Professor George Willis
Professor
School of Mathematical and Physical Sciences (Mathematics)
 Email:george.willis@newcastle.edu.au
 Phone:(02) 4921 5666
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 allembracing 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 infinitedimensional spaces may be approximated by finitedimensional 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; padic analysis; finite and profinite groups; and Lie and algebraic groups. The workshop Totally Disconnected Groups, Graphs and Geometry held in Blaubeuren, Germany, from May 7th12th 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 
Publications
For publications that are currently unpublished or inpress, details are shown in italics.
Chapter (1 outputs)
Year  Citation  Altmetrics  Link 

2003  Willis GA, 'Harmonic Analysis and amenability', Introduction to Banach Algebras, Operators and Harmonic Analysis, CUP, Cambridge 321 (2003) [B2] 
Journal article (65 outputs)
Year  Citation  Altmetrics  Link  

2016 
Baumgartner U, Ramagge J, Willis GA, 'Scalemultiplicative semigroups and geometry: Automorphism groups of trees', Groups, Geometry, and Dynamics, 10 10511075 (2016) Â© European Mathematical Society.A scalemultiplicative semigroup in a totally disconnected, locally compact group G is one for which the restriction of the scale function on G is... [more] Â© European Mathematical Society.A scalemultiplicative semigroup in a totally disconnected, locally compact group G is one for which the restriction of the scale function on G is multiplicative The maximal scalemultiplicative semigroups in groups acting 2transitively on the set of ends of trees without leaves are determined and shown to correspond to geometric features of the tree.


2015 
Willis GA, 'The scale and tidy subgroups for endomorphisms of totally disconnected locally compact groups', MATHEMATISCHE ANNALEN, 361 403442 (2015) [C1]


2015 
Banks C, Elder M, Willis GA, 'Simple groups of automorphisms of trees determined by their actions on finite subtrees', JOURNAL OF GROUP THEORY, 18 235261 (2015) [C1]


2015 
Hofmann KH, Willis GA, 'Continuity Characterizing Totally Disconnected Locally Compact Groups', JOURNAL OF LIE THEORY, 25 17 (2015) [C1]


2014 
Caprace PE, Reid CD, Willis GA, 'Limits of contraction groups and the tits core', Journal of Lie Theory, 24 957967 (2014) [C1]


2014 
Willis GA, 'The scale and tidy subgroups for endomorphisms of totally disconnected locally compact groups', Mathematische Annalen, 361 403442 (2014) Â© 2014, SpringerVerlag Berlin Heidelberg.The scale of an endomorphism, (Formula presented.), of a totally disconnected, locally compact group G is the minimum index (Formula pre... [more] Â© 2014, SpringerVerlag Berlin Heidelberg.The scale of an endomorphism, (Formula presented.), of a totally disconnected, locally compact group G is the minimum index (Formula presented.), for U a compact, open subgroup of G. A structural characterization of subgroups at which the minimum is attained is established. This characterization extends the notion of subgroup tidy for a from the previously understood case when a is an automorphism to the case when a is merely an endomorphism.


2014 
Willis GA, 'The nub of an automorphism of a totally disconnected, locally compact group', Ergodic Theory and Dynamical Systems, 34 13651394 (2014) [C1]


2013 
Shalom Y, Willis GA, 'Commensurated Subgroups of Arithmetic Groups, Totally Disconnected Groups and Adelic Rigidity', GEOMETRIC AND FUNCTIONAL ANALYSIS, 23 16311683 (2013) [C1]


2013 
Caprace PE, Reid CD, Willis GA, 'Locally normal subgroups of simple locally compact groups', Comptes Rendus Mathematique, 351 657661 (2013) [C1]


2012 
Baumgartner U, Moller RG, Willis GA, 'Hyperbolic groups have flatrank at most 1', Israel Journal of Mathematics, 190 365388 (2012) [C1]


2012  Willis GA, 'Probability measures on semigroups: Convolution products, random walks and random matrices [Book Review]', SIAM Review, 54 414416 (2012) [C3]  
2010 
Baumgartner U, Schlichting G, Willis GA, 'Geometric characterization of flat groups of automorphisms', Groups, Geometry, and Dynamics, 4 113 (2010) [C1]


2010 
Ghahramani F, Read CJ, Willis GA, 'Closed ideal structure and cohomological properties of certain radical Banach algebras', Proceedings of the London Mathematical Society, 100 533559 (2010) [C1]


2010 
Glockner H, Willis GA, 'Classification of the simple factors appearing in composition series of totally disconnected contraction groups', Journal Fur Die Reine Und Angewandte Mathematik, 141169 (2010) [C1]


2009 
Baumgartner U, Laca M, Ramagge J, Willis GA, 'Hecke algebras from groups acting on trees and HNN extensions', Journal of Algebra, 321 30653088 (2009) [C1]


2007 
Baumgartner U, Remy B, Willis GA, 'Flat rank of automorphism groups of buildings', Transformation Groups, 12 413436 (2007) [C1]


