Understanding the fundamental group of an algebraic variety, a topological invariant, using purely algebro-geometric data is a long-standing question in algebraic geometry. Grothendieck showed how to recover the completion of the fundamental group using algebraic covers, while Nori gave an interpretation of this completion in terms of vector bundles.

In order to generalize Nori's result to not necessarily projective varieties, vector bundles are not enough, we need complicated objects called "parabolic bundles", defined by Metha and Seshadri for curves. After explaining the ideas of Grothendieck, Nori and Borne, I will discuss joint work with Borne, in which we define parabolic sheaves in a very general context, by connecting the theory to logarithmic geometry.