or determine uniquely the behavior of the solutions near the singularities.
The answer is positive for a class of equations that are called rigid systems. We have recently discovered that rigid systems describe a class of fundamental equations that lie in the heart of the 2D Conformal field theories. Moreover we used for the first time a procedure developed in the last decades for the solutions of rigid systems to provide new results in CFTs. In this talk, I will try to introduce to the (beautiful) mathematics behind the Fuchsian systems, and I will try to give you an idea of the reason why these equations are related to the conformal symmetry.