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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

CodeDescriptionPercentage
010105Group Theory And Generalisations100

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
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Highlighted Publications

For publications that are currently unpublished or in-press, details are shown in italics.

YearCitationAltmetricsLink
2004Willis GA, 'Tidy subgroups for commuting automorphisms of totally disconnected groups: An analogue of simultaneous triangularisation of Matrices', New York Journal of Mathematics, 10 1-35 (2004) [C1]
2001Willis GA, 'Further properties of the scale function on a totally disconnected group', Journal of Algebra, 237 142-164 (2001) [C1]
2004Baumgartner U, Willis GA, 'Contraction groups and scales of automorphisms of totally disconnected locally compact groups', Israel Journal of Mathematics, 142 221-248 (2004) [C1]
2001Willis GA, 'Factorization in finite-codimensional ideals of group algebras', Proc. London Math. Soc., 82 676-700 (2001) [C1]

Publications

For publications that are currently unpublished or in-press, details are shown in italics.

Click on a category title below to expand the list of citations for that specific category.

Chapter (1 outputs)

YearCitationAltmetricsLink
2003Willis GA, 'Harmonic Analysis and amenability', Introduction to Banach Algebras, Operators and Harmonic Analysis, CUP, Cambridge 321 (2003) [B2]

Journal article (51 outputs)

YearCitationAltmetricsLink
2014Willis GA, 'The nub of an automorphism of a totally disconnected, locally compact group', Ergodic Theory and Dynamical Systems, 34 1365-1394 (2014) [C1]
2014Caprace P-E, Reid CD, Willis GA, 'Limits of contraction groups and the tits core', Journal of Lie Theory, 24 957-967 (2014) [C1]

Co-authors: COLIN D REID

2014Hofmann KH, Willis GA, 'Continuity characterizing totally disconnected locally compact groups', Journal of Lie Theory, 25 1-7 (2014)
2014Willis GA, 'The scale and tidy subgroups for endomorphisms of totally disconnected locally compact groups', Mathematische Annalen, (2014)
2013Caprace P-E, Reid CD, Willis GA, 'Locally normal subgroups of simple locally compact groups', Comptes Rendus Mathematique, 351 657-661 (2013) [C1]
2013Shalom Y, Willis GA, 'Commensurated Subgroups of Arithmetic Groups, Totally Disconnected Groups and Adelic Rigidity', GEOMETRIC AND FUNCTIONAL ANALYSIS, 23 1631-1683 (2013) [C1]
2012Baumgartner U, Moller RG, Willis GA, 'Hyperbolic groups have flat-rank at most 1', Israel Journal of Mathematics, 190 365-388 (2012) [C1]
2012Willis GA, 'Probability measures on semigroups: Convolution products, random walks and random matrices [Book Review]', SIAM Review, 54 414-416 (2012) [C3]
2010Ghahramani F, Read CJ, Willis GA, 'Closed ideal structure and cohomological properties of certain radical Banach algebras', Proceedings of the London Mathematical Society, 100 533-559 (2010) [C1]
2010Baumgartner U, Schlichting G, Willis GA, 'Geometric characterization of flat groups of automorphisms', Groups, Geometry, and Dynamics, 4 1-13 (2010) [C1]
2010Glockner H, Willis GA, 'Classification of the simple factors appearing in composition series of totally disconnected contraction groups', Journal Fur Die Reine Und Angewandte Mathematik, 141-169 (2010) [C1]
2009Baumgartner U, Laca M, Ramagge J, Willis GA, 'Hecke algebras from groups acting on trees and HNN extensions', Journal of Algebra, 321 3065-3088 (2009) [C1]
2007Baumgartner U, Remy B, Willis GA, 'Flat rank of automorphism groups of buildings', Transformation Groups, 12 413-436 (2007) [C1]
2007Willis GA, 'Compact open subgroups in simple totally disconnected groups', Journal of Algebra, 312 405-417 (2007) [C1]
2006Baumgartner U, Ramagge J, Willis GA, 'A compactly generated group whose Hecke algebras admit no bounds on their representations', Glasgow Mathematical Journal, 48 193-201 (2006) [C1]
2006Dani SG, Shah NA, Willis GA, 'Locally compact groups with dense orbits under Z(d)-actions by automorphisms', Ergodic Theory and Dynamical Systems, 26 1443-1465 (2006) [C1]
2006Baumgartner U, Willis GA, 'The direction of an automorphism of a totally disconnected locally compact group', Mathematische Zeitschrift, 252 393-428 (2006) [C1]
2004Willis GA, 'A noncommutative half-angle formula', Bulletin of Australian Mathematical Society, 69 369-382 (2004) [C1]
2004Willis GA, 'Tidy subgroups for commuting automorphisms of totally disconnected groups: An analogue of simultaneous triangularisation of Matrices', New York Journal of Mathematics, 10 1-35 (2004) [C1]
2004Baumgartner U, Willis GA, 'Contraction groups and scales of automorphisms of totally disconnected locally compact groups', Israel Journal of Mathematics, 142 221-248 (2004) [C1]
2004Abdollahi A, Rejali A, Willis GA, 'Group Properties characterised by configurations', Illinois Journal of Mathematics, 48 861-873 (2004) [C1]
2001Kepert AG, Willis G, 'Scale Functions and Tree Ends', Journal of Australian Mathematics Society, 70 273-292 (2001) [C1]

