Associate Professor of Mathematics Courtney Gibbons recently published "A Hypergraph Characterization of Nearly Complete Intersections" in the Springer volume Women in Commutative Algebra with five undergraduate co-authors, including Chiara Bondi '22.
The paper provides a way to encode a square-free monomial ideal as a hypergraph, then use the hypergraph's structure to determine if the ideal is a nearly complete intersection. The team also developed a method for using the hypergraph's skeleton to calculate the free resolution of its associated nearly complete intersection ideal, providing a combinatorial interpretation of classical techniques in homological algebra.
Gibbons posed the paper's central research question as a visiting REU mentor for the Clemson COURAGE 2020 virtual REU (where Bondi was joined by undergraduate team members Yuye Ke, Spencer Martin, Shrunal Pothagoni, and Ada Stelzer, all from different institutions). The main result builds on research done by Charlie Miller '20 and former Visiting Assistant Professor of Mathematics Branden Stone.
