• arrangements
• configuration spaces
• representation theory

This work deals with hyperplane arrangements, with particular attention on the braid arrangement, and with configuration spaces. We give some basic notions on the Orlik-Solomon algebra, on the complement of an arrangement and on its cohomology algebra.
The cohomology algebra of the complement of the braid arrangement is an important object in representation theory, since it carries a natural action of the symmetric group Sn and an extended action. We study some results on the location of some irreducible representations in the decomposition of the cohomology algebra of the complement of the braid arrangement and, more generally, on the cohomology algebra of the configuration spaces. Moreover, we present some new remarks on the location of some irreducible representations of the symmetric group in the decomposition of the cohomology algebra of the complement of the braid arrangement and in the decomposition of the cohomology algebra of the c onfiguration spaces.
Finally we give some basic notions on representation stability and we present a result due to Church and Farb which prove that the sequence of the cohomology groups of the complement of the braid arrangement is uniformly stable.