Co-authors: ANDREW KEPERT

2001Rosenblatt JM, Willis GA, 'Weak convergence is not strong convergence for amenable groups', Canadian Math. Bull., 44 231-241 (2001) [C1]
2001Willis GA, 'The number of prime factors of the scale function on a compactly generated group is finite', Bulletin London Mathematical Society, 33 168-174 (2001) [C1]
2001Willis GA, 'Further properties of the scale function on a totally disconnected group', Journal of Algebra, 237 142-164 (2001) [C1]
2001Willis GA, 'Factorization in finite-codimensional ideals of group algebras', Proc. London Math. Soc., 82 676-700 (2001) [C1]
2001Glockner H, Willis GA, '$p$-adic Lie groups', Forum Math, 13 273-292 (2001) [C1]
2001Glockner H, Willis GA, 'Uniscalar p-adic Lie groups', FORUM MATHEMATICUM, 13 413-421 (2001)
2000Willis GA, Ghahramani F, Runde V, 'Derivations on Group Algebras', Proceedings of the London Mathematical Society, 80 360-390 (2000) [C1]
2000Willis GA, 'An extension of a non-commutative Choquet-Deny Theorem', Proceedings of the American Mathematical Society, 128 111-118 (2000) [C1]
2000Willis GA, Loy RJ, Read CJ, Runde V, 'Amenable and weakly amenable Banach algebras with compact multiplication', Journal of Functional Analysis, 171 78-114 (2000) [C1]
1997Gronbaek N, Willis GA, 'Embedding nilpotent finite dimensional Banach algebras into amenable Banach algebras', JOURNAL OF FUNCTIONAL ANALYSIS, 145 99-107 (1997)
1997Ross KA, Willis G, 'Riemann sums and modular functions on locally compact groups', PACIFIC JOURNAL OF MATHEMATICS, 180 325-331 (1997)
1997Willis G, 'Totally disconnected, nilpotent, locally compact groups', BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 55 143-146 (1997)
1996Ghahramani F, Loy RJ, Willis GA, 'Amenability and weak amenability of second conjugate Banach algebras', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 124 1489-1497 (1996)
1996Lau ATM, Loy RJ, Willis GA, 'Amenability of Banach and C-*-algebras on locally compact groups', STUDIA MATHEMATICA, 119 161-178 (1996)
1996Jaworski W, Rosenblatt J, Willis G, 'Concentration functions in locally compact groups', MATHEMATISCHE ANNALEN, 305 673-691 (1996)
1995WILLIS GA, 'COMPRESSIBLE OPERATORS AND THE CONTINUITY OF HOMOMORPHISMS FROM ALGEBRAS OF OPERATORS', STUDIA MATHEMATICA, 115 251-259 (1995)
1995WILLIS G, 'TOTALLY DISCONNECTED GROUPS AND PROOFS OF CONJECTURES OF HOFMANN AND MUKHERJEA', BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 51 489-494 (1995)
1994WILLIS G, 'THE STRUCTURE OF TOTALLY DISCONNECTED, LOCALLY COMPACT-GROUPS', MATHEMATISCHE ANNALEN, 300 341-363 (1994)
1994DALES HG, LOY RJ, WILLIS GA, 'HOMOMORPHISMS AND DERIVATIONS FROM B(E)', JOURNAL OF FUNCTIONAL ANALYSIS, 120 201-219 (1994)
1994Gronbaek N, Johnson BE, Willis GA, 'AMENABILITY OF BANACH ALGEBRAS OF COMPACT OPERATORS', ISRAEL JOURNAL OF MATHEMATICS, 87 289-324 (1994)
1994LOY RJ, WILLIS GA, 'THE APPROXIMATION PROPERTY AND NILPOTENT IDEALS IN AMENABLE BANACH-ALGEBRAS', BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 49 341-346 (1994)
1992Willis GA, 'The compact approximation property does not imply the approximation property', Studia Mathematica, 99-108 (1992)
1991MORAN W, WILLIS GA, 'BOUNDARIES AND MODULAR IDEALS ON LOCALLY COMPACT-GROUPS', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 112 819-827 (1991)
1990WILLIS GA, 'PROBABILITY-MEASURES ON GROUPS AND SOME RELATED IDEALS IN GROUP-ALGEBRAS', JOURNAL OF FUNCTIONAL ANALYSIS, 92 202-263 (1990)
1989LOY RJ, WILLIS GA, 'CONTINUITY OF DERIVATIONS ON B(E) FOR CERTAIN BANACH SPACES-E', JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 40 327-346 (1989)
1988WILLIS GA, 'CONTINUITY OF TRANSLATION INVARIANT LINEAR FUNCTIONALS ON C0(G) FOR CERTAIN LOCALLY COMPACT GROUPS-G', MONATSHEFTE FUR MATHEMATIK, 105 161-164 (1988)
1986WILLIS GA, 'THE CONTINUITY OF DERIVATIONS AND MODULE HOMOMORPHISMS', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 40 299-320 (1986)
1986WILLIS GA, 'TRANSLATION INVARIANT FUNCTIONALS ON LP(G) WHEN G IS NOT AMENABLE', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 41 237-250 (1986)
1982Willis GA, 'Approximate Units in Finite Codimensional Ideals of Group Algebras', Journal of the London Mathematical Society, s2-26 143-154 (1982)
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Review (2 outputs)

