Dr Amy Glen
PhD (Pure Maths) Adelaide, BSc (Hons), BSc (Math. & Comp. Sci.)

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I am a Lecturer in Mathematics and Statistics within the School of Engineering and Information Technology.

I obtained my PhD in Pure Mathematics from The University of Adelaide (Australia), where I was later appointed as an Associate Lecturer in the School of Mathematical Sciences. Following my appointment in Adelaide, I moved to Canada to take up a position as a CRM-ISM Postdoctoral Research Fellow (see here) in the Laboratoire de Combinatoire et d’Informatique Mathématique (LaCIM) at the Université du Québec à Montréal. I then moved to Iceland to join the Combinatorics group in The Mathematics Institute at Reykjavík University, before moving back home to Australia to take up a position at Murdoch University.

Find out more about me at my website.

In 2017, my teaching involvement at Murdoch University will be as follows.

• Jan Trimester in Dubai: MAS167 - Computational Mathematics (coordination)
• Semester 1: MAS162 - Foundations of Discrete Mathematics (coordination, lectures, tutes, external tutoring)
• Semester 2: 
  • MAS161 - Calculus & Matrix Algebra (coordination, lectures, tutorials, external tutoring)
  • MAS225 - Discrete Mathematics & Management Science (50% coordination, lectures, tutorials)
• Sept Trimester in Singapore: MAS162 - Foundations of Discrete Mathematics (coordination)
• Sept Trimester in Dubai: MAS167 - Computational Mathematics (coordination)

In previous years, I have also been involved in the teaching of the following units at Murdoch University.

• MAS130 - Calculus & Matrix Algebra (coordination)
• MAS164 – Fundamentals of Mathematics (external tutoring)
• MAS4013 – Applied Combinatorics & Discrete Mathematics (Honours unit)

Further details about my teaching can be found on the teaching page at my website.

Research Interests: Combinatorics; Discrete Mathematics; Number Theory
Main Research Area: Combinatorics on words

My research interests fall under the broad areas of Combinatorics, Discrete Mathematics, and Number Theory. I am especially interested in combinatorics on words, from algebraic and geometric points of view, and its applications in Number Theory.

Much of my research to date has focussed on repetitions (including abelian repetitions) and periodicity (including quasiperiodicity) in finite and infinite words (particularly Sturmian and episturmian words, including the well-known Fibonacci word, and also the Thue-Morse sequence), as well as other combinatorial regularities and patterns occurring in words, such as recurring factors, Lyndon words, palindromes, and related notions of word complexity, lexicographic ordering, and distribution of real numbers modulo 1 from a combinatorial perspective. Some of these topics have applications to a wide variety of other scientific fields, ranging from theoretical computer science (digital imagery, pattern recognition) to theoretical physics (quasicrystal modelling) and molecular biology (DNA sequences).

I am happy to supervise Honours and PhD projects in any of the areas mentioned above. Feel free to e-mail me, or if you’re in Perth, drop by my office to discuss possible topics. To get an idea of the sorts of things I work on, see my publications or talks.

Sir Walter Murdoch Distinguished Collaborator Scheme (2014-2016): $10,000/year
With Professor Bill Smyth (McMaster University, Canada)

Teaching Awards & Nominations

2017: Inducted into the Murdoch Learning Excellence Academy (LEAD) as a Murdoch LEAD Senior Fellow

Murdoch LEAD (Learning Excellence Academy) promotes and celebrates excellence and leadership in learning and teaching at Murdoch. Murdoch LEAD Fellowships recognise staff who demonstrate excellence, leadership, creativity and innovation in their learning and teaching practice. The main aim of the Academy is to build a community of practitioners who will model, promote, mentor and lead best practices in learning and teaching for both the university and the sector.

Conferences & Workshops

2017

• Dec 12-15: 61st Annual Meeting of the Australian Mathematical Society, Macquarie University, Sydney, Australia [Incoming Chair of the AustMS Student Conference Support Committee]
• Dec 4-9: 5th International Combinatorics Conference (5ICC), Monash University, Melbourne, Australia [CMSA Council Member]
• Sept 24-26: WIMSIG Conference 2o17: Celebration of Women in Australian Mathematical Sciences, The University of South Australia, Adelaide, Australia [Website Editor and speaker in the Algebra & Discrete Mathematics session]

