Lefschetz Properties and Artinian Algebras (16w5114)


(Northeastern University)

Sara Faridi (Dalhousie University)

Rosa Maria Miro Roig (Universitat de Barcelona)

(University of Göttingen)

Junzo Watanabe (Professor, Tokai University, Japan)


The Banff International Research Station will host the "Lefschetz Properties and Artinian Algebras (HALF)" workshop from March 13th to March 18th, 2016.

The study of the Lefschetz properties of commutative algebras in their own right began only relatively recently and seems to go back to a paper of R.P. Stanley in 1977 which connected the strong Lefschetz property with diverse combinatorial structures, among them the Sperner property of a finite poset, using a mixture of algebraic geometry, commutative algebra, and combinatorics. It is only in the last dozen years or so that several research teams around the globe have begun reorganizing the theory of commutative Artin algebras from this viewpoint, and a research monograph summarizing portions of this program appeared in 2013. These groups and isolated individual researchers are scattered about in Japan, the United States, and Europe. However, there has been a lack of overlap in the results they have obtained and the methods they employ. A small workshop with only 14 participants was held in September 2012 at the Hawaii Tokai International College to allow for an exchange of recent advances, ideas, and problems face to face. The fruits of this workshop are remarkable, with no less than a half dozen manuscripts resulting from it, and the study of Lefschetz properties has begun to attract more and more researchers. This is particularly the case because the literature being relatively small makes the area accessible to young postdoc's and advanced graduate students, especially because of the many open problems. A similar workshop is planned for March 2015 in Gottingen. This workshop in 2016 will have a larger group of 20 to 25 participants. The isolated setting of BIRS, its geographically central location for the participants, and the success of workshops attended by some of the organizers there, make BIRS an ideal setting.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).