|The Brill-Noether problem for higher rank is concerned with
describing the moduli space of stable vector bundles over a curve
having a prescribed number of sections. One way of studying this
problem is via coherent systems, that is, pairs (E,V) consisting of a
vector bundle E and a subspace V of global sections subject to a
In this talk we will mention some generalities about the moduli space of coherent systems and present results on the nonemptiness of such spaces, including recent joint work with Brambila-Paz in the case when the number of sections is bigger than the rank.