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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 2-105

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.