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

CodeDescriptionPercentage
010105Group Theory and Generalisations70
080201Analysis of Algorithms and Complexity15
080203Computational Logic and Formal Languages15

Professional Experience

Academic appointment

DatesTitleOrganisation / Department
29/05/2015 - 29/06/2015LecturerThe University of Queensland
School of Mathematics and Physics
Australia
1/01/2015 - Membership European Association for Theoretical Computer Science
United Kingdom
1/01/2012 - Fellow ARC
ARC - Discovery - Future Fellowships
University of Newcastle
School of Mathematical and Physical Sciences
Australia
1/01/2012 - 1/12/2015ARC Future FellowUniversity of Newcastle
School of Mathematical and Physical Sciences
Australia
1/01/2011 - 1/12/2011LecturerUniversity of Newcastle
School of Mathematical and Physical Sciences
Australia
1/08/2006 - 1/01/2008Assistant ProfessorStevens Institute of Technology
Department of Mathematical Sciences
United States
1/01/2006 - 1/06/2006LecturerUniversity of Wollongong
School of Mathematics and Applied Statistics
Australia
1/02/2004 - 1/08/2005Research FellowUniversity of St. Andrews
Centre for Interdisciplinary Research in Computational Algebra
United Kingdom
1/09/2002 - 1/01/2004Visiting Assistant ProfessorTufts University
Mathematics
United States
1/01/2001 - Membership American Mathematical Society
United States
1/09/2000 - 1/07/2002Visiting Assistant ProfessorTexas A&M University
Mathematics
United States
1/01/1997 - 31/12/2023MembershipAustralian 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)

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 (36 outputs)

YearCitationAltmetricsLink
2015Elder 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)
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)
DOI10.1515/jgth-2014-0041Author URL
Co-authorsGeorge Willis
2015BURILLO J, ELDER MURRAY, 'METRIC PROPERTIES OF BAUMSLAG¿SOLITAR GROUPS', International Journal of Algebra and Computation, 150510182331000-150510182331000 (2015)
DOI10.1142/S0218196715500198
2015Ciobanu L, Diekert V, Elder MJ, 'Solution Sets for Equations over Free Groups are EDT0L Languages', Lecture Notes in Computer Science, 9135 134-145 (2015)
DOI10.1007/978-3-662-47666-6_11
2015Elder MJ, Rechnitzer A, Janse van Rensberg EJ, 'Random Sampling of Trivial Words in Finitely Presented Groups', Experimental Mathematics, (2015)
DOI10.1080/10586458.2015.1005853
2015Elder 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 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 c<inf>n</inf> 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)

