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Partialy supported by WELCOME TO POLAND program of NAWA grant no. PPI/WTP/2022/1/00063

Conference on Lefschetz Properties

The study of Lefschetz properties for Artinian algebras traces its roots back to S. Lefschetz's pioneering work on Lefschetz theory for projective manifolds, which was well established by the late 1950s. While many significant Artinian graded algebras arise as cohomology rings of algebraic varieties or manifolds, recent developments have revealed instances of Lefschetz properties beyond such geometric settings, encompassing Coxeter groups or matroids. This renewal of interest in understanding the Lefschetz property and the Artinian algebras that exhibit them has created a systematic exploration of this fascinating subject.

The concept of Lefschetz properties provides a fertile ground for researchers with diverse backgrounds, bridging connections across multiple branches of mathematics. Central to its study are Gorenstein algebras (also known as Poincaré duality algebras), which pique the interest of not only algebraic geometers but also researchers in commutative algebra, algebraic topology, and combinatorics. Unexpected methods and surprising connections between seemingly unrelated topics have led to essential results in this area, naturally attracting a diverse community of researchers.

Over the past two decades, remarkable progress has been made in investigating the Weak Lefschetz Property (WLP) and the Strong Lefschetz Property (SLP) from various perspectives, inspired and enriched by advancements in algebraic geometry, commutative algebra, combinatorics, and related fields. Our workshop aims to highlight these significant developments, fostering further progress by encouraging the exchange of diverse viewpoints. The purpose of this conference is to bring together researchers from different areas, providing a unique opportunity for interdisciplinary collaboration and the emergence of new and unexpected research partnerships.

One of the notable outcomes of this gathering is the opportunity for young researchers, in particular those attending the Preparatory School, to interact and collaborate with established experts they might not have encountered otherwise. Additionally, as Lefschetz properties remain actively studied, participants are likely to gain valuable insights and ideas for guiding their current and future students in fruitful directions.

Join us in this stimulating environment, where diverse minds converge to explore the intriguing realm of Lefschetz properties, advancing the boundaries of knowledge and fostering new avenues of exploration.