Rigid local systems: from Gauss to the proof of Sato-Tate conjecture

Rigid local systems are natural generalizations of the solution sheaves of Gauss hypergeometric differential equations. A unifying desription of all irreducible rigid local systems exists by Katz' work on the middle convolution. We describe Katz work and show how it can be applied in the context of the Sato-Tate conjecture (work of Taylor et al.). In the end of the talk, we outline how one can extend the results of Shepherd-Barron, Harris and Taylor to other groups than GL_2, e.g. to Galois representations of type G2.