A hyperplane arrangement is a collection of codimension 1 subspaces in an n-dimensional vector space. Already you can ask a number of questions about a hyperplane arrangement, such as:

- How many chambers (maximal open regions) does this arrangement cut up the plane?
- Is there a polytope corresponding to this arrangement?
- What is the topology of the complement of this arrangement?

For the majority of the course we will follow Orlik and Terao's book on hyperplane arrangements, augmented with more recent results discovered within the past decade.

COURSE OUTLINE

- Introduction to hyperplane arrangements
- The intersection lattice, the lattice of regions and oriented matroids
- The characteristic polynomial
- Supersolvable and graphic arrangements
- The module of derivations
- Free arrangements
- The topology of the complement of arrangements
- Coxeter groups and reflection arrangements
- Other topics, as time permits.

PREREQUISITES: A course in linear algebra. Knowledge of algebraic topology (homology, cohomology, ...) is useful, but not necessary.

http://www.ms.uky.edu/~readdy/715/Hyperplane/