Dr Murray Elder

ARC Future Fellowship

School of Mathematical and Physical Sciences (Mathematics)

Career Summary

Biography

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

I currently hold an ARC Future Fellowship from January 2012 until December 2015, and in January 2016 I take up a continuing position as Senior Lecturer.

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.

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. 

Collaborations
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


Qualifications

  • Doctor of Philosophy, University of Melbourne
  • Bachelor of Applied Science, La Trobe University
  • Postgraduate Diploma, University of Melbourne
  • Master of Science, University of Melbourne

Keywords

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

Fields of Research

Code Description Percentage
010105 Group Theory and Generalisations 70
080201 Analysis of Algorithms and Complexity 15
080203 Computational Logic and Formal Languages 15

Professional Experience

Academic appointment

Dates Title Organisation / Department
29/05/2015 - 29/06/2015 Lecturer The University of Queensland
School of Mathematics and Physics
Australia
1/01/2012 -  Fellow ARC
ARC - Discovery - Future Fellowships
University of Newcastle
School of Mathematical and Physical Sciences
Australia
1/01/2012 - 1/12/2015 ARC Future Fellow University of Newcastle
School of Mathematical and Physical Sciences
Australia
1/01/2011 - 1/12/2011 Lecturer University of Newcastle
School of Mathematical and Physical Sciences
Australia
1/08/2006 - 1/01/2008 Assistant Professor Stevens Institute of Technology
Department of Mathematical Sciences
United States
1/01/2006 - 1/06/2006 Lecturer University of Wollongong
School of Mathematics and Applied Statistics
Australia
1/02/2004 - 1/08/2005 Research Fellow University of St. Andrews
Centre for Interdisciplinary Research in Computational Algebra
United Kingdom
1/09/2002 - 1/01/2004 Visiting Assistant Professor Tufts University
Mathematics
United States
1/09/2000 - 1/07/2002 Visiting Assistant Professor Texas A&M University
Mathematics
United States

Membership

Dates Title Organisation / Department
1/01/2015 -  Membership European Association for Theoretical Computer Science
United Kingdom
1/01/2001 -  Membership American Mathematical Society
United States
1/01/1997 - 31/12/2023 Membership Australian mathematical society
Australia
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Publications

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


Book (1 outputs)

Year Citation Altmetrics Link
2005 Burillo 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 (36 outputs)

Year Citation Altmetrics Link
2015 Elder MJ, Lee G, Rechnitzer A, 'Permutations generated by a depth 2 stack and an infinite stack in series are algebraic', Electronic Journal of Combinatorics, 22 (2015)
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)
DOI 10.1515/jgth-2014-0041 Author URL
Co-authors George Willis
2015 Burillo J, Elder M, 'Metric properties of Baumslag¿Solitar groups', International Journal of Algebra and Computation, 1-13 (2015)
DOI 10.1142/S0218196715500198
2015 Ciobanu L, Diekert V, Elder MJ, 'Solution Sets for Equations over Free Groups are EDT0L Languages', Lecture Notes in Computer Science, 9135 134-145 (2015)
DOI 10.1007/978-3-662-47666-6_11
2015 Elder MJ, Rechnitzer A, Janse van Rensberg EJ, 'Random Sampling of Trivial Words in Finitely Presented Groups', Experimental Mathematics, (2015)
DOI 10.1080/10586458.2015.1005853
2015 Elder M, Lee G, Rechnitzer A, 'Permutations generated by a depth 2 stack and an infinite stack in series are algebraic', Electronic Journal of Combinatorics, 22 (2015)

We prove that the class of permutations generated by passing an ordered sequence 12... n through a stack of depth 2 and an in nite stack in series is in bi-jection with an unambig... [more]

We prove that the class of permutations generated by passing an ordered sequence 12... n through a stack of depth 2 and an in nite stack in series is in bi-jection with an unambiguous context-free language, where a permutation of length n is encoded by a string of length 3n. It follows that the sequence counting the number of permutations of each length has an algebraic generating function. We use the explicit context-free grammar to compute the generating function:(formula presented) where cn is the number of permutations of length n that can be generated, and (formula presented) is a simple variant of the Catalan generating function. This in turn implies that (formula presented)

