Problems in Lefschetz and Liaison Theory (24rit014)


(University of Notre Dame)


The Banff International Research Station will host the "Problems in Lefschetz and Liaison Theory" workshop in Banff from March 24 to March 31, 2024.

Two areas of great interest in Algebraic Geometry and Commutative Algebra are Lefschetz Theory and Liaison Theory. In both cases, very exciting open problems remain, and the team members are senior researchers coming together to attack these problems. The goal is to get a better understanding of some basic structure. Lefschetz Theory provides a study of the algebraic structure in certain objects called rings, and in particular to get a sense of whether multiplication by a polynomial of degree 1 behaves in a way that one could naively expect it to behave, at least in different natural categories of rings. Liaison Theory provides an equivalence relation for geometric objects called varieties in an ambient space called projective space, and one of the open questions involves a geometric understanding of the structure of an equivalence class under this equivalence relation.

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).