Staff Profile


Career Summary


My research website is:

I received my PhD from the University of Melbourne in 2001. My supervisor was Prof. Walter Neumann (now at Columbia University, USA) and my topic was automatic and geometric group theory. Since then I have held postdocs, research and teaching positions at Texas A&M University (USA), Tufts University (USA), St Andrews University (Scotland), The University of Wollonong (Australia), Stevens Institute of Technology (USA), The University of Queensland (Australia), and The University of Newcastle (Australia). I currently hold an ARC Future Fellowship at the University of Newcastle from January 2012 until December 2015.


  • Doctor of Philosophy, University of Melbourne, 07/03/2001
  • Master of Science, University of Melbourne, 10/09/1997
  • Postgraduate Diploma, University of Melbourne, 09/12/1995
  • Bachelor of Applied Science, La Trobe University, 06/05/1994


Research keywords

  • Algebra
  • Automata and formal languages
  • Complexity theory
  • Enumerative combinatorics
  • Geometric group theory
  • Group theory
  • Self-similar groups
  • Totally disconnected locally compact groups

Research expertise

My research interests include geometric group theory, complexity theory, automata and language theory, and enumerative combinatorics. Check my webpage for more details and my publications.


  • English

Fields of Research

010105Group Theory And Generalisations70
080201Analysis Of Algorithms And Complexity15
080203Computational Logic And Formal Languages15


Body relevant to professional practice.

  • Member - Australian Mathematical Society
  • Member - American Mathematical Society
  • Member - European Association for Theoretical Computer Science


Fellow ARC
School of Mathematical and Physical Sciences (Australia)
01/01/2012 - 01/12/2015


I have written papers with the following researchers (in alphabetical order)

Michael Albert, University of Otago, New Zealand

Christopher Banks, University of Newcastle, Australia

Martin Bridson, Oxford University, England

Tara Brough, St Andrews, Scotland

José Burillo, Universitat Politècnica de Catalunya, Spain

Ben Burton, University of Queensland, Australia

Laura Ciobanu, Universite de Neuchatel, Switzerland

Sean Cleary, City University of New York, USA

Nick Davis, University of Melbourne, Australia

Volker Diekert, Stuttgart, Germany

Will Dison, Bristol University, England

Gillian Elston, Hofstra University, USA

Éric Fusy, LIX, Ecole Polytechnique, France

Susan Hermiller, University of Nebraska, USA

Arkadius Kalka, Bar-Ilan University, Israel

Mark Kambites, Manchester University, England

Geoffrey Lee, University of Newcastle, Australia

Jon McCammond, University of California Santa Barbara, USA

John Meier, Lafayette College, USA

Gretchen Ostheimer, Hofstra University, USA

Andrew Rechnitzer, University of British Columbia, Canada

Buks van Rensburg, York University, Canada

Lawrence Reeves, University of Melbourne, Australia

Tim Riley, Cornell University, USA

Zoran Šunic, Texas A&M University, USA

Jennifer Taback, Bowdoin University, USA

Stephan Tillmann, University of Sydney, Australia

Paul Westcott, National Australia Bank, Australia

George Willis, University of Newcastle, Australia

Thomas Wong, University of British Columbia, Canada

Robert Young, Courant Institute, USA

Mike Zabrocki, York University, Canada


Teaching expertise

Check my webpage for details of past courses taught and some teaching materials.

I have been lecturing undergraduate and postgrad courses since my first postdoc at Texas A&M in 2000. I have taught in the US, Scottish and Australian systems.



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.