2016

• Dec 12-16: Invited Speaker @ 40th Australasian Conference on Combinatorial Mathematics & Combinatorial Computing (40ACCMCC), The University of Newcastle, Australia
• Oct 11: Women in STEM Roundtable Meeting and Morning Tea at Government House in Perth upon the invitation of Professor Lyn Beazley AO FTSE (Science Ambassador and WA Australian of the Year 2015) and Her Excellency the Honourable Kerry Sanderson AC (Governor of Western Australia)
• Sept 23-26: Invited Speaker @ Number Theory Down Under 4, The University of Newcastle

2015

• Sept 28 – Oct 1: 59th Annual Meeting of the Australian Mathematical Society, Flinders University, Adelaide, South Australia
• Oct 26-29: StringMasters @ Murdoch 2015, Murdoch University, Perth, Western Australia
• Dec 11-12: 39th Australasian Conference on Combinatorial Mathematics & Combinatorial Computing (39ACCMCC), The University of Queensland, Brisbane, Australia

2014

• March 9–14: Combinatorics & Algorithmics of Strings, Schloss Dagstuhl, Germany
• Dec 1–5: 38th Australasian Conference on Combinatorial Mathematics & Combinatorial Computing (38ACCMCC), Victoria University of Wellington, New Zealand
• Dec 8–12: 8th Australia – New Zealand Mathematics Convention, The University of Melbourne, Australia

2013

• April 22–26: Fields Workshop on Challenges in Combinatorics on Words, Fields Institute, Toronto, Canada
• Sept 30 – Oct 3: 57th Annual Meeting of the Australian Mathematical Society,  University of Sydney
• Dec 9–13: 37th Australasian Conference on Combinatorial Mathematics & Combinatorial Computing (37ACCMCC), The University of Western Australia

2012

• Feb 16–17: Mini-Conference: Combinatorics, Representations, and Structure of Lie Type, Department of Mathematics and Statistics, The University of Melbourne, Australia.
  
• Feb 19–24: Outstanding Challenges in Combinatorics on Words, Banff International Research Station (BIRS), Banff Centre, Canada.

I am a founder and director of the Centre for Combinatorics on Words and Applications at Murdoch University and am a member of the following professional societies and groups.

• Australian Mathematical Society - AustMS (since 2003)
• AustMS Women in Mathematics Special Interest Group (since 2012)
• Canadian Mathematical Society (since 2008)
• Combinatorial Mathematics Society of Australasia (Life Member)

I also have on-going administrative involvement with some of these professional societies and groups in the following capacities.

• AustMS Student Conference Support Committee (Incoming Chair 2017, Chair 2018, Outgoing Chair 2019)
• Council of the CMSA (since Dec 2013)
• Webmaster of the AustMS WIMSIG (since early 2013)

I have been a referee for the following peer-reviewed journals and conferences.

• Advances in Applied Mathematics
• Discrete Applied Mathematics
• Discrete Mathematics
• Discrete Mathematics and Theoretical Computer Science
• Developments in Language Theory 2009-2011, 2013 (conference)
• Electronic Journal of Combinatorics
• European Journal of Combinatorics
• Fundamenta Informaticae
• Gazette of the Australian Mathematical Society
• Information and Computation (journal)
• Information Processing Letters
• INTEGERS (Electronica Journal of Combinatorial Number Theory)
• International Conference on Words 2007, 2009, 2013, 2015, 2017
• International Journal of Algebra and Computation
• International Journal of Foundations of Computer Science
• International Workshop on Combinatorial Image Analysis 2008
• ISRN Combinatorics
• Journal de Théorie des Nombres de Bordeaux
• Journal of Combinatorial Theory, Series A
• Journal of Computer and System Sciences
• Journal of Discrete Algorithms
• Journal of Integer Sequences
• Journal of Mathematical Analysis and Applications
• Kybernetika
• Mathematical Reviews (AMS MathSciNet)
• RAIRO Theoretical Informatics and Applications
• Theoretical Computer Science
• 5th International Conference on Language and Automata Theory and Applications 2011
• 16th International Symposium on Fundamentals of Computation Theory 2007
• 28th International Symposium on Theoretical Aspects of Computer Science 2011
• 34th International Symposium on Theoretical Aspects of Computer Science 2017
• 35th International Symposium on Mathematical Foundations of Computer Science 2010
• 41st International Colloquium on Automata, Languages & Programming 2014
• 43rd International Colloquium on Automata, Languages & Programming 2016

• Member, Dean’s Advisory Group – Engineering & IT (since 2017)
• Member, School Research Committee – Engineering & IT (since 2017)
• Member, School International Committee – Engineering & IT (2016-17)
• Member, School Board – Engineering & IT (since 2013)
• Convenor, Mathematics & Statistics Seminar Series (since 2009)
• Coordinator, Maths & Stats Clinic (2010-2013)

• 2012-2014: Rosie Murray, Honours in Mathematics & Statistics, Murdoch University. Thesis: “Topics in Combinatorics on Words”.
• 2011: William Stelbovics, Honours in Mathematics & Statistics, Murdoch University (co-supervised with Dr Brenton Clarke). Thesis: “The History of the Normal Distribution”.
  

