Joint C&O/PureMath Colloquium - Soffia Arnadottir

Title: Graphs in algebra and algebra in graphs

Abstract:

How do algebraic properties of a graph relate to its graph theoretic properties? What are algebraic properties of graphs? What does the spectrum of a graph tell us about its structure? What is a Cayley graph?In this talk I will discuss at least a non-empty subset of these questions and give some partial answers to them. Terms like 'bipartite', 'strongly regular' and 'vertex transitive' might be thrown around, and there is even a possibility we learn something about the eigenvectors of Cayley graphs of abelian groups (spoiler: they are the characters of the group).