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 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 |
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010105 | Group Theory and Generalisations | 100 |
Professional Experience
UON Appointment
Dates | Title | Organisation / Department |
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25/04/2014 - | Professor | University of Newcastle School of Mathematical and Physical Sciences Australia |
Academic appointment
Dates | Title | Organisation / Department |
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1/04/2009 - 1/01/2015 | Fellow - APF (ARC) | University of Newcastle School of Mathematical and Physical Sciences Australia |
Membership
Dates | Title | Organisation / Department |
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Associate Editor - Australian Mathematical Society | Australian mathematical society Australia |
Invitations
Participant
Year | Title / Rationale |
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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 in-press, details are shown in italics.
Chapter (1 outputs)
Year | Citation | Altmetrics | Link |
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2003 | Willis GA, 'Harmonic Analysis and amenability', Introduction to Banach Algebras, Operators and Harmonic Analysis, CUP, Cambridge 321 (2003) [B2] |
Journal article (52 outputs)
Year | Citation | Altmetrics | Link | ||||||
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2015 | Willis GA, 'The scale and tidy subgroups for endomorphisms of totally disconnected locally compact groups', MATHEMATISCHE ANNALEN, 361 403-442 (2015)
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2015 | Banks C, Elder M, Willis GA, 'Simple groups of automorphisms of trees determined by their actions on finite subtrees', JOURNAL OF GROUP THEORY, 18 235-261 (2015)
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2014 | Hofmann KH, Willis GA, 'Continuity characterizing totally disconnected locally compact groups', Journal of Lie Theory, 25 1-7 (2014) [C1] For a locally compact group G and its compact space SUB(G) of closed subgroups let ¿G : G ! SUB(G) denote the function which attaches to an element g of G the closed subgroup hgi generated by it. It is shown that G is totally disconnected if and only if G is continuous. Several other functions which associate with an element of G in a natural way a closed subgroup of G are discussed with respect to their continuity in totally disconnected locally compact groups. | ||||||||
2014 | Caprace P-E, Reid CD, Willis GA, 'Limits of contraction groups and the tits core', Journal of Lie Theory, 24 957-967 (2014) [C1]
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2014 | Willis GA, 'The nub of an automorphism of a totally disconnected, locally compact group', Ergodic Theory and Dynamical Systems, 34 1365-1394 (2014) [C1]
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2013 | Shalom Y, Willis GA, 'Commensurated Subgroups of Arithmetic Groups, Totally Disconnected Groups and Adelic Rigidity', GEOMETRIC AND FUNCTIONAL ANALYSIS, 23 1631-1683 (2013) [C1]
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2013 | Caprace P-E, Reid CD, Willis GA, 'Locally normal subgroups of simple locally compact groups', Comptes Rendus Mathematique, 351 657-661 (2013) [C1]
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2012 | Baumgartner U, Moller RG, Willis GA, 'Hyperbolic groups have flat-rank at most 1', Israel Journal of Mathematics, 190 365-388 (2012) [C1]
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2012 | Willis GA, 'Probability measures on semigroups: Convolution products, random walks and random matrices [Book Review]', SIAM Review, 54 414-416 (2012) [C3] | ||||||||
2010 | Baumgartner U, Schlichting G, Willis GA, 'Geometric characterization of flat groups of automorphisms', Groups, Geometry, and Dynamics, 4 1-13 (2010) [C1]
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2010 | Ghahramani F, Read CJ, Willis GA, 'Closed ideal structure and cohomological properties of certain radical Banach algebras', Proceedings of the London Mathematical Society, 100 533-559 (2010) [C1]
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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, 141-169 (2010) [C1]
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2009 | Baumgartner 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]
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2007 | Baumgartner U, Remy B, Willis GA, 'Flat rank of automorphism groups of buildings', Transformation Groups, 12 413-436 (2007) [C1]
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2007 | Willis GA, 'Compact open subgroups in simple totally disconnected groups', Journal of Algebra, 312 405-417 (2007) [C1]
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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 1443-1465 (2006) [C1]
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2006 | Baumgartner U, Willis GA, 'The direction of an automorphism of a totally disconnected locally compact group', Mathematische Zeitschrift, 252 393-428 (2006) [C1]
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2006 | Baumgartner 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]
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2004 | Willis GA, 'A noncommutative half-angle formula', Bulletin of Australian Mathematical Society, 69 369-382 (2004) [C1]
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2004 | Abdollahi A, Rejali A, Willis GA, 'Group Properties characterised by configurations', Illinois Journal of Mathematics, 48 861-873 (2004) [C1]
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2004 | Baumgartner U, Willis GA, 'Contraction groups and scales of automorphisms of totally disconnected locally compact groups', Israel Journal of Mathematics, 142 221-248 (2004) [C1]
