Algebra & Geometry Seminar

Speaker: Jason McCullough
Title: Hyperplane Arrangements and Orlik-Solomon Algebras
Abstract: Hyperplane Arrangements are a classical topic. The cohomology ring of the complement was famously computed by Orlikand Solomon in 1980. It can be represented as a quotient of an exterior algebra with defining relations coming from the intersection lattice, meaning the cohomology ring is combinatorially determined. The first talk will be introductory with several examples. The second week I will address a question of Shelton and Yuzvinsky regarding whether Koszul Orlik-Solomon algebras having defining ideals with quadratic Groebner bases. We give a negative answer to their question, showing that there are rational K(pi,1) hyperplane complements whose intersection lattice is not supersolvable. This is joint work with Chayim Lowen and Tuong Le (two of June Huh’s grad students).