MIT Combinatorics Seminar
The Face Semigroup Algebra of a Hyperplane Arrangement
Franco Saliola (Cornell University)
Email: saliola@gmail.com
Wednesday, February 15, 2006 4:30 pm Room 2105
ABSTRACT

A finite collection of hyperplanes in a real vector
space
partition the vector space into subsets called the `faces' of the
arrangement. The set of faces has an associative product and the
resulting semigroup algebra turns out to have connections with
probability and algebraic combinatorics. The talk will begin
with a
survey of these connections and will explain how the geometry and
combinatorics of the hyperplane arrangement give nice results
about
the structure of the algebra. In particular, I will describe the quiver
of the algebra, say that it is a Koszul
algebra; and explain why the algebra
depends only on the combinatorics of the arrangement.


