Associate Professor Murray Elder

Associate Professor Murray Elder

Associate Professor

School of Mathematical and Physical Sciences (Mathematics)

Career Summary

Biography

Please see my research website for correct and up-to-date information: https://sites.google.com/site/melderau


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

  • Automata and formal languages
  • Complexity theory
  • Enumerative combinatorics
  • Geometric group theory

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

UON Appointment

Title Organisation / Department
Associate Professor University of Newcastle
School of Mathematical and Physical Sciences
Australia

Academic appointment

Dates Title Organisation / Department
1/01/2012 - 31/12/2015 ARC Future Fellow University of Newcastle
School of Mathematical and Physical Sciences
Australia
1/01/2011 - 31/12/2011 Lecturer University of Newcastle
School of Mathematical and Physical Sciences
Australia
1/01/2008 - 31/12/2010 Lecturer The University of Queensland
School of Mathematics and Physics
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
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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For publications that are currently unpublished or in-press, details are shown in italics.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 (37 outputs)

Year Citation Altmetrics Link
2016 Brough T, Ciobanu L, Elder MJ, Zetzsche G, 'Permutations of context-free, ET0L and indexed languages', Discrete Mathematics & Theoretical Computer Science, 17 167-178 (2016) [C1]
2016 Burton B, Elder MJ, Kalka A, Tillmann S, '2-manifold recognition is in logspace', Journal of Computational Geometry, 7 70-85 (2016) [C1]
DOI 10.20382/jocg.v7i1a4
2016 Elder MJ, Taback J, 'Thompson's group F is 1-counter graph automatic', Groups Complexity Cryptology, 8 21-33 (2016) [C1]
DOI 10.1515/gcc-2016-0001
2016 Ciobanu L, Diekert V, Elder M, 'Solution sets for equations over free groups are EDT0L languages', International Journal of Algebra and Computation, 26 843-886 (2016)

© World Scientific Publishing Company.We show that, given an equation over a finitely generated free group, the set of all solutions in reduced words forms an effectively constru... [more]

© World Scientific Publishing Company.We show that, given an equation over a finitely generated free group, the set of all solutions in reduced words forms an effectively constructible EDT0L language. In particular, the set of all solutions in reduced words is an indexed language in the sense of Aho. The language characterization we give, as well as further questions about the existence or finiteness of solutions, follow from our explicit construction of a finite directed graph which encodes all the solutions. Our result incorporates the recently invented recompression technique of Jez, and a new way to integrate solutions of linear Diophantine equations into the process. As a byproduct of our techniques, we improve the complexity from quadratic nondeterministic space in previous works to NSPACE(n log n) here.

DOI 10.1142/S0218196716500363
2015 Burillo J, Elder M, 'Metric properties of Baumslag-Solitar groups', International Journal of Algebra and Computation, 25 799-811 (2015) [C1]

© 2015 World Scientific Publishing Company.We compute estimates for the word metric of Baumslag-Solitar groups in terms of the Britton's lemma normal form. As a corollary, we fin... [more]

© 2015 World Scientific Publishing Company.We compute estimates for the word metric of Baumslag-Solitar groups in terms of the Britton's lemma normal form. As a corollary, we find lower bounds for the growth rate for the groups BS(p, q) with 1 < p = q.

DOI 10.1142/S0218196715500198
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) [C1]
DOI 10.1515/jgth-2014-0041
Citations Scopus - 1Web of Science - 1
Co-authors George Willis
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) [C1]
Citations Scopus - 1
2015 Elder MJ, Rechnitzer A, Janse van Rensberg EJ, 'Random Sampling of Trivial Words in Finitely Presented Groups', Experimental Mathematics, 24 391-409 (2015) [C1]
DOI 10.1080/10586458.2015.1005853
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
Citations Scopus - 5Web of Science - 4
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
Citations Scopus - 1Web of Science - 1
2014 Davis N, Elder MJ, Reeves L, 'Non-contracting groups generated by (3,2)-automata', Algebra and Discrete Mathematics, 17 20-32 (2014) [C1]
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
Citations Scopus - 3Web of Science - 3
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 - 3Web of Science - 1
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 - 4
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 - 5Web of Science - 4
2010 Elder MJ, Rechnitzer A, 'Some geodesic problems for finitely generated groups', Groups Complexity Cryptology, 2 223-229 (2010) [C1]
Citations Scopus - 5
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 - 6Web of Science - 4
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 - 3Web 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 Scopus - 1Web 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 - 9Web of Science - 7
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
Citations Web of Science - 2
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
Citations Web of Science - 12
2006 Elder M, 'Permutations generated by a stack of depth 2 and an infinite stack in series', ELECTRONIC JOURNAL OF COMBINATORICS, 13 (2006) [C1]
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
Citations Web of Science - 5
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
Citations Web of Science - 3
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
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
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
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
Citations Web of Science - 5
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
Citations Web of Science - 5
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
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
Citations Web of Science - 4
2002 Elder M, McCammond J, 'Curvature testing in 3-dimensional metric polyhedral complexes', EXPERIMENTAL MATHEMATICS, 11 143-158 (2002) [C1]
Citations Web of Science - 6
Show 34 more journal articles

