The monodromy of the local holomorphic solutions of Gauss's hypergeometric equation defines a linear representation of the fundamental group of the Riemann sphere with 3 points removed. This monodromy is therefore determined by matrices A,B,C verifying the relation ABC=I. Riemann was the first to realize that in the irreducible case, the conjugacy classes for each one of these matrices (which correspond to local information of the equation around the corresponding singular points) determine the simultaneous conjugacy class for the three matrices and thus the representation. In modern terminology
(after, N. Katz, P. Deligne and others), these representations are now called rigid.

In this seminar I will give a short account of this historic motivation and then explain how to generalize these ideas to representations that arise as the monodromy of systems of linear PDE. The approach will mainly algebraic, although some topological ideas will be required, giving a geometrical flavor to the problem. (Joint work with O. Neto)