2014Elder M, Taback J, 'C-graph automatic groups', Journal of Algebra, 413 289-319 (2014) [C1]
DOI10.1016/j.jalgebra.2014.04.021Author URL
CitationsScopus - 1
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]
DOI10.1142/S0218196714500106
2014Davis N, Elder MJ, Reeves L, 'Non-contracting groups generated by (3,2)-automata', Algebra and Discrete Mathematics, 17 20-32 (2014) [C1]
Author URL
2013Elder M, Elston G, Ostheimer G, 'On groups that have normal forms computable in logspace', Journal of Algebra, 381 260-281 (2013) [C1]
DOI10.1016/j.jalgebra.2013.01.036Author URL
CitationsScopus - 2Web of Science - 1
2012Bridson MR, Burillo J, Elder MJ, Sunic Z, 'On groups whose geodesic growth is polynomial', International Journal of Algebra and Computation, 22 (2012) [C1]
DOI10.1142/S0218196712500488
CitationsScopus - 2
2012Elder MJ, 'A short introduction to self-similar groups', Gazette of the Australian Mathematical Society, 39 125-133 (2012) [C2]
2012Elder MJ, Rechnitzer A, Wong T, 'On the cogrowth of Thompson's group F', Groups - Complexity - Cryptology, 4 301-320 (2012) [C1]
CitationsScopus - 2
2010Cleary S, Elder MJ, Rechnitzer A, Taback J, 'Random subgroups of Thompson's group F', Groups Geometry and Dynamics, 4 91-126 (2010) [C1]
DOI10.4172/GGD/76
CitationsScopus - 4Web of Science - 3
2010Elder MJ, Rechnitzer A, 'Some geodesic problems for finitely generated groups', Groups Complexity Cryptology, 2 223-229 (2010) [C1]
2010Elder M, Rechnitzer A, 'Some geodesic problems in groups', Groups, Complexity, Cryptology, 2 223-229 (2010)
DOI10.1515/GCC.2010.014
CitationsScopus - 4
2010Elder MJ, 'A linear-time algorithm to compute geodesics in solvable Baumslag-Solitar groups', Illinois Journal of Mathematics, 54 109-128 (2010) [C1]
DOI10.1214/10-AAP256
CitationsScopus - 4Web of Science - 2
2010Elder MJ, Fusy E, Rechnitzer A, 'Counting elements and geodesics in Thompson's group F', Journal of Algebra, 324 102-121 (2010) [C1]
DOI10.1016/j.jalgebra.2010.02.035
CitationsScopus - 2Web of Science - 1
2009Dison W, Elder MJ, Riley TR, Young R, 'The Dehn function of Stallings' group', Geometric and Functional Analysis, 19 406-422 (2009) [C1]
DOI10.1007/s00039-009-0011-9
CitationsWeb of Science - 1
2008Elder MJ, Kambites M, Ostheimer G, 'On groups and counter automata', International Journal of Algebra and Computation, 18 1345-1364 (2008) [C1]
DOI10.1142/S0218196708004901
CitationsScopus - 7Web of Science - 6
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]
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]
DOI10.1016/j.jalgebra.2005.11.016Author URL
CitationsWeb of Science - 1
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]
DOI10.1016/j.aam.2005.05.007Author URL
CitationsWeb of Science - 10
2006Elder M, 'Permutations generated by a stack of depth 2 and an infinite stack in series', ELECTRONIC JOURNAL OF COMBINATORICS, 13 (2006) [C1]
Author URL
CitationsWeb of Science - 1
2005Elder M, 'A context-free and a 1-counter geodesic language for a Baumslag-Solitar group', THEORETICAL COMPUTER SCIENCE, 339 344-371 (2005) [C1]
DOI10.1016/j.tcs.2005.03.026Author URL
CitationsWeb of Science - 3
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)
2005Elder M, Hermiller S, 'Minimal almost convexity', JOURNAL OF GROUP THEORY, 8 239-266 (2005) [C1]
DOI10.1515/jgth.2005.8.2.239Author URL
CitationsWeb of Science - 2
2005Elder M, 'Regular geodesic languages and the falsification by fellow traveler property', ALGEBRAIC AND GEOMETRIC TOPOLOGY, 5 129-134 (2005) [C1]
DOI10.2140/agt.2005.5.129Author URL
CitationsWeb of Science - 3
2004Elder MJ, 'A non-Hopfian almost convex group', JOURNAL OF ALGEBRA, 271 11-21 (2004) [C1]
DOI10.1016/j.jalgebra.2003.04.004Author URL
CitationsWeb of Science - 2
2004Elder M, McCammond J, 'CAT(0) is an algorithmic property', GEOMETRIAE DEDICATA, 107 25-46 (2004) [C1]
DOI10.1023/B:GEOM.0000049096.63639.e3Author URL
CitationsWeb of Science - 3
2004Elder MJ, 'Ld groups are almost convex and have sub-cubic Dehn function', Algebraic and Geometric Topology, 4 23-29 (2004) [C1]
2003Elder M, McCammond J, Meier J, 'Combinatorial conditions that imply word-hyperbolicity for 3-manifolds', TOPOLOGY, 42 1241-1259 (2003) [C1]
DOI10.1016/S0040-9383(02)00100-3Author URL
CitationsWeb of Science - 4
2003Elder MJ, 'The loop shortening property and almost convexity', GEOMETRIAE DEDICATA, 102 1-18 (2003) [C1]
DOI10.1023/B:GEOM.0000006500.20513.d2Author URL
CitationsWeb of Science - 4
2003Elder MJ, 'Patterns theory and geodesic automatic structure for a class of groups', INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 13 203-230 (2003) [C1]
DOI10.1142/S0218196703001274Author URL
CitationsWeb of Science - 2
2002Elder MJ, 'Finiteness and the falsification by fellow traveler property', GEOMETRIAE DEDICATA, 95 103-113 (2002) [C1]
DOI10.1023/A:1021273013372Author URL
CitationsWeb of Science - 3
2002Elder M, McCammond J, 'Curvature testing in 3-dimensional metric polyhedral complexes', EXPERIMENTAL MATHEMATICS, 11 143-158 (2002) [C1]
Author URL
CitationsWeb of Science - 5
Show 33 more journal articles