• 2009-2010: Dr Steven Widmer, PhD in Mathematics, Université Claude Bernard – Lyon 1 (co-supervised with Professor Luca Zamboni). Thesis: “Topics in Word Complexity”.

Chapters

• Glen, A., Halldórsson, B., Kitaev, S., (2009),Crucial words for abelian powers,In: Developments in Language Theory - Lecture Notes in Computer Science, Springer, pages 264 to 275.

Journals

• Glen, A., Simpson, J., Smyth, W., (2017), Counting Lyndon factors, The Electronic Journal of Combinatorics, 24, 3, .
• Glen, A., Levé, F., (2015), Generalized trapezoidal words, Journal of Combinatorial Theory, Series A, 136, November 2015, pages 96 - 125.
• Glen, A., Simpson, J., (2013), The total run length of a word, Theoretical Computer Science, 501, , pages 41 - 48.
• Glen, A., Avgustinovich, S., Halldórsson, B., Kitaev, S., (2010), On shortest crucial words avoiding abelian powers, Discrete Applied Mathematics, 158, 6, pages 605 - 607.
• Glen, A., Halldórsson, B., Kitaev, S., (2010), Crucial abelian k-power-free words, Discrete Mathematics and Theoretical Computer Science (Online Edition), 12, 5, pages 83 - 96.
• Allouche, J., Glen, A., (2010), Extremal properties of (epi)Sturmian sequences and distribution modulo 1, L'Enseignement Mathematique. Monographies, 56, 2, pages 365 - 401.
• Glen, A., Bucci, M., De Luca, A., Zamboni, L., (2009), A connection between palindromic and factor complexity using return words, Advances in Applied Mathematics, 42, 1, pages 60 - 74.
• Glen, A., Allouche, J., (2009), Distribution modulo 1 and the lexicographic world, Annales des Sciences Mathematiques du Quebec, 33, 2, pages 125 - 143.
• Glen, A., Bucci, M., De Luca, A., Zamboni, L., (2009), A new characteristic property of rich words, Theoretical Computer Science, 410, , pages 2860 - 2863.
• Glen, A., Levé, F., Richomme, G., (2008), Quasiperiodic and Lyndon episturmian words, Theoretical Computer Science, 409, , pages 578 - 600.
• Glen, A., Lauve, A., Saliola, F., (2008), A note on the Markoff condition and central words, Information Processing Letters, 105, , pages 241 - 244.
• Glen, A., Justin, J., Pirillo, G., (2008), Characterizations of finite and infinite episturmian words via lexicographic orderings, European Journal of Combinatorics, 29, 1, pages 45 - 58.
• Glen, A., (2008), A characterization of fine words over a finite alphabet, Theoretical Computer Science, 391, , pages 51 - 60.
• Glen, A., (2007), Powers in a class of A-strict standard episturmian words, Theoretical Computer Science, 380, , pages 330 - 354.
• Glen, A., Blondin-Massé, A., Brlek, S., Labbé, S., (2007), On the Critical Exponent of Generalized Thue-Morse Words, Discrete Mathematics and Theoretical Computer Science (Online Edition), 9, 1, pages 293 - 304.
• Glen, A., (2006), Occurrences of palindromes in characteristic Sturmian words, Theoretical Computer Science, 352, , pages 31 - 46.
• Glen, A., (2006), On Sturmian and episturmian words, and related topics, Australian Mathematical Society. Bulletin, 74, , pages 155 - 160.
• Glen, A., (2004), Conjugates of characteristic Sturmian words generated by morphisms, European Journal of Combinatorics, 25, , pages 1025 - 1037.
• Glen, A., Scott, P., (2004), Euler and his contribution to Number Theory, Australian Mathematics Teacher, 60, 1, pages 2 - 5.

Conference

• Glen, A., Levé, F., Richomme, G., (2008),Directive words of episturmian words,In: 12th Journes Montoises d'Informatique Thorique.
• Glen, A., (2007),Order and quasiperiodicity in episturmian words,In: 6th International Conference on Words.
• Glen, A., (2006),A characterization of fine words over a finite alphabet,In: International School and Conference on Combinatorics, Automata & Number Theory (CANT 2006).
• Glen, A., (2005),Powers in a class of A-strict standard episturmian words,In: 5th International Conference on Words.