Séminaire du LPTMS: Raoul Santachiara

The Riemann-Hilbert problem asks whether the global properties (i.e. their the analytic continuation) of a space of holomorphic functions allows to determine uniquely the  linear ordinary complex differential equation (of Fuchsian type) of which they are solutions.  The answer is positive for a class of  equations that are called rigid systems. We have recently observed that the 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 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.