Faculty of Science and Information Technology

Associate Professor George Willis

• B.Sc. (1976), BSc. Hons. (1977), University of Adelaide
• Ph.D. (1981), University of Newcastle upon Tyne
  Thesis title: Derivations on group algebras, factorization in cofinite ideals and topologies on B(X).

• Totally disconnected locally compact groups
  A structure theory for these groups is being developed that is beginning to parallel the theory of Lie groups. Totally disconnected groups occur as symmetry groups of discrete structures and the theory has links with other areas of mathematics such as: number theory; harmonic analysis; graph theory; geometry of relational structure such as trees and buildings; CAT (0) and hyperbolic spaces; ergodic theory and dynamical systems; p-adic analysis; finite and profinite groups; and Lie and algebraic groups. The workshop Totally Disconnected Groups, Graphs and Geometry held in Blaubeuren, Germany, from May 7^th-12^th 2008, explored some of these links. The basics of the new structure theory are described at http://en.wikipedia.org/wiki/Totally_disconnected_group
• Beyond the spectrum
  This research aims to develop methods for analyzing radical Banach algebras that would apply in realms beyond the reach of such widely applied spectral methods as: eigenvalues; the spectrum of linear operators; and the Fourier, Laplace and, more generally, Gel'fand transforms.
• Topological algebra
  Other areas of topological algebra of interest include: approximate identities and factorization; random walks on groups; abstract harmonic analysis, cohomology of Banach algebras and amenability; operator algebras; and Banach space approximation properties.

• Computer Assisted Research Mathematics and its Applications (CARMA)
• Functional Analysis

• More than $500,000 in ARC funds in the last 10 years, including: three Discovery Grants; one Linkage International Grant; and one Linkage International Professorial Fellowship Grant.
• A Grant of $44,000 from the Volkswagen Foundation to support the workshop Totally Disconnected Groups, Graphs and Geometry. Grants from AMSI to support conferences Lie Theory, Lattices and Dynamics (Newcastle, 2005) and Amenability in Groups and Algebras (Canberra, 2006).

• Invited Speaker at the British Mathematical Colloquium held at Birmingham in May 2003. Plenary speaker at numerous international research conferences on Banach algebras and geometric group theory.
• Member of the Australian and American Mathematical Societies.

• I teach a range of courses in algebras, analysis and discrete mathematics, from first year to Honours level. Beginning in 2008, I am teaching an Honours course on Topological Groups on the Access Grid.

• I have supervised numerous Honours and Vacation Scholar projects on topics related to totally disconnected groups and Banach algebras and am currently supervising a PhD project.

• Associate editor of the Journal of the Australian Mathematical Society