Mats Boij: The Weak Lefschetz Property for artinian Gorenstein algebras

Recall that a graded artinian algebra has the Weak Lefschetz Property (WLP) if the multiplication maps by a general linear form all have maximal rank. I will review what is known about the WLP for artinian Gorenstein algebras. In recent work together with Migliore, Miró-Roig , Nagel and Zanello, we studied in particular the case of artinian Gorenstein algebras of codimension three. These studies lead to some interesting connections to projective geometry, which I will also describe.