2014 Elder M, Taback J, 'C-graph automatic groups', Journal of Algebra, 413 289-319 (2014) [C1]
DOI 10.1016/j.jalgebra.2014.04.021 Author URL
Citations Scopus - 1
2014 Elder 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]
DOI 10.1142/S0218196714500106
2014 Davis N, Elder MJ, Reeves L, 'Non-contracting groups generated by (3,2)-automata', Algebra and Discrete Mathematics, 17 20-32 (2014) [C1]
Author URL
2013 Elder M, Elston G, Ostheimer G, 'On groups that have normal forms computable in logspace', Journal of Algebra, 381 260-281 (2013) [C1]
DOI 10.1016/j.jalgebra.2013.01.036 Author URL
Citations Scopus - 2Web of Science - 1
2012 Bridson MR, Burillo J, Elder MJ, Sunic Z, 'On groups whose geodesic growth is polynomial', International Journal of Algebra and Computation, 22 (2012) [C1]
DOI 10.1142/S0218196712500488
Citations Scopus - 2
2012 Elder MJ, 'A short introduction to self-similar groups', Gazette of the Australian Mathematical Society, 39 125-133 (2012) [C2]
2012 Elder MJ, Rechnitzer A, Wong T, 'On the cogrowth of Thompson's group F', Groups - Complexity - Cryptology, 4 301-320 (2012) [C1]
Citations Scopus - 2
2010 Cleary S, Elder MJ, Rechnitzer A, Taback J, 'Random subgroups of Thompson's group F', Groups Geometry and Dynamics, 4 91-126 (2010) [C1]
DOI 10.4172/GGD/76
Citations Scopus - 4Web of Science - 3
2010 Elder MJ, Rechnitzer A, 'Some geodesic problems for finitely generated groups', Groups Complexity Cryptology, 2 223-229 (2010) [C1]
Citations Scopus - 4
2010 Elder M, Rechnitzer A, 'Some geodesic problems in groups', Groups, Complexity, Cryptology, 2 223-229 (2010)
DOI 10.1515/GCC.2010.014
Citations Scopus - 4
2010 Elder MJ, 'A linear-time algorithm to compute geodesics in solvable Baumslag-Solitar groups', Illinois Journal of Mathematics, 54 109-128 (2010) [C1]
DOI 10.1214/10-AAP256
Citations Scopus - 4Web of Science - 2
2010 Elder MJ, Fusy E, Rechnitzer A, 'Counting elements and geodesics in Thompson's group F', Journal of Algebra, 324 102-121 (2010) [C1]
DOI 10.1016/j.jalgebra.2010.02.035
Citations Scopus - 2Web of Science - 1
2009 Dison W, Elder MJ, Riley TR, Young R, 'The Dehn function of Stallings' group', Geometric and Functional Analysis, 19 406-422 (2009) [C1]
DOI 10.1007/s00039-009-0011-9
Citations Web of Science - 1
2008 Elder MJ, Kambites M, Ostheimer G, 'On groups and counter automata', International Journal of Algebra and Computation, 18 1345-1364 (2008) [C1]
DOI 10.1142/S0218196708004901
Citations Scopus - 7Web of Science - 6
2007 Elder MJ, 'G-automata, counter languages and the Chomsky hierarchy', Proceedings of Groups St Andrews 2005, London Mathematical Society Lecture Note Series, 339 (2007) [E1]
2006 Cleary 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]
DOI 10.1016/j.jalgebra.2005.11.016 Author URL
Citations Web of Science - 1
2006 Albert 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]
DOI 10.1016/j.aam.2005.05.007 Author URL
Citations Web of Science - 10
2006 Elder M, 'Permutations generated by a stack of depth 2 and an infinite stack in series', ELECTRONIC JOURNAL OF COMBINATORICS, 13 (2006) [C1]
Author URL
Citations Web of Science - 1
2005 Elder M, 'A context-free and a 1-counter geodesic language for a Baumslag-Solitar group', THEORETICAL COMPUTER SCIENCE, 339 344-371 (2005) [C1]
DOI 10.1016/j.tcs.2005.03.026 Author URL
Citations Web of Science - 3
2005 Elder MJ, Vatter V, 'Problems and Conjectures presented at the Third International Conference on Permutation Patterns, University of Florida, March 7-11, 2005', ArXiv, (2005)
2005 Elder M, Hermiller S, 'Minimal almost convexity', JOURNAL OF GROUP THEORY, 8 239-266 (2005) [C1]
DOI 10.1515/jgth.2005.8.2.239 Author URL
Citations Web of Science - 2
2005 Elder M, 'Regular geodesic languages and the falsification by fellow traveler property', ALGEBRAIC AND GEOMETRIC TOPOLOGY, 5 129-134 (2005) [C1]
DOI 10.2140/agt.2005.5.129 Author URL
Citations Web of Science - 3
2004 Elder MJ, 'A non-Hopfian almost convex group', JOURNAL OF ALGEBRA, 271 11-21 (2004) [C1]
DOI 10.1016/j.jalgebra.2003.04.004 Author URL
Citations Web of Science - 2
2004 Elder M, McCammond J, 'CAT(0) is an algorithmic property', GEOMETRIAE DEDICATA, 107 25-46 (2004) [C1]
DOI 10.1023/B:GEOM.0000049096.63639.e3 Author URL
Citations Web of Science - 3
2004 Elder MJ, 'Ld groups are almost convex and have sub-cubic Dehn function', Algebraic and Geometric Topology, 4 23-29 (2004) [C1]
2003 Elder M, McCammond J, Meier J, 'Combinatorial conditions that imply word-hyperbolicity for 3-manifolds', TOPOLOGY, 42 1241-1259 (2003) [C1]
DOI 10.1016/S0040-9383(02)00100-3 Author URL
Citations Web of Science - 4
2003 Elder MJ, 'The loop shortening property and almost convexity', GEOMETRIAE DEDICATA, 102 1-18 (2003) [C1]
DOI 10.1023/B:GEOM.0000006500.20513.d2 Author URL
Citations Web of Science - 4
2003 Elder MJ, 'Patterns theory and geodesic automatic structure for a class of groups', INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 13 203-230 (2003) [C1]
DOI 10.1142/S0218196703001274 Author URL
Citations Web of Science - 2
2002 Elder MJ, 'Finiteness and the falsification by fellow traveler property', GEOMETRIAE DEDICATA, 95 103-113 (2002) [C1]
DOI 10.1023/A:1021273013372 Author URL
Citations Web of Science - 3
2002 Elder M, McCammond J, 'Curvature testing in 3-dimensional metric polyhedral complexes', EXPERIMENTAL MATHEMATICS, 11 143-158 (2002) [C1]
Author URL
Citations Web of Science - 5
Show 33 more journal articles

