Staff Profile

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Career Summary

Biography

My research website is: https://sites.google.com/site/melderau

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.

Qualifications

  • 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

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 https://sites.google.com/site/melderau/papers for more details and my publications.

Languages

  • English

Fields of Research

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

Memberships

Body relevant to professional practice.

  • Member - Australian Mathematical Society

Collaboration

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

José Burillo, Universitat Politècnica de Catalunya, Spain

Laura Ciobanu, Universite de Neuchatel, Switzerland

Sean Cleary, City University of New York, USA

Nick Davis, University of Melbourne, Australia

Will Dison, Bristol University, England

Gillian Elston, Hofstra University, USA

Éric Fusy, LIX, Ecole Polytechnique, France

Susan Hermiller, University of Nebraska, USA

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

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

Teaching expertise

Check my webpage https://sites.google.com/site/melderau/teaching 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.

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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.

Book (1 outputs)

YearCitationAltmetricsLink
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 (27 outputs)

YearCitationAltmetricsLink
2014Elder M, Taback J, 'C-graph automatic groups', Journal of Algebra, 413 289-319 (2014) [C1]
2014Davis N, Elder MJ, Reeves L, 'Non-contracting groups generated by (3,2)-automata', Algebra and Discrete Mathematics, 17 20-32 (2014)
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)
2013Elder M, Elston G, Ostheimer G, 'On groups that have normal forms computable in logspace', Journal of Algebra, 381 260-281 (2013) [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, Rechnitzer A, Wong T, 'On the cogrowth of Thompson's group F', Groups - Complexity - Cryptology, 4 301-320 (2012) [C1]
2012Elder MJ, 'A short introduction to self-similar groups', Gazette of the Australian Mathematical Society, 39 125-133 (2012) [C2]
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, Rechnitzer A, 'Some geodesic problems for finitely generated groups', Groups Complexity Cryptology, 2 223-229 (2010) [C1]
2010Cleary S, Elder M, Rechnitzer A, Taback J, 'Random subgroups of Thompson's group F', GROUPS GEOMETRY AND DYNAMICS, 4 91-126 (2010) [C1]
2010Elder M, Fusy E, Rechnitzer A, 'Counting elements and geodesics in Thompson's group F', JOURNAL OF ALGEBRA, 324 102-121 (2010) [C1]
2009Dison W, Elder M, Riley TR, Young R, 'THE DEHN FUNCTION OF STALLINGS' GROUP', GEOMETRIC AND FUNCTIONAL ANALYSIS, 19 406-422 (2009) [C1]
2008Elder M, Kambites M, Ostheimer G, 'ON GROUPS AND COUNTER AUTOMATA', INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 18 1345-1364 (2008) [C1]
2006Elder M, 'Permutations generated by a stack of depth 2 and an infinite stack in series', ELECTRONIC JOURNAL OF COMBINATORICS, 13 (2006) [C1]
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]
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, Hermiller S, 'Minimal almost convexity', JOURNAL OF GROUP THEORY, 8 239-266 (2005) [C1]
2005Elder M, 'Regular geodesic languages and the falsification by fellow traveler property', ALGEBRAIC AND GEOMETRIC TOPOLOGY, 5 129-134 (2005) [C1]
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 24 more

Conference (1 outputs)

YearCitationAltmetricsLink
2007Elder MJ, 'G-automata, counter languages and the Chomsky hierarchy', Proceedings of Groups St Andrews 2005, London Mathematical Society Lecture Note Series, St Andrews, Scotland (2007) [E1]
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Grants and Funding

Summary

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
SchemeRole
Visiting FellowshipChief Investigator
Total AmountFunding StartFunding Finish
$10,00020142014
GNo:G1401050

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

Project Team
Doctor Murray Elder
SchemeRole
Near Miss GrantChief Investigator
Total AmountFunding StartFunding Finish
$10,00020142014
GNo:G1301377

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

Project Team
Doctor Murray Elder
SchemeRole
PVC Conference Assistance GrantChief Investigator
Total AmountFunding StartFunding Finish
$2,00020142014
GNo:G1401186

2013 (1 grants)

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

Project Team
Doctor Murray Elder
SchemeRole
Future Fellowship SupportChief Investigator
Total AmountFunding StartFunding Finish
$24,00020132016
GNo:G1301119

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 ProjectsInvestigator
Total AmountFunding StartFunding Finish
$325,00020122014
GNo:G1100080

2011 (3 grants)

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

Project Team
Doctor Murray Elder
SchemeRole
Future FellowshipsChief Investigator
Total AmountFunding StartFunding Finish
$565,46820112015
GNo:G1100435

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
SchemeRole
Discovery ProjectsChief Investigator
Total AmountFunding StartFunding Finish
$20,70020112013
GNo:G1001059

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

Project Team
Doctor Murray Elder
SchemeRole
New Staff GrantChief Investigator
Total AmountFunding StartFunding Finish
$3,00020112011
GNo:G1001071
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Research Supervision

Number of current supervisions3
Total current UoN PhD EFTSL1.5

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)Co-SupervisorTopological Algebra
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
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Dr Murray Elder

Work Phone(02) 4921 7472
Fax(02) 4921 6898
Email
PositionARC Future Fellowship
School of Mathematical and Physical Sciences
Faculty of Science and Information Technology
The University of Newcastle, Australia
Focus AreaMathematics
Office
V125,
Mathematics Building,
Callaghan
University Drive
Callaghan NSW 2308
Australia
URL:www.newcastle.edu.au/profile/murray-elder
Linksites.google.com/site/melderau/