Staff Profile
Career Summary
Biography
A continuing theme of George Willis's research since he received a PhD from the University of Newcastle upon Tyne in 1981 has been the interaction between algebra and topology. However, the focus of his research has shifted from analysis to algebra, and he has also moved from being primarily a problem solver to being a creator of new mathematics.
His early work was in functional analysis, which is an all-embracing framework for such fundamental techniques as Fourier and Laplace transforms and the spectral theory of linear operators. In a subject called `automatic continuity', he demonstrated that algebraic properties determine topological ones in many circumstances and he has also established the strongest known results that distinguish between approximate and exact factorization. Most notably, he showed in 1991 that the compact approximation property for Banach spaces does not imply the approximation property, thus answering a question that had been open for 20 years. This result sheds light on how well infinite-dimensional spaces may be approximated by finite-dimensional ones.
In his more recent work, since moving to Newcastle (Australia) in 1992, he has done much to create the modern structure theory of totally disconnected, locally compact groups by introducing the notions of scale, tidy subgroups and flatness. Some of this work has been surveyed in the book `Banach algebras and the general theory of *-algebras', Volume II, Cambridge University Press (2001) by T. W. Palmer, where it is called `Willis theory' and said to provide `a whole new level of insight'. It has also been described in Mathematical Reviews as offering `genuinely original insights' into a `notoriously intractable' subject. Links with ergodic theory, geometric group theory and with arithmetic groups are currently being explored, amongst others.
Qualifications
- PhD, University of Newcastle upon Tyne - England
- Bachelor of Science (Honours), University of Adelaide
- Bachelor of Science, University of Adelaide
Research
Research keywords
- Algebra
- Functional analysis
- Group theory
Research expertise
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 7th-12th 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
Fields of Research
| Code | Description | Percentage |
|---|---|---|
| 010105 | Group Theory And Generalisations | 100 |
Memberships
Editorial Board.
- Associate Editor - Australian Mathematical Society
Appointments
| ARC - Aust Research Fellowship (level B C) ARC (Australia) | 01/01/2006 - 01/12/2006 |
| Fellowship APF Australian Research Council (Australia) | 01/04/2009 |
Invitations
| Locally comnpact groups beyond Lie theory Université Louvain la Neuve, Belgium (Conference Presentation - non published.) | 2013 |
| Banach Algebras 2007 Laval University, Quebec, Canada (Conference Presentation - non published.) | 2007 |
| British Mathematical Colloquium London Mathematical Society, United Kingdom (Conference Presentation - non published.) | 2003 |
| `Lie Groups, Representations and Discrete Mathematics' Workshop Princeton Insitute for Advanced Study, United States (Invitations to speak at Princeton IAS) | 2006 |
| Topological transitivity of group actions La Trobe University, Australia (PHD Examiner.) | 2007 |
| London Mathematical Society Lecturer London Mathematical Society, United Kingdom ( ) | 2007 |
Grants and Funding
Summary
| Number of grants | 16 |
|---|---|
| Total funding | $1,741,987 |
For project grants received where the lead institution is other than the University of Newcastle, details are shown in italics.
Click on a grant title below to expand the full details for that specific grant.
