Jesse Huang, University of Waterloo
Cohen-Macaulay Modules
Cohen-Macaulay modules are central objects of study in commutative algebra, with deep connections to algebraic geometry, singularity theory, and homological algebra. In this talk, we give a brief overview of the connection between Cohen-Macaulay modules and geometric objects, particularly how these modules can be used to study the local behavior of varieties at singular points. Several classical examples, including modules over regular local rings and isolated singularities, will illustrate the practical utility of Cohen-Macaulay theory in understanding algebraic structures. We will also touch on Cohen-Macaulay modules over toric Gorenstein rings and the role of mirror symmetry in the study of these modules.
MC 5403