ABSTRACT: A hyperplane arrangement is a collection of codimension
one affine subspaces of n-space. Combinatorics, topology, algebra
and geometry all play a role in the study of these objects. I'll
begin with an overview of the area; in particular I'll discuss
Brieskorn's theorem that the Poincare polynomial of the (complement
of) a complex arrangement can be interpreted solely in combinatorial
terms, and Terao's theorem, which (for certain special arrangements)
relates the Poincare polynomial to a graded module over the polynomial
ring.  In the second part of the talk, I'll concentrate on central three
arrangements (i.e. configurations of lines in P^2), and show that in
this setting, Terao's theorem may be reformulated in the language
of algebraic geometry to apply to all arrangements, i.e. the Poincare
polynomial is the Chern polynomial of a rank two vector bundle on P^2.
I'll examine which arrangements give rise to stable bundles, and discuss
the jump locus of these bundles. I'll define all concepts (sheaves
on P^n, Chern classes, etc.) in a concrete manner.