Comparing algebraic invariants of graph-defined ideals

This project will study a relationship between graph (network) theory and algebraic objects known as ideals. Graph theory is a major branch of mathematics with diverse applications to society and industry, including transportation system modelling, social media marketing, and statistical models, among others. To study a graph, one can use the algebraic structure of a ideal to encode important information about the properties of the graph. This encoding comes in the form of certain numbers, known as invariants, that are associated to the ideal. The regularity, projective dimension, and h-polynomial are three algebraic invariants that are widely studied in the literature. This project aims to investigate certain graph properties by computing and comparing these invariants. The value of the regularity, in particular, is closely related to the existence of cycles in the corresponding graph, which is of great interest in both pure and applied graph theory. This project will leverage supercomputer resources to compute these invariants and develop new results for several classes of graphs and ideals. Such computations and results will be invaluable to other researchers as they formulate questions for future study, and provide the fundamental knowledge necessary to further develop connections between this area and industry.

Faculty Supervisor:

Adam Van Tuyl

Student:

Partner:

Shizuoka University

Discipline:

Mathematics

Sector:

Education

University:

McMaster University

Program: