Our proposed research project is concerned with those C*-algebras that are generated by discrete groups. In particular, we will study the various properties, such as amenability, of these groups and their corresponding C*-algebras, and summarize the current theory regarding them. We would then like to investigate these properties within the context of the group C*-algebra of the Richard Thompson group; a rather unusual example of a discrete group, proposed in 1965 as the first potential counterexample to the now-disproven von Neumann conjecture on non-amenable groups.
The University of New South Wales
Daniel Dunmore is a third-year undergraduate student at the University of New South Wales, where he is currently pursuing an Advanced Science (Honours) degree, with majors in mathematics and physics. His academic interests lie broadly in the areas of pure mathematics, mathematical physics and theoretical physics, with a particular focus on topics in abstract algebra, such as operator algebras and group theory.