Max Carter is a second-year Bachelor of Mathematics student at the University of Newcastle majoring in pure and applied mathematics. During his studies, Max has developed a strong interest in pure mathematics, specifically in topics within abstract algebra, combinatorics and analysis. Max has aspirations of pursuing a postgraduate research degree once he completes his undergraduate studies. In his spare time, Max is a keen mountain-bike racer; he enjoys training and competing in events.
Free Products of Graphs
Symmetries of graphs are 0-dimensional, and such symmetries are investigated through the algebraic technique of totally disconnected, locally compact groups. In this project we are interested in highly symmetric, infinite graphs and one way to form such graphs is by gluing together infinitely many copies of finite graphs by using the notion of a free product of graphs. There are a number of different definitions for a free product of graphs in the literature and in this project we aim to compare these definitions alongside a new definition made in the theory of totally disconnected, locally compact groups.