2012 (1 grants)
Theory and applications of symmetries of relational structures$325,000
Funding Body: ARC (Australian Research Council)
| Project Team | ||
|---|---|---|
| Professor George Willis, Doctor Murray Elder | ||
| Scheme | Role | |
| Discovery Projects | Chief Investigator | |
| Total Amount | Funding Start | Funding Finish |
| $325,000 | 2012 | 2014 |
| GNo:G1100080 | ||
2009 (2 grants)
Totally disconnected groups in algebra and geometry$381,868
Funding Body: ARC (Australian Research Council)
| Project Team | ||
|---|---|---|
| Professor George Willis, Assoc. Prof Jacqui Ramagge | ||
| Scheme | Role | |
| Discovery Projects | Chief Investigator | |
| Total Amount | Funding Start | Funding Finish |
| $381,868 | 2009 | 2013 |
| GNo:G0188711 | ||
Computer Assisted Research Mathematics and its Applications$267,361
Funding Body: University of Newcastle
| Project Team | ||
|---|---|---|
| Laureate Professor Jon Borwein, Professor Natashia Boland, Associate Professor Brailey Sims, Professor George Willis | ||
| Scheme | Role | |
| Priority Research Centre | Investigator | |
| Total Amount | Funding Start | Funding Finish |
| $267,361 | 2009 | 2012 |
| GNo:G0189866 | ||
2008 (1 grants)
New Applications of Totally Disconnected Groups$20,000
Funding Body: University of Newcastle
| Project Team | ||
|---|---|---|
| Professor George Willis, Dr Jacqueline Ramagge | ||
| Scheme | Role | |
| Near Miss Grant | Chief Investigator | |
| Total Amount | Funding Start | Funding Finish |
| $20,000 | 2008 | 2008 |
| GNo:G0188399 | ||
2007 (1 grants)
Totally disconnected groups, graphs and geometry$73,787
Funding Body: Volkswagen Foundation
| Scheme | Role | |
|---|---|---|
| Conference funding | Chief Investigator | |
| Total Amount | Funding Start | Funding Finish |
| $73,787 | 2007 | 2007 |
| GNo:5656980 | ||
2006 (1 grants)
Totally disconnected groups, representations and discrete mathematics.$60,000
Funding Body: ARC (Australian Research Council)
| Project Team | ||
|---|---|---|
| Professor George Willis | ||
| Scheme | Role | |
| Linkage International Fellowship | Chief Investigator | |
| Total Amount | Funding Start | Funding Finish |
| $60,000 | 2006 | 2006 |
| GNo:G0185350 | ||
2005 (2 grants)
Geometric representation of small-rank totally disconnected groups$234,000
Funding Body: ARC (Australian Research Council)
| Project Team | ||
|---|---|---|
| Professor George Willis, Dr Jacqueline Ramagge | ||
| Scheme | Role | |
| Discovery Projects | Chief Investigator | |
| Total Amount | Funding Start | Funding Finish |
| $234,000 | 2005 | 2007 |
| GNo:G0184324 | ||
International Conference in Mathematics and Applications, 15-17 December 2005$2,070
Funding Body: University of Newcastle
| Project Team | ||
|---|---|---|
| Professor George Willis | ||
| Scheme | Role | |
| Travel Grant | Chief Investigator | |
| Total Amount | Funding Start | Funding Finish |
| $2,070 | 2005 | 2005 |
| GNo:G0185950 | ||
2003 (1 grants)
Lie-type methods for totally disconnected groups.$28,800
Funding Body: ARC (Australian Research Council)
| Project Team | ||
|---|---|---|
| Professor George Willis | ||
| Scheme | Role | |
| Linkage International Award | Chief Investigator | |
| Total Amount | Funding Start | Funding Finish |
| $28,800 | 2003 | 2005 |
| GNo:G0182680 | ||
2002 (2 grants)
Totally disconnected groups and their algebras$185,000
Funding Body: ARC (Australian Research Council)
| Project Team | ||
|---|---|---|
| Professor George Willis, Dr Jacqueline Ramagge | ||
| Scheme | Role | |
| Discovery Projects | Chief Investigator | |
| Total Amount | Funding Start | Funding Finish |
| $185,000 | 2002 | 2004 |
| GNo:G0181137 | ||
Visit of Dr Niels Laustsen, from 11 May 2002 to 21 June 2002$2,400
Funding Body: University of Newcastle
| Project Team | ||
|---|---|---|
| Professor George Willis | ||
