The study of Lefschetz properties for Artinian algebras was motivated by the Lefschetz theory for projective manifolds, begun by S. Lefschetz, and well established by the late 1950's. Many of the important Artinian graded algebras appear as cohomology rings of an algebraic variety or manifold, though recent important developments have demonstrated important cases of the Lefschetz properties beyond such geometric settings (such as Coxeter groups or matroids). This renews interest in understanding the Lefschetz property, and Artinian algebras that admit them, systematically.

 

Lefschetz properties form a fertile meeting ground for researchers with quite diverse backgrounds. Indeed, this subject matter has connections to many branches of mathematics, as a central object of study in it are Gorenstein algebras (also known as Poincaré duality algebras), which are of strong interest not only in algebraic geometry, but also in commutative algebra, algebraic topology, and combinatorics. In particular, some of the important results in the area have been obtained by using unexpected methods and finding unexpected connections between apparently different topics, naturally bringing together a diverse set of researchers.

 

In the last two decades there has been fascinating progress on the study of the Weak Lefschetz Property (WLP) and the Strong Lefschetz Property (SLP) from different perspectives, inspired in part by, and contributing to, developments in algebraic geometry, commutative algebra and combinatorics among others. Our workshop will highlight the most significant developments, with the aim of spurring further progress in the field stimulated by the contact of different points of view. More precisely, the purpose of this workshop is to bring together researchers from different areas, who might not otherwise cross paths, in order to share different points of view and to foster new and unexpected collaborations.

 

One consequence is that young researchers have the opportunity to collaborate with established experts, who they otherwise would not have the chance to interact with. In addition, since Lefschetz properties are very actively studied, it is expected that participants will also gain ideas for directions in which to guide their current and future students.