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Professor George Willis

Professor

School of Mathematical and Physical Sciences (Mathematics)

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.

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


Qualifications

  • PhD, University of Newcastle upon Tyne - England
  • Bachelor of Science (Honours), University of Adelaide
  • Bachelor of Science, University of Adelaide

Keywords

  • Algebra
  • Functional analysis
  • Group theory

Fields of Research

Code Description Percentage
010105 Group Theory and Generalisations 100

Professional Experience

UON Appointment

Title Organisation / Department
Professor University of Newcastle
School of Mathematical and Physical Sciences
Australia

Academic appointment

Dates Title Organisation / Department
1/04/2009 - 1/01/2015 Fellow - APF (ARC) University of Newcastle
School of Mathematical and Physical Sciences
Australia

Membership

Dates Title Organisation / Department
1/01/2013 -  Editor - Journal of the Australian Mathematical Society Australian mathematical society
Australia

Awards

Member

Year Award
2014 Fellow of the Australian Academy of Science
Australian Academy of Sciences

Invitations

Participant

Year Title / Rationale
2013 Locally compact groups beyond Lie theory
Plenary speaker at a conference on `Locally comnpact groups beyond Lie theory' which follows on a conference that I organized in 2007. Interest in this subject has grown substantially following advances made in some of my papers in the 1990's. It is rapidly gaining momentum significant new progress is now being made.
2007 Banach Algebras 2007
Organisation: Laval University, Quebec Description: Plenary speaker at the major international conference on Banach algebras held every two years.
2007 London Mathematical Society Lecturer
Organisation: London Mathematical Society Description: Award of funds covering travel and accommodation to deliver at least three seminar talks at three UK institutions.
2006 `Lie Groups, Representations and Discrete Mathematics' Workshop
Organisation: Princeton Insitute for Advanced Study Description: Two invitations to speak in research seminar at the Institute for Advanced Study, Princeton, New Jersey. The only person to speak twice in this seminar on 2006.
2003 British Mathematical Colloquium
Organisation: London Mathematical Society Description: Invited speaker at the annual meeting for British mathematics.

PhD Examiner

Year Title / Rationale
2007 Topological transitivity of group actions
Organisation: La Trobe University
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Grants and Funding

Summary

Number of grants 19
Total funding $5,071,140

Click on a grant title below to expand the full details for that specific grant.


20171 grants / $2,837,519

Zero-dimensional symmetry and its ramifications$2,837,519

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Professor George Willis
Scheme Australian Laureate Fellowships
Role Lead
Funding Start 2017
Funding Finish 2022
GNo G1601240
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

20161 grants / $7,853

2016 International Visitor from University of Oxford, UK$7,853

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Professor George Willis, Professor John Wilson
Scheme International Research Visiting Fellowship
Role Lead
Funding Start 2016
Funding Finish 2016
GNo G1501031
Type Of Funding Internal
Category INTE
UON Y

20151 grants / $459,265

Scale-Multiplicative Semigroups and Geometry$459,265

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Professor George Willis, Prof Jacqui Ramagge
Scheme Discovery Projects
Role Lead
Funding Start 2015
Funding Finish 2017
GNo G1400383
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

20121 grants / $349,516

Theory and applications of symmetries of relational structures$349,516

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Professor George Willis, Associate Professor Murray Elder
Scheme Discovery Projects
Role Lead
Funding Start 2012
Funding Finish 2014
GNo G1100080
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

20092 grants / $649,229

Totally disconnected groups in algebra and geometry$381,868

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Professor George Willis, Prof Jacqui Ramagge
Scheme Discovery Projects
Role Lead
Funding Start 2009
Funding Finish 2013
GNo G0188711
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

Computer Assisted Research Mathematics and its Applications$267,361

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Laureate Professor Jon Borwein, Conjoint Professor Natashia Boland, Associate Professor Brailey Sims, Professor George Willis
Scheme Priority Research Centre
Role Investigator
Funding Start 2009
Funding Finish 2012
GNo G0189866
Type Of Funding Internal
Category INTE
UON Y

20081 grants / $20,000

New Applications of Totally Disconnected Groups$20,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Professor George Willis, Dr Jacqueline Ramagge
Scheme Near Miss Grant
Role Lead
Funding Start 2008
Funding Finish 2008
GNo G0188399
Type Of Funding Internal
Category INTE
UON Y

20071 grants / $73,787

Totally disconnected groups, graphs and geometry$73,787

Funding body: VolkswagenStiftung

Funding body VolkswagenStiftung
Project Team

George Willis

Scheme Conference Funding
Role Lead
Funding Start 2007
Funding Finish 2007
GNo
Type Of Funding International - Non Competitive
Category 3IFB
UON N

20061 grants / $60,000

Totally disconnected groups, representations and discrete mathematics.$60,000

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Professor George Willis
Scheme Linkage International Fellowship
Role Lead
Funding Start 2006
Funding Finish 2006
GNo G0185350
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

20052 grants / $236,070

Geometric representation of small-rank totally disconnected groups$234,000

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Professor George Willis, Dr Jacqueline Ramagge
Scheme Discovery Projects
Role Lead
Funding Start 2005
Funding Finish 2007
GNo G0184324
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

International Conference in Mathematics and Applications, 15-17 December 2005$2,070

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Professor George Willis
Scheme Travel Grant
Role Lead
Funding Start 2005
Funding Finish 2005
GNo G0185950
Type Of Funding Internal
Category INTE
UON Y