YearCitationAltmetricsLink
2002Willis GA, 'The Honors Class: Hilbert's Problems and Their Solvers; Benjamin H. Yandell', Australian Mathematical Society Gazette (2002) [D1]
2002Willis GA, 'Banach algebras and the general theory of *-algebras: Vol II, *-algebras', Bulletin of London Mathematical Society (2002) [D1]

Conference (3 outputs)

YearCitationAltmetricsLink
2007Glockner H, Willis GA, 'Directions of automorphisms of lie groups over local fields compared to the directions of lie algebra automorphisms', Topology Proceedings, Castellon, Spain (2007) [E1]
2004Willis GA, 'A canonical form for automorphisms of totally disconnected locally compact groups', Proceedings of a Workshop at the Erwin Schrodinger Institute, Vienna (2004) [E1]
2002Gloeckner H, Willis GA, 'Topologization of Hecke C*-algebras', Proceedings of Spring Topology and Dynamics Conference, Auburn, Alabama, USA (2002) [E1]
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Grants and Funding

Summary

Number of grants17
Total funding$2,185,887

- Indicates that the researcher may be seeking students for this project.

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

2015 (1 grants)

Scale-Multiplicative Semigroups and Geometry$443,900
Funding Body: ARC (Australian Research Council)

Project Team
Professor George Willis, Professor Jacqui Ramagge
SchemeRole
Discovery ProjectsChief Investigator
Total AmountFunding StartFunding Finish
$443,90020152017
GNo:G1400383

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
SchemeRole
Discovery ProjectsChief Investigator
Total AmountFunding StartFunding Finish
$325,00020122014
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, Professor Jacqui Ramagge
SchemeRole
Discovery ProjectsChief Investigator
Total AmountFunding StartFunding Finish
$381,86820092013
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
SchemeRole
Priority Research CentreInvestigator
Total AmountFunding StartFunding Finish
$267,36120092012
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
SchemeRole
Near Miss GrantChief Investigator
Total AmountFunding StartFunding Finish
$20,00020082008
GNo:G0188399