2007 
Willis GA, 'Compact open subgroups in simple totally disconnected groups', Journal of Algebra, 312 405417 (2007) [C1]


2006 
Dani SG, Shah NA, Willis GA, 'Locally compact groups with dense orbits under Z(d)actions by automorphisms', Ergodic Theory and Dynamical Systems, 26 14431465 (2006) [C1]


2006 
Baumgartner U, Willis GA, 'The direction of an automorphism of a totally disconnected locally compact group', Mathematische Zeitschrift, 252 393428 (2006) [C1]


2006 
Baumgartner U, Ramagge J, Willis GA, 'A compactly generated group whose Hecke algebras admit no bounds on their representations', Glasgow Mathematical Journal, 48 193201 (2006) [C1]


2004 
Willis GA, 'A noncommutative halfangle formula', Bulletin of Australian Mathematical Society, 69 369382 (2004) [C1]


2004 
Abdollahi A, Rejali A, Willis GA, 'Group Properties characterised by configurations', Illinois Journal of Mathematics, 48 861873 (2004) [C1]


2004 
Baumgartner U, Willis GA, 'Contraction groups and scales of automorphisms of totally disconnected locally compact groups', Israel Journal of Mathematics, 142 221248 (2004) [C1]


2004 
Willis GA, 'Tidy subgroups for commuting automorphisms of totally disconnected groups: An analogue of simultaneous triangularisation of Matrices', New York Journal of Mathematics, 10 135 (2004) [C1]


2001 
Glockner H, Willis GA, 'Uniscalar padic Lie groups', FORUM MATHEMATICUM, 13 413421 (2001) [C1]


2001 
Rosenblatt JM, Willis GA, 'Weak convergence is not strong convergence for amenable groups', Canadian Math. Bull., 44 231241 (2001) [C1]


2001 
Willis GA, 'Further properties of the scale function on a totally disconnected group', Journal of Algebra, 237 142164 (2001) [C1]


2001 
Willis GA, 'The number of prime factors of the scale function on a compactly generated group is finite', Bulletin London Mathematical Society, 33 168174 (2001) [C1]


2001 
Willis GA, 'Factorization in finitecodimensional ideals of group algebras', Proc. London Math. Soc., 82 676700 (2001) [C1]


2001 
Kepert AG, Willis G, 'Scale Functions and Tree Ends', Journal of Australian Mathematics Society, 70 273292 (2001) [C1]


2000 
Willis GA, Loy RJ, Read CJ, Runde V, 'Amenable and weakly amenable Banach algebras with compact multiplication', Journal of Functional Analysis, 171 78114 (2000) [C1]


2000 
Willis GA, Ghahramani F, Runde V, 'Derivations on Group Algebras', Proceedings of the London Mathematical Society, 80 360390 (2000) [C1]


2000 
Willis GA, 'An extension of a noncommutative ChoquetDeny Theorem', Proceedings of the American Mathematical Society, 128 111118 (2000) [C1]


Show 62 more journal articles 
Review (2 outputs)
Year  Citation  Altmetrics  Link 

2002  Willis GA, 'The Honors Class: Hilbert's Problems and Their Solvers; Benjamin H. Yandell', Australian Mathematical Society Gazette (2002) [D1]  
2002  Willis GA, 'Banach algebras and the general theory of *algebras: Vol II, *algebras', Bulletin of London Mathematical Society (2002) [D1] 
Conference (3 outputs)
EditResearch Supervision
Number of supervisions
Total current UON EFTSL
Current Supervision
Commenced  Level of Study  Research Title / Program / Supervisor Type 

2014  PhD 
Poisson Boundaries and Random Walks on Totally Disconnected Groups PhD (Mathematics), Faculty of Science, The University of Newcastle Principal Supervisor 
2014  PhD 
Topological Algebra PhD (Mathematics), Faculty of Science, The University of Newcastle Principal Supervisor 
2013  PhD 
On the Interconnectedness , via Random Walks , of Cogrowth Rates and the FÃ¸lner Function PhD (Mathematics), Faculty of Science, The University of Newcastle CoSupervisor 
Past Supervision
Year  Level of Study  Research Title / Program / Supervisor Type 

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 CliffordValued Functions PhD (Mathematics), Faculty of Science, The University of Newcastle CoSupervisor 
2014  PhD 
Nonlinear Analysis in Geodesic Spaces PhD (Mathematics), Faculty of Science, The University of Newcastle CoSupervisor 
2011  PhD 
Connections Between Geometrical and Fixed Point Properties PhD (Mathematics), Faculty of Science, The University of Newcastle CoSupervisor 
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 CoSupervisor 
Research Collaborations
The map is a representation of a researchers coauthorship with collaborators across the globe. The map displays the number of publications against a country, where there is at least one coauthor 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... 
News
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 ScaleMultiplicative Semigroups and Geometry.
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
george.willis@newcastle.edu.au  
Phone  (02) 4921 5666 
Fax  (02) 4921 6898 
Office
Room  V131 

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