Algebra/Topology Seminar

Speaker: Nasrin Altafi

Title: Hilbert functions of Gorenstein algebras

Abstract: Gorenstein algebras can be found in many different areas in mathematics, although it is rather subtle to determine the ones satisfying specific properties. In this talk, I discuss the Hilbert functions of Artinian Gorenstein algebras. The weak and the strong Lefschetz properties mean that the multiplication maps by powers of a general linear form have maximal rank. Artinian algebras with the Lefschetz properties have more restrictive Hilbert functions. In 1995, T. Harima characterized Hilbert functions of Artinian Gorenstein algebras with the weak Lefschetz property. I will give a generalization of this for such algebras with the strong Lefschetz property. I will also discuss some of the interesting open problems and known results on this topic.