Rigid Local Systems

Riemann introduced the concept of a "local system" on P1-{a finite set of points} nearly 140 years ago. His idea was to study n th order linear differential equations by studying the rank n local systems (of local holomorphic solutions) to which they gave rise. His first application was to study the classical Gauss hypergeometric function, which he did by studying rank-two local systems on P1- {0,1,infinity}. His investigation was successful, largely because any such (irreducible) local system i