Thesis / Dissertation (2 outputs)

Year Citation Altmetrics Link
2001 Elder MJ, Automaticity, almost convexity and falsification by fellow traveler properties of some finitely presented groups, The University of Melbourne (2001)
1997 Elder MJ, Coxeter groups and the Moussong Complex, The University of Melbourne (1997)
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Grants and Funding

Summary

Number of grants 10
Total funding $1,197,468

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


20143 grants / $22,000

The logical complexity of problems in group theory$10,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Doctor Murray Elder
Scheme Near Miss Grant
Role Lead
Funding Start 2014
Funding Finish 2014
GNo G1301377
Type Of Funding Internal
Category INTE
UON Y

Faculty Visiting Fellowship 2014$10,000

Funding body: University of Newcastle - Faculty of Science & IT

Funding body University of Newcastle - Faculty of Science & IT
Project Team Doctor Murray Elder
Scheme Visiting Fellowship
Role Lead
Funding Start 2014
Funding Finish 2014
GNo G1401050
Type Of Funding Internal
Category INTE
UON Y

Faculty PVC Conference Assistance Grant 2014$2,000

Funding body: University of Newcastle - Faculty of Science & IT

Funding body University of Newcastle - Faculty of Science & IT
Project Team Doctor Murray Elder
Scheme PVC Conference Assistance Grant
Role Lead
Funding Start 2014
Funding Finish 2014
GNo G1401186
Type Of Funding Internal
Category INTE
UON Y

20131 grants / $24,000

DVC(R) Research Support for Future Fellow (FT11)$24,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Doctor Murray Elder
Scheme Future Fellowship Support
Role Lead
Funding Start 2013
Funding Finish 2013
GNo G1301119
Type Of Funding Internal
Category INTE
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 Investigator
Funding Start 2012
Funding Finish 2012
GNo G1100080
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

20115 grants / $826,468

Algorithmic and computational advances in geometric group theory$565,468

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Doctor Murray Elder
Scheme Future Fellowships
Role Lead
Funding Start 2011
Funding Finish 2011
GNo G1100435
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

Generic complexity in computational topology: Breaking through the bottlenecks$234,300

The project will focus on key computational problems in three-dimensional topology, with the aims of illuminating the theoretical limitations of such problems, developing new computational tools for solving them, and applying these tools to a variety of applications. The project will generate theoretical research, practical software, and rich experimental data.
Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team
Scheme Unknown
Role Lead
Funding Start 2011
Funding Finish 2013
GNo
Type Of Funding External
Category EXTE
UON Y

Generic complexity in computational topology: Breaking through the bottlenecks$20,700

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Dr Benjamin Burton, Doctor Murray Elder, Dr Stephan Tillmann
Scheme Discovery Projects
Role Lead
Funding Start 2011
Funding Finish 2011
GNo G1001059
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

Efficient computations in infinite groups$3,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Doctor Murray Elder
Scheme New Staff Grant
Role Lead
Funding Start 2011
Funding Finish 2011
GNo G1001071
Type Of Funding Internal
Category INTE
UON Y

Efficient computations in infinite groups$3,000

Funding body: University of Newcastle - Faculty of Science & IT

Funding body University of Newcastle - Faculty of Science & IT
Project Team
Scheme New Staff Grant
Role Lead
Funding Start 2011
Funding Finish 2011
GNo
Type Of Funding Internal
Category INTE
UON Y
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Research Supervision

Current Supervision

Commenced Research Title / Program / Supervisor Type
2014 Topological Algebra
Mathematics, Faculty of Science and Information Technology
Co-Supervisor
2013 Automorphisms of Totally Disconnected, Locally Compact Groups and the Continuity of the Scale
Mathematics, Faculty of Science and Information Technology
Co-Supervisor
2011 Structure of Discrete and Non-discrete Locally Primitive Groups Acting on Trees
Mathematics, Faculty of Science and Information Technology
Co-Supervisor
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Dr Murray Elder

Position

ARC Future Fellowship
School of Mathematical and Physical Sciences
Faculty of Science and Information Technology

Focus area

Mathematics

Contact Details

Email murray.elder@newcastle.edu.au
Phone (02) 4921 7472
Fax (02) 4921 6898

Office

Room V125
Building Mathematics Building
Location Callaghan
University Drive
Callaghan, NSW 2308
Australia
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