Conference (1 outputs)

Year Citation Altmetrics Link
2015 Ciobanu L, Diekert V, Elder M, 'Solution sets for equations over free groups are EDT0L languages', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (2015) [E1]

© Springer-Verlag Berlin Heidelberg 2015.We show that, given a word equation over a finitely generated free group, the set of all solutions in reduced words forms an EDT0L langua... [more]

© Springer-Verlag Berlin Heidelberg 2015.We show that, given a word equation over a finitely generated free group, the set of all solutions in reduced words forms an EDT0L language. In particular, it is an indexed language in the sense of Aho. The question of whether a description of solution sets in reduced words as an indexed language is possible has been open for some years [9,10], apparently without much hope that a positive answer could hold. Nevertheless, our answer goes far beyond: they are EDT0L, which is a proper subclass of indexed languages. We can additionally handle the existential theory of equations with rational constraints in free products ¿1=i=sFi, where each Fi is either a free or finite group, or a free monoid with involution. In all cases the result is the same: the set of all solutions in reduced words is EDT0L. This was known only for quadratic word equations by [8], which is a very restricted case. Our general result became possible due to the recent recompression technique of Jez. In this paper we use a new method to integrate solutions of linear Diophantine equations into the process and obtain more general results than in the related paper [5]. For example, we improve the complexity from quadratic nondeterministic space in [5] to quasi-linear nondeterministic space here. This implies an improved complexity for deciding the existential theory of non-abelian free groups: NSPACE(n log n). The conjectured complexity is NP, however, we believe that our results are optimal with respect to space complexity, independent of the conjectured NP.

DOI 10.1007/978-3-662-47666-6_11
Citations Scopus - 1Web of Science - 2

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 9
Total funding $1,382,720

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


20161 grants / $422,552

The language complexity of problems in algebra and logic$422,552

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Associate Professor Murray Elder, Dr Laura Ciobanu, Professor Volker Diekert
Scheme Discovery Projects
Role Lead
Funding Start 2016
Funding Finish 2018
GNo G1500017
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

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 Associate Professor 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 Associate Professor 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 Associate Professor 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 Associate Professor Murray Elder
Scheme Future Fellowship Support
Role Lead
Funding Start 2013
Funding Finish 2016
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, Associate Professor Murray Elder
Scheme Discovery Projects
Role Investigator
Funding Start 2012
Funding Finish 2014
GNo G1100080
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

20113 grants / $589,168

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

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Associate Professor Murray Elder
Scheme Future Fellowships
Role Lead
Funding Start 2011
Funding Finish 2015
GNo G1100435
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
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, Associate Professor Murray Elder, Dr Stephan Tillmann
Scheme Discovery Projects
Role Lead
Funding Start 2011
Funding Finish 2013
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 Associate Professor Murray Elder
Scheme New Staff Grant
Role Lead
Funding Start 2011
Funding Finish 2011
GNo G1001071
Type Of Funding Internal
Category INTE
UON Y
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Research Supervision

Number of supervisions

Completed0
Current2

Total current UON EFTSL

PhD1.3

Current Supervision

Commenced Level of Study Research Title / Program / Supervisor Type
2016 PhD Language Complexity of Problems in Algebra and Logic with Solution Sets
PhD (Mathematics), Faculty of Science and Information Technology, The University of Newcastle
Principal Supervisor
2013 PhD On the Interconnectedness, via Random Walks, of Cogrowth Rates and the Folner Function
PhD (Mathematics), Faculty of Science and Information Technology, The University of Newcastle
Principal Supervisor
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News

Australian Research Council (ARC)

ARC Discovery Projects funding success 2016

November 4, 2015

Dr Murray Elder, Dr Laura Ciobanu and Professor Volker Diekert have been awarded $417,000 in ARC Discovery Project funding commencing in 2016 for their research project The language complexity of problems in algebra and logic.

Associate Professor Murray Elder

Position

Associate Professor
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
Link Personal webpage

Office

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