| Scheme | Role | |
| Visitor Grant | Chief Investigator | |
| Total Amount | Funding Start | Funding Finish |
| $2,400 | 2002 | 2002 |
| GNo:G0181911 | ||
2001 (2 grants)
1. International Conf on Banach Algebras & Cohomology, England, 25-28 June. 2. Random Walks & Geometry, Austria, June/July. 3. BALTICON 2001, Denmark, 5-18 Aug$2,500
Funding Body: University of Newcastle
| Project Team | ||
|---|---|---|
| Professor George Willis | ||
| Scheme | Role | |
| Travel Grant | Chief Investigator | |
| Total Amount | Funding Start | Funding Finish |
| $2,500 | 2001 | 2001 |
| GNo:G0180986 | ||
Prof Fereidoun Ghahramani, From 18 Feb to 21 April 2001$2,055
Funding Body: University of Newcastle
| Project Team | ||
|---|---|---|
| Professor George Willis | ||
| Scheme | Role | |
| Visitor Grant | Chief Investigator | |
| Total Amount | Funding Start | Funding Finish |
| $2,055 | 2001 | 2001 |
| GNo:G0180587 | ||
2000 (1 grants)
Analysis of radical algebras.$5,000
Funding Body: University of Newcastle
| Project Team | ||
|---|---|---|
| Professor George Willis | ||
| Scheme | Role | |
| Project Grant | Chief Investigator | |
| Total Amount | Funding Start | Funding Finish |
| $5,000 | 2000 | 2000 |
| GNo:G0178919 | ||
1997 (2 grants)
Symmetry and a structure theory for totally disconnected, locally compact groups.$150,000
Funding Body: ARC (Australian Research Council)
| Project Team | ||
|---|---|---|
| Professor George Willis | ||
| Scheme | Role | |
| Large Grant | Chief Investigator | |
| Total Amount | Funding Start | Funding Finish |
| $150,000 | 1997 | 1999 |
| GNo:G0176189 | ||
Random Walks and Discrete Potential Theory, Cortona, Italy, 22-28 June 1997$2,146
Funding Body: University of Newcastle
| Project Team | ||
|---|---|---|
| Professor George Willis | ||
| Scheme | Role | |
| Travel Grant | Chief Investigator | |
| Total Amount | Funding Start | Funding Finish |
| $2,146 | 1997 | 1997 |
| GNo:G0179608 | ||
Research Supervision
| Number of current supervisions | 5 |
|---|---|
| Total current UoN PhD EFTSL | 1.9 |
For supervisions undertaken at an institution other that the University of Newcastle, details are shown in italics, and the institution name is listed below the program name.
Current Supervision
| Commenced | Proposed Completion | Program | Supervisor Type | Research Title |
|---|---|---|---|---|
| 2013 | 2017 | PhD (Mathematics) | Principal Supervisor | Commuting Automorphisms of Compact, Totally Disconnected Groups |
| 2011 | 2015 | PhD (Mathematics) | Principal Supervisor | Structure of Discrete and Non-discrete Locally Primitive Groups Acting on Trees |
| 2009 | 2013 | PhD (Mathematics) | Co-Supervisor | Fourier and Wavelet Analysis of Clifford-Valued Functions |
| 2006 | 2010 | PhD (Mathematics) | Principal Supervisor | On Automorphism Groups of Trees |
| 2003 | 2012 | PhD (Mathematics) | Co-Supervisor | Metric Fixed Point THeory and Related Banach Space Geometry |
Past Supervision
| Year | Program | Supervisor Type | Research Title |
|---|---|---|---|
| 2011 | PhD (Mathematics) | Co-Supervisor | Connections Between Geometrical and Fixed Point Properties |
| 2011 | PhD (Mathematics) | Principal Supervisor | The Categorical Properties of Higher Rank Graphs and Applications to their Graph Algebras |
| 2005 | PhD (Mathematics) | Co-Supervisor | A New Structure for Generalized Metric Spaces - with Applications to Fixed Point Theory |
Professor George Willis
| Work Phone | (02) 4921 5666 |
|---|---|
| Fax | (02) 4921 6898 |
| George.Willis@newcastle.edu.au | |
| Position | Professor Head of Mathematics School of Mathematical and Physical Sciences Faculty of Science and Information Technology |
| Focus Area | Mathematics |
| Office | V131, Mathematics, Callaghan University Drive Callaghan NSW 2308 Australia |
| URL: | www.newcastle.edu.au/profile/george-willis |
