The Strong and Weak Lefschetz Properties

Aim and scope

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 property 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.

The themes of the workshop are the Weak Lefschetz Property - WLP - and the Strong Lefschetz Property - SLP. Among the topics to be studied in the meeting, we list:

- SLP and WLP for Complete Intersections, Gorenstein algebras, Jacobian ideals;

- Questions about the characteristic;

- Connections with classical algebraic geometry;

- Unexpected hypersurfaces and arrangements:

- Lefschetz property and the existence of isotropic subspaces in the Hodge-Riemann bilinear form;

- Lefschetz properties and Jordan type properties;

- Artinian reductions of Stanley-Reisner rings;

- Connections with invariant theory and representation theory.

Organizing and Scientific Committe

Emilia MEZZETTI (scientific responsible - Università degli studi di Trieste)

Karim ADIPRASITO (Hebrew University of Jerusalem and University of Copenhagen)

Roberta DI GENNARO (Università degli Studi di Napoli "Federico II")