Date/Time Date(s) - 04/11/202511:30 am - 12:30 pm
Location: Online
Speaker: John Lim (Clemson)
Title: Square-free monomial ideals via open neighborhoods of graphs.
Abstract: A key branch of commutative algebra, combinatorial commutative algebra, focuses on the study of square-free monomial ideals using combinatorial structures. Many techniques have been developed to analyze these ideals, particularly through the use of simplicial complexes and (hyper)graphs. This talk explores square-free monomial ideals through the lens of open neighborhood ideals of finite simple graphs. We will explore which types of tree graphs have a Cohen-Macaulay open neighborhood ideal, and how these ideals and their corresponding graphs arise in different algebraic or combinatorial settings. Furthermore, we will answer what types of square-free monomial ideals can be realized as the open neighborhood ideal of a finite simple graph.