The content of the first three lectures:
The first hour was an introduction to the subject, culminating with the formulation of Goresky-MacPherson theorem. Then we continued with some lattice theory that we need, such as geometric semilattices.
We went through the theory of Möbius function for posets at a rather fast pace. And have started with Poincare and characteristic polynomials of hyperplane arrangements. We have proved some first results about these polynomials, such as the formula for the Poincare polynomial of a coning construction and Poincare polynomial of a direct product of two arrangements.
We have finished studying the combinatorics of Poincare polynomials of hyperplane arrangements. We proved the Deletion-Restriction Theorem and derived several corollaries, among them Zaslavsky theorem counting the number of regions in the complement of an arrangement and Stanley's theorem counting the number of acyclic orientations of a graph. After that we looked at why do Poincare polynomials factorize (into real linear factors). We proved the theorem of Stanley that a Poincare polynomial of a supersolvable arrangement factorizes.
Contact Information:
E-post: kozlov "at" math "dot" kth "dot" se
phone : 790-6655
office : 3528, Matematiska Institutionen, KTH