Book (1 outputs)

2005Burillo J, Cleary S, Elder MJ, Taback J, Ventura E, Geometric Methods in Group Theory, American Mathematical Society, Providence, Rhode Island, 230 (2005) [A3]

Journal article (31 outputs)

2015Banks 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)
2014Davis N, Elder MJ, Reeves L, 'Non-contracting groups generated by (3,2)-automata', Algebra and Discrete Mathematics, 17 20-32 (2014) [C1]
2014Elder M, Rechnitzer A, Janse van Rensburg EJ, Wong T, 'The cogrowth series for BS(N, N) is D-finite', International Journal of Algebra and Computation, 24 171-187 (2014) [C1]
2014Elder M, Taback J, 'C-graph automatic groups', Journal of Algebra, 413 289-319 (2014) [C1]
2013Elder M, Elston G, Ostheimer G, 'On groups that have normal forms computable in logspace', Journal of Algebra, 381 260-281 (2013) [C1]
2012Elder MJ, Rechnitzer A, Wong T, 'On the cogrowth of Thompson's group F', Groups - Complexity - Cryptology, 4 301-320 (2012) [C1]
2012Bridson MR, Burillo J, Elder MJ, Sunic Z, 'On groups whose geodesic growth is polynomial', International Journal of Algebra and Computation, 22 (2012) [C1]
2012Elder MJ, 'A short introduction to self-similar groups', Gazette of the Australian Mathematical Society, 39 125-133 (2012) [C2]
2010Elder MJ, Rechnitzer A, 'Some geodesic problems for finitely generated groups', Groups Complexity Cryptology, 2 223-229 (2010) [C1]
2010Cleary S, Elder MJ, Rechnitzer A, Taback J, 'Random subgroups of Thompson's group F', Groups Geometry and Dynamics, 4 91-126 (2010) [C1]
2010Elder MJ, 'A linear-time algorithm to compute geodesics in solvable Baumslag-Solitar groups', Illinois Journal of Mathematics, 54 109-128 (2010) [C1]
2010Elder MJ, Fusy E, Rechnitzer A, 'Counting elements and geodesics in Thompson's group F', Journal of Algebra, 324 102-121 (2010) [C1]
2010Elder M, Rechnitzer A, 'Some geodesic problems in groups', Groups, Complexity, Cryptology, 2 223-229 (2010)
2009Dison W, Elder MJ, Riley TR, Young R, 'The Dehn function of Stallings' group', Geometric and Functional Analysis, 19 406-422 (2009) [C1]
2008Elder MJ, Kambites M, Ostheimer G, 'On groups and counter automata', International Journal of Algebra and Computation, 18 1345-1364 (2008) [C1]
2007Elder MJ, 'G-automata, counter languages and the Chomsky hierarchy', Proceedings of Groups St Andrews 2005, London Mathematical Society Lecture Note Series, 339 (2007) [E1]
2006Albert MH, Elder M, Rechnitzer A, Westcott P, Zabrocki M, 'On the Stanley-Wilf limit of 4231-avoiding permutations and a conjecture of arratia', ADVANCES IN APPLIED MATHEMATICS, 36 96-105 (2006) [C1]
2006Cleary S, Elder M, Taback J, 'Cone types and geodesic languages for lamplighter groups and Thompson's group F', JOURNAL OF ALGEBRA, 303 476-500 (2006) [C1]
2006Elder M, 'Permutations generated by a stack of depth 2 and an infinite stack in series', ELECTRONIC JOURNAL OF COMBINATORICS, 13 (2006) [C1]
2005Elder M, Hermiller S, 'Minimal almost convexity', JOURNAL OF GROUP THEORY, 8 239-266 (2005) [C1]
2005Elder M, 'A context-free and a 1-counter geodesic language for a Baumslag-Solitar group', THEORETICAL COMPUTER SCIENCE, 339 344-371 (2005) [C1]
2005Elder M, 'Regular geodesic languages and the falsification by fellow traveler property', ALGEBRAIC AND GEOMETRIC TOPOLOGY, 5 129-134 (2005) [C1]
2005Elder MJ, Vatter V, 'Problems and Conjectures presented at the Third International Conference on Permutation Patterns, University of Florida, March 7-11, 2005', ArXiv, (2005)
2004Elder M, McCammond J, 'CAT(0) is an algorithmic property', GEOMETRIAE DEDICATA, 107 25-46 (2004) [C1]
2004Elder MJ, 'A non-Hopfian almost convex group', JOURNAL OF ALGEBRA, 271 11-21 (2004) [C1]
2004Elder MJ, 'Ld groups are almost convex and have sub-cubic Dehn function', Algebraic and Geometric Topology, 4 23-29 (2004) [C1]
2003Elder MJ, 'Patterns theory and geodesic automatic structure for a class of groups', INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 13 203-230 (2003) [C1]
2003Elder M, McCammond J, Meier J, 'Combinatorial conditions that imply word-hyperbolicity for 3-manifolds', TOPOLOGY, 42 1241-1259 (2003) [C1]
2003Elder MJ, 'The loop shortening property and almost convexity', GEOMETRIAE DEDICATA, 102 1-18 (2003) [C1]
2002Elder M, McCammond J, 'Curvature testing in 3-dimensional metric polyhedral complexes', EXPERIMENTAL MATHEMATICS, 11 143-158 (2002) [C1]
2002Elder MJ, 'Finiteness and the falsification by fellow traveler property', GEOMETRIAE DEDICATA, 95 103-113 (2002) [C1]
Show 28 more