20031 grants / $28,800

Lie-type methods for totally disconnected groups.$28,800

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Professor George Willis
Scheme Linkage International Award
Role Lead
Funding Start 2003
Funding Finish 2005
GNo G0182680
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

20022 grants / $187,400

Totally disconnected groups and their algebras$185,000

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Professor George Willis, Dr Jacqueline Ramagge
Scheme Discovery Projects
Role Lead
Funding Start 2002
Funding Finish 2004
GNo G0181137
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

Visit of Dr Niels Laustsen, from 11 May 2002 to 21 June 2002$2,400

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Professor George Willis
Scheme Visitor Grant
Role Lead
Funding Start 2002
Funding Finish 2002
GNo G0181911
Type Of Funding Internal
Category INTE
UON Y

20012 grants / $4,555

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

Funding body University of Newcastle
Project Team Professor George Willis
Scheme Travel Grant
Role Lead
Funding Start 2001
Funding Finish 2001
GNo G0180986
Type Of Funding Internal
Category INTE
UON Y

Prof Fereidoun Ghahramani, From 18 Feb to 21 April 2001$2,055

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Professor George Willis
Scheme Visitor Grant
Role Lead
Funding Start 2001
Funding Finish 2001
GNo G0180587
Type Of Funding Internal
Category INTE
UON Y

20001 grants / $5,000

Analysis of radical algebras.$5,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Professor George Willis
Scheme Project Grant
Role Lead
Funding Start 2000
Funding Finish 2000
GNo G0178919
Type Of Funding Internal
Category INTE
UON Y

19972 grants / $152,146

Symmetry and a structure theory for totally disconnected, locally compact groups.$150,000

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Professor George Willis
Scheme Large Grant
Role Lead
Funding Start 1997
Funding Finish 1999
GNo G0176189
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

Random Walks and Discrete Potential Theory, Cortona, Italy, 22-28 June 1997$2,146

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Professor George Willis
Scheme Travel Grant
Role Lead
Funding Start 1997
Funding Finish 1997
GNo G0179608
Type Of Funding Internal
Category INTE
UON Y
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Research Supervision

Number of supervisions

Completed7
Current3

Total current UON EFTSL

PhD1.15

Current Supervision

Commenced Level of Study Research Title Program Supervisor Type
2017 PhD Optimization, Iterated Projections and the Douglas-Rachford Method in the Construction of Multidimensional Wavelets PhD (Mathematics), Faculty of Science, The University of Newcastle Co-Supervisor
2014 PhD Poisson Boundaries and Random Walks on Totally Disconnected Groups PhD (Mathematics), Faculty of Science, The University of Newcastle Principal Supervisor
2014 PhD Teaching and Learning in Tertiary Algebra PhD (Mathematics), Faculty of Science, The University of Newcastle Principal Supervisor

Past Supervision

Year Level of Study Research Title Program Supervisor Type
2017 PhD On the Interconnectedness , via Random Walks , of Cogrowth Rates and the Følner Function PhD (Mathematics), Faculty of Science, The University of Newcastle Co-Supervisor
2015 PhD Tree Actions Associated with the Scale of an Automorphism of a Totally Disconnected Locally Compact Group PhD (Mathematics), Faculty of Science, The University of Newcastle Principal Supervisor
2014 PhD Fourier and Wavelet Analysis of Clifford-Valued Functions PhD (Mathematics), Faculty of Science, The University of Newcastle Co-Supervisor
2014 PhD Nonlinear Analysis in Geodesic Spaces PhD (Mathematics), Faculty of Science, The University of Newcastle Co-Supervisor
2011 PhD Connections Between Geometrical and Fixed Point Properties PhD (Mathematics), Faculty of Science, The University of Newcastle Co-Supervisor
2011 PhD The Categorical Properties of Higher Rank Graphs and Applications to their Graph Algebras PhD (Mathematics), Faculty of Science, The University of Newcastle Principal Supervisor
2005 PhD A New Structure for Generalized Metric Spaces - with Applications to Fixed Point Theory PhD (Mathematics), Faculty of Science, The University of Newcastle Co-Supervisor
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Research Collaborations

The map is a representation of a researchers co-authorship with collaborators across the globe. The map displays the number of publications against a country, where there is at least one co-author based in that country. Data is sourced from the University of Newcastle research publication management system (NURO) and may not fully represent the authors complete body of work.

Country Count of Publications
Australia 55
Canada 9
United States 6
Germany 5
United Kingdom 4
More...
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News

George Willis

UON researchers awarded $4.5m in ARC fellowships

June 5, 2017

Three University of Newcastle (UON) researchers have today been awarded more than $4.5m in prestigious Australian Research Council (ARC) fellowships.

Australian Research Council (ARC)

ARC Discovery Project funding success

November 21, 2014

Professor George Willis has been awarded more than $443,000 in ARC Discovery Project funding commencing in 2015 for his research project Scale-Multiplicative Semigroups and Geometry.

Professor George Willis

Academy honours top UON mathematician

March 26, 2014

The Australian Academy of Science has today elected University of Newcastle mathematician Professor George Willis as a Fellow, the most senior honour a scientist can receive in Australia.

Professor George Willis

Position

Professor
School of Mathematical and Physical Sciences
Faculty of Science

Focus area

Mathematics

Contact Details

Email george.willis@newcastle.edu.au
Phone (02) 4921 5666
Fax (02) 4921 6898

Office

Room V126
Building Mathematics Building
Location Callaghan
University Drive
Callaghan, NSW 2308
Australia
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