Thesis / Dissertation (2 outputs)

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

Summary

Number of grants10
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 bodyUniversity of Newcastle
Project TeamDoctor Murray Elder
SchemeNear Miss Grant
RoleLead
Funding Start2014
Funding Finish2014
GNoG1301377
Type Of FundingInternal
CategoryINTE
UONY

Faculty Visiting Fellowship 2014$10,000

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

Funding bodyUniversity of Newcastle - Faculty of Science & IT
Project TeamDoctor Murray Elder
SchemeVisiting Fellowship
RoleLead
Funding Start2014
Funding Finish2014
GNoG1401050
Type Of FundingInternal
CategoryINTE
UONY

Faculty PVC Conference Assistance Grant 2014$2,000

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

Funding bodyUniversity of Newcastle - Faculty of Science & IT
Project TeamDoctor Murray Elder
SchemePVC Conference Assistance Grant
RoleLead
Funding Start2014
Funding Finish2014
GNoG1401186
Type Of FundingInternal
CategoryINTE
UONY

20131 grants / $24,000

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

Funding body: University of Newcastle

Funding bodyUniversity of Newcastle
Project TeamDoctor Murray Elder
SchemeFuture Fellowship Support
RoleLead
Funding Start2013
Funding Finish2013
GNoG1301119
Type Of FundingInternal
CategoryINTE
UONY

20121 grants / $325,000

Theory and applications of symmetries of relational structures$325,000

Funding body: ARC (Australian Research Council)

Funding bodyARC (Australian Research Council)
Project TeamProfessor George Willis, Doctor Murray Elder
SchemeDiscovery Projects
RoleInvestigator
Funding Start2012
Funding Finish2012
GNoG1100080
Type Of FundingAust Competitive - Commonwealth
Category1CS
UONY

20115 grants / $826,468

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

Funding body: ARC (Australian Research Council)

Funding bodyARC (Australian Research Council)
Project TeamDoctor Murray Elder
SchemeFuture Fellowships
RoleLead
Funding Start2011
Funding Finish2011
GNoG1100435
Type Of FundingAust Competitive - Commonwealth
Category1CS
UONY

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 bodyARC (Australian Research Council)
Project Team
SchemeUnknown
RoleLead
Funding Start2011
Funding Finish2013
GNo
Type Of FundingExternal
CategoryEXTE
UONY

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

Funding body: ARC (Australian Research Council)

Funding bodyARC (Australian Research Council)
Project TeamDr Benjamin Burton, Doctor Murray Elder, Dr Stephan Tillmann
SchemeDiscovery Projects
RoleLead
Funding Start2011
Funding Finish2011
GNoG1001059
Type Of FundingAust Competitive - Commonwealth
Category1CS
UONY

Efficient computations in infinite groups$3,000

Funding body: University of Newcastle

Funding bodyUniversity of Newcastle
Project TeamDoctor Murray Elder
SchemeNew Staff Grant
RoleLead
Funding Start2011
Funding Finish2011
GNoG1001071
Type Of FundingInternal
CategoryINTE
UONY

Efficient computations in infinite groups$3,000

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

Funding bodyUniversity of Newcastle - Faculty of Science & IT
Project Team
SchemeNew Staff Grant
RoleLead
Funding Start2011
Funding Finish2011
GNo
Type Of FundingInternal
CategoryINTE
UONY
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Research Supervision

Current Supervision

CommencedResearch Title / Program / Supervisor Type
2014Topological Algebra
Mathematics, Faculty of Science and Information Technology
Co-Supervisor
2013Automorphisms of Totally Disconnected, Locally Compact Groups and the Continuity of the Scale
Mathematics, Faculty of Science and Information Technology
Co-Supervisor
2011Structure 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

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

Office

RoomV125
BuildingMathematics Building
LocationCallaghan
University Drive
Callaghan, NSW 2308
Australia
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