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Number theory

PhD opportunities
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Exploring the magic of numbers

Number Theory is one of the oldest branches of pure mathematics and is concerned with the structure of natural numbers (e.g. 1, 2, 3, 4). Number theorists study prime numbers (2, 3, 5, 7, etc.) as well as the properties of positive integers. Elementary number theory tackles questions using properties of numbers directly and is used to solve equations with rational or integer solutions. Analytic number theory relies on tools from calculus and analysis.

Modern number theory research at Ƶ uses a mix of these two methods, often flavoured with a computational component of research.

Associated schools, institutes & centres

Study with us

We offer PhD programs in mathematics and statistics and actively encourage new applications. Scholarships of $35,000 (AUD) are available for PhD applicants who achieved H1 (High Distinction) in their undergraduate program and have completed a Master by Research. If you are interested in applying, please contactt.trudgian@adfa.edu.au.

We particularly encourage female mathematicians to apply.

Our researchers
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Bryce Kerr

DECRA
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Professor Timothy Trudgian

Timothy Trudgian

Professor
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Aleksander Simonic

Aleksander Simonic

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  • We have a vibrant group of students and faculty in number theory. Our students, from seven different countries, collaborate with each other and with the visitors we regularly host at our department. Students also pursue their own research, focussing on a mixture of reading classical and modern texts and tackling unsolved problems early in their PhDs.

    We work closely with our colleagues in theto publish work and organise joint conferences. We visit Sydney regularly and also travel to stimulating meetings in Australia, includingand the December meeting of the.

    Since Ƶ provides generous travel support to researchers, several of our students and faculty may have the opportunity to attend overseas conferences. Students can also take advantage of Canberra’s location, and in their holidays travel to many beautiful scenic locations in Australia: an absolute must!

    • Garcia, S. R., Lee, E. S., 2022,, The Ramanujan Journal 57: 1169–1191.

    • Chen, C., Kerr, B., Maynard, J. and Shparlinski, I. E., 2022,. Mathematische Annalen (in press).

    • Johnston, D,, 2022,. Canadian Mathematical Bulletin (in press)

    • Simonič, A., Trudgian, T. and Turnage-Butterbaugh, C., 2022,, Transactions of the American Mathematical Society, 375(05), pp.3239-3265.

    • Mossinghoff, M. J., Starichkova, V. V. and Trudgian, T. S., 2022, Journal of Number Theory 240: 641–655.

    • Booker, A. R., Hathi, S., Mossinghoff, M. J. and Trudgian, T. S., 2022,. The Ramanujan Journal, 58(3), 913-941.

    • Simonič, A., 2022,, Journal of Number Theory 231: 464-491.

    • Francis, F. J., Lee, E. S., 2022,, Integers, 22, #A14, pp. 1–10.

    • Kerr, B., Mérai, L., and Shparlinski, I. E., 2021,. Revista Matemática Iberoamericana (in press).

    • Bordignon, M., 2021,, Revista Matemática Iberoamericana 38, no. 4, pp. 1101–1127

    • Cully-Hugill, M.; T Trudgian, 2021,, The Ramanujan Journal 56.1: 141-149.

    • Lee, E. S., 2021,, Journal of Number Theory 224: 307-322.

    • Francis, F. J., 2021,, Journal of Number Theory, 228, 87-107.

    • Kobayashi M;TrudgianT, 2020, '',Journal ofNumber Theory, vol. 215, pp. 138–148

    • Kerr B;McGownKJ;TrudgianT, 2020, '',Journal ofNumber Theory, vol. 215, pp. 20–27

    • McGownKJ;TrudgianT, 2020, '',Proceedings of the American Mathematical Society, vol. 148, pp. 1049–1061

    • Simonič A, 2020, '',Bulletin of the Australian Mathematical Society, vol. 101, pp. 226–232

    • Bordignon M, 2020, '',Journal of Number Theory, vol. 210, pp. 481–487

    • Simonič, Aleksander, 2020,. J. Math. Anal. Appl., 124303, 41 pp.

    • Akbary,Amir;Francis, Forrest J., 2020,.Math. Comp.,993–1026

    • Bordignon M, 2019, '',Journal of Number Theory, vol. 201, pp. 68–76

    • StarichkovaV, 2018, ', Regular and chaotic dynamics, vol. 23, no. 6, pp. 767-784

  • We proudly host a range of high-calibrevisitors to the university. Recent visits include:

    • , University of Michigan, December 2023
    • , Oxford, December 2023
    • , University of Manchester, September 2023
    • , La Trobe University, September 2023
    • , La Trobe University, September 2023
    • , University of Calabria, August 2023
    • , UNSW Sydney, May 2023
    • Neea Palojärvi, University of Helsinki, March 2023
    • , University of Melbourne, November 2022
    • , Macquarie University, October 2022
    • , UNSW Sydney, October 2022
    • Angus McAndrew, ANU, September 2022
    • Ayreena Bakhtawar, Scuola Normale Superiore, August 2022
    • , UNSW Sydney, August 2022
    • , Tutte Institute and Carleton University, February 2020
    • , Institute for Advanced Study, February 2020
    • , University of Cambridge, January 2020
    • , University of Mississippi, January 2020
    • , University of Cambridge, November 2019
    • , UNSW Sydney, November 2019
    • , Lake Forest College, October 2019
    • , University College, London, September 2019
    • , Aix Marseille University, September 2019
    • , UNSW Sydney, April 2019
    • , Stanford University, March 2019
    • , California State University,Chico, January-March 2019
    • , University of Mississippi, January 2019
    • , University of British Columbia, November 2018
    • , University of Bristol, September 2018
    • , RIKEN, September 2018
    • , Carleton College, March 2018
    • , University of Queensland, May 2024

    Please get in touch if you would like to visit and we can arrange a seminar.