## Lefschetz Properties in Algebra, Geometry and Combinatorics (hybrid meeting)

 dc.date.accessioned 2020-11-03T09:15:22Z dc.date.available 2020-11-03T09:15:22Z dc.date.issued 2020 dc.identifier.uri http://publications.mfo.de/handle/mfo/3804 dc.description.abstract The themes of the workshop are the Weak Lefschetz Property - WLP - and the Strong Lefschetz Property - SLP. The name of these properties, referring to Artinian algebras, is motivated by the Lefschetz theory for projective manifolds, initiated by S. Lefschetz, and well established by the late 1950's. In fact, Lefschetz properties of Artinian algebras are algebraic generalizations of the Hard Lefschetz property of the cohomology ring of a smooth projective complex variety. The investigation of the Lefschetz properties of Artinian algebras was started in the mid 1980's and nowadays is a very active area of research. Although there were limited developments on this topic in the 20th century, in the last years this topic has attracted increasing attention from mathematicians of different areas, such as commutative algebra, algebraic geometry, combinatorics, algebraic topology and representation theory. One of the main features of the WLP and the SLP is their ubiquity and the quite surprising and still not completely understood relations with other themes, including linear configurations, interpolation problems, vector bundle theory, plane partitions, splines, $d$-webs, differential geometry, coding theory, digital image processing, physics and the theory of statistical designs, etc. among others. dc.title Lefschetz Properties in Algebra, Geometry and Combinatorics (hybrid meeting) dc.identifier.doi 10.14760/OWR-2020-31 local.series.id OWR-2020-31 local.subject.msc 05 local.subject.msc 06 local.subject.msc 13 local.subject.msc 14 local.subject.msc 17 local.date-range 27 Sep - 03 Oct 2020 local.workshopcode 2040a local.workshoptitle Lefschetz Properties in Algebra, Geometry and Combinatorics (hybrid meeting) local.organizers Martina Juhnke-Kubitzke, Osnabrück; Juan Migliore, Notre Dame; Rosa Miró-Roig, Barcelona; Justyna Szpond, Krakow local.report-name Workshop Report 2020,31 local.opc-photo-id 2040a local.publishers-doi 10.4171/OWR/2020/31 local.ems-reference Juhnke-Kubitzke Martina, Migliore Juan C., Miró-Roig Rosa Maria, Szpond Justyna: Lefschetz Properties in Algebra, Geometry and Combinatorics. Oberwolfach Rep. 17 (2020), 1539-1600. doi: 10.4171/OWR/2020/31
﻿

Report