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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 1-35 (2004) [C1]
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2001 | Rosenblatt JM, Willis GA, 'Weak convergence is not strong convergence for amenable groups', Canadian Math. Bull., 44 231-241 (2001) [C1]
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2001 | Willis GA, 'Further properties of the scale function on a totally disconnected group', Journal of Algebra, 237 142-164 (2001) [C1]
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2001 | Willis 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]
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2001 | Willis GA, 'Factorization in finite-codimensional ideals of group algebras', Proc. London Math. Soc., 82 676-700 (2001) [C1]
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2001 | Kepert AG, Willis G, 'Scale Functions and Tree Ends', Journal of Australian Mathematics Society, 70 273-292 (2001) [C1]
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2001 | Glockner H, Willis GA, 'Uniscalar p-adic Lie groups', FORUM MATHEMATICUM, 13 413-421 (2001)
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2001 | Glockner H, Willis GA, 'Uniscalar p-adic Lie groups', Forum Math, 13 273-292 (2001) [C1]
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2000 | Willis 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]
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2000 | Willis GA, Ghahramani F, Runde V, 'Derivations on Group Algebras', Proceedings of the London Mathematical Society, 80 360-390 (2000) [C1]
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2000 | Willis GA, 'An extension of a non-commutative Choquet-Deny Theorem', Proceedings of the American Mathematical Society, 128 111-118 (2000) [C1]
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Show 49 more journal articles |
Review (2 outputs)
Year | Citation | Altmetrics | Link |
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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)
EditGrants and Funding
Summary
Number of grants | 17 |
---|---|
Total funding | $2,185,887 |
Click on a grant title below to expand the full details for that specific grant.
20151 grants / $443,900
Scale-Multiplicative Semigroups and Geometry$443,900
Funding body: ARC (Australian Research Council)
Funding body | ARC (Australian Research Council) |
---|---|
Project Team | Professor George Willis, Professor Jacqui Ramagge |
Scheme | Discovery Projects |
Role | Lead |
Funding Start | 2015 |
Funding Finish | 2015 |
GNo | G1400383 |
Type Of Funding | Aust Competitive - Commonwealth |
Category | 1CS |
UON | Y |
20121 grants / $325,000
Theory and applications of symmetries of relational structures$325,000
Funding body: ARC (Australian Research Council)
Funding body | ARC (Australian Research Council) |
---|---|
Project Team | Professor George Willis, Doctor Murray Elder |
Scheme | Discovery Projects |
Role | Lead |
Funding Start | 2012 |
Funding Finish | 2012 |
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, Professor Jacqui Ramagge |
Scheme | Discovery Projects |
Role | Lead |
Funding Start | 2009 |
Funding Finish | 2009 |
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 | 2009 |
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 | |
Scheme | Conference Funding |
Role | Lead |
Funding Start | 2007 |
Funding Finish | 2007 |
GNo | |
Type Of Funding | International - Non Competitive |
Category | 3IFB |
UON | Y |
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 | 2005 |
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 | 2003 |
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 | 2002 |
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 | 1997 |
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 |
Research Supervision
Current Supervision
Commenced | Research Title / Program / Supervisor Type |
---|---|
2014 | Topological Algebra Mathematics, Faculty of Science and Information Technology Principal Supervisor |
2014 | Poisson Boundaries and Random Walks on Totally Disconnected Groups Mathematics, Faculty of Science and Information Technology Principal Supervisor |
2013 | Automorphisms of Totally Disconnected, Locally Compact Groups and the Continuity of the Scale Mathematics, Faculty of Science and Information Technology Principal Supervisor |
2011 | Structure of Discrete and Non-discrete Locally Primitive Groups Acting on Trees Mathematics, Faculty of Science and Information Technology Principal Supervisor |
Past Supervision
Year | Research Title / Program / Supervisor Type |
---|---|
2015 | Tree Actions Associated with the Scale of an Automorphism of a Totally Disconnected Locally Compact Group Mathematics, Faculty of Science and Information Technology Principal Supervisor |
2014 | Fourier and Wavelet Analysis of Clifford-Valued Functions Mathematics, Faculty of Science and Information Technology Co-Supervisor |
2014 | Nonlinear Analysis in Geodesic Spaces Mathematics, Faculty of Science and Information Technology Co-Supervisor |
2011 | Connections Between Geometrical and Fixed Point Properties Mathematics, Faculty of Science and Information Technology Co-Supervisor |
2011 | The Categorical Properties of Higher Rank Graphs and Applications to their Graph Algebras Mathematics, Faculty of Science and Information Technology Principal Supervisor |
2005 | A New Structure for Generalized Metric Spaces - with Applications to Fixed Point Theory Mathematics, Faculty of Science and Information Technology Co-Supervisor |
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 Scale-Multiplicative 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 and Information Technology
Focus area
Mathematics
Contact Details
george.willis@newcastle.edu.au | |
Phone | (02) 4921 5666 |
Fax | (02) 4921 6898 |
Office
Room | V131 |
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Building | Mathematics |
Location | Callaghan University Drive Callaghan, NSW 2308 Australia |