Grants and Funding


Number of grants8
Total funding$960,168

- 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.

2014 (3 grants)

Faculty Visiting Fellowship 2014$10,000
Funding Body: University of Newcastle - Faculty of Science & IT

Project Team
Doctor Murray Elder
Visiting FellowshipChief Investigator
Total AmountFunding StartFunding Finish

The logical complexity of problems in group theory$10,000
Funding Body: University of Newcastle

Project Team
Doctor Murray Elder
Near Miss GrantChief Investigator
Total AmountFunding StartFunding Finish

Faculty PVC Conference Assistance Grant 2014$2,000
Funding Body: University of Newcastle - Faculty of Science & IT

Project Team
Doctor Murray Elder
PVC Conference Assistance GrantChief Investigator
Total AmountFunding StartFunding Finish

2013 (1 grants)

DVC(R) Research Support for Future Fellow (FT11)$24,000
Funding Body: University of Newcastle

Project Team
Doctor Murray Elder
Future Fellowship SupportChief Investigator
Total AmountFunding StartFunding Finish

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
Discovery ProjectsInvestigator
Total AmountFunding StartFunding Finish

2011 (3 grants)

Algorithmic and computational advances in geometric group theory$565,468
Funding Body: ARC (Australian Research Council)

Project Team
Doctor Murray Elder
Future FellowshipsChief Investigator
Total AmountFunding StartFunding Finish

Generic complexity in computational topology: Breaking through the bottlenecks$20,700
Funding Body: ARC (Australian Research Council)

Project Team
Dr Benjamin Burton, Doctor Murray Elder, Dr Stephan Tillmann
Discovery ProjectsChief Investigator
Total AmountFunding StartFunding Finish

Efficient computations in infinite groups$3,000
Funding Body: University of Newcastle

Project Team
Doctor Murray Elder
New Staff GrantChief Investigator
Total AmountFunding StartFunding Finish

Research Supervision

Number of current supervisions2
Total current UoN PhD EFTSL1

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

Current Supervision

ProgramSupervisor TypeResearch Title
20132017PhD (Mathematics)Co-SupervisorAutomorphisms of Totally Disconnected, Locally Compact Groups and the Continuity of the Scale
20112015PhD (Mathematics)Co-SupervisorStructure of Discrete and Non-discrete Locally Primitive Groups Acting on Trees

Dr Murray Elder

Work Phone(02) 4921 7472
Fax(02) 4921 6898
PositionARC Future Fellowship
School of Mathematical and Physical Sciences
Faculty of Science and Information Technology
The University of Newcastle, Australia
Focus AreaMathematics
Mathematics Building,
University Drive
Callaghan NSW 2308