2007 (1 grants)

Totally disconnected groups, graphs and geometry$73,787
Funding Body: Volkswagen Foundation

SchemeRole
Conference fundingChief Investigator
Total AmountFunding StartFunding Finish
$73,78720072007
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
SchemeRole
Linkage International FellowshipChief Investigator
Total AmountFunding StartFunding Finish
$60,00020062006
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
SchemeRole
Discovery ProjectsChief Investigator
Total AmountFunding StartFunding Finish
$234,00020052007
GNo:G0184324

International Conference in Mathematics and Applications, 15-17 December 2005$2,070
Funding Body: University of Newcastle

Project Team
Professor George Willis
SchemeRole
Travel GrantChief Investigator
Total AmountFunding StartFunding Finish
$2,07020052005
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
SchemeRole
Linkage International AwardChief Investigator
Total AmountFunding StartFunding Finish
$28,80020032005
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
SchemeRole
Discovery ProjectsChief Investigator
Total AmountFunding StartFunding Finish
$185,00020022004
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
SchemeRole
Visitor GrantChief Investigator
Total AmountFunding StartFunding Finish
$2,40020022002
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
SchemeRole
Travel GrantChief Investigator
Total AmountFunding StartFunding Finish
$2,50020012001
GNo:G0180986

Prof Fereidoun Ghahramani, From 18 Feb to 21 April 2001$2,055
Funding Body: University of Newcastle

Project Team
Professor George Willis
SchemeRole
Visitor GrantChief Investigator
Total AmountFunding StartFunding Finish
$2,05520012001
GNo:G0180587

2000 (1 grants)

Analysis of radical algebras.$5,000
Funding Body: University of Newcastle

Project Team
Professor George Willis
SchemeRole
Project GrantChief Investigator
Total AmountFunding StartFunding Finish
$5,00020002000
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
SchemeRole
Large GrantChief Investigator
Total AmountFunding StartFunding Finish
$150,00019971999
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
SchemeRole
Travel GrantChief Investigator
Total AmountFunding StartFunding Finish
$2,14619971997
GNo:G0179608
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Research Supervision

Number of current supervisions5
Total current UoN PhD EFTSL2.65

For supervisions undertaken at an institution other that the University of Newcastle, the institution name is listed below the program name.

Current Supervision

CommencedProposed
Completion
ProgramSupervisor TypeResearch Title
20142018PhD (Mathematics)Principal SupervisorClassification of Simple Totally Disconnected Groups.
20142018PhD (Mathematics)Principal SupervisorTopological Algebra
20132017PhD (Mathematics)Principal SupervisorAutomorphisms of Totally Disconnected, Locally Compact Groups and the Continuity of the Scale
20112015PhD (Mathematics)Principal SupervisorStructure of Discrete and Non-discrete Locally Primitive Groups Acting on Trees
20062010PhD (Mathematics)Principal SupervisorTree Actions Associated with the Scale of an Automorphism of a Totally Disconnected Locally Compact Group

Past Supervision

YearProgramSupervisor TypeResearch Title
2014PhD (Mathematics)Co-SupervisorNonlinear Analysis in Geodesic Spaces
2014PhD (Mathematics)Co-SupervisorFourier and Wavelet Analysis of Clifford-Valued Functions
2011PhD (Mathematics)Co-SupervisorConnections Between Geometrical and Fixed Point Properties
2011PhD (Mathematics)Principal SupervisorThe Categorical Properties of Higher Rank Graphs and Applications to their Graph Algebras
2005PhD (Mathematics)Co-SupervisorA New Structure for Generalized Metric Spaces - with Applications to Fixed Point Theory
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Professor George Willis

Work Phone(02) 4921 5666
Fax(02) 4921 6898
Email
PositionProfessor
School of Mathematical and Physical Sciences
Faculty of Science and Information Technology
The University of Newcastle, Australia
Focus AreaMathematics
Office
V131,
Mathematics,
Callaghan
University Drive
Callaghan NSW 2308
Australia
URL:www.newcastle.edu.au/profile/george-willis