Cohen-Macaulay Rings (Cancelled) (23rit008)

The Banff International Research Station will host the "Cohen-Macaulay Rings" workshop in Banff from April 7 to April 14, 2023.

The aim of our project is to interpret, via algebra, the shape of geometric objects. Empty areas, or holes, in geometric objects - for example the hollow area inside a ball or a doughnut - can be measured via a mathematical tool called homology. The computations to find homology are done via algebraic equations.

Our goal in this research is to find which algebraic equations produce predictable holes in geometric objects. Our particular focus is on the "Cohen-Macaulay'' property, which ensures ideal geometric behaviour under certain algebraic conditions. We plan to investigate what those conditions imply for the relevant algebraic equations.

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. BIRS 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).