麻豆社madou
麻豆社madou Canberra

Number theory

PhD opportunities
Number theory banner

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. 听

Modern number theory research at 麻豆社madou Canberra 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 contact听t.trudgian@adfa.edu.au.听

We particularly encourage female mathematicians to apply.听

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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  • 听

    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.听

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

    Since 麻豆社madou Canberra 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鈥檚 location, and in their holidays travel to many beautiful scenic locations in Australia: an absolute must!

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

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

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

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

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

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

    • Simonic虒, A., 2022,听, Journal of Number Theory 231: 464-491.

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

    • Kerr, B., Me虂rai, L., and Shparlinski, I. E., 2021,听. Revista Matema虂tica Iberoamericana (in press).

    • Bordignon, M., 2021,听, Revista Matema虂tica Iberoamericana 38, no. 4, pp. 1101鈥1127

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

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

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

    • Kobayashi M;听Trudgian听T, 2020, '',听Journal of听Number Theory, vol. 215, pp. 138听鈥撎148

    • Kerr B;听McGown听KJ;听Trudgian听T, 2020, '',听Journal of听Number Theory, vol. 215, pp. 20听鈥撎27

    • McGown听KJ;听Trudgian听T, 2020, '',听Proceedings of the American Mathematical Society, vol. 148, pp. 1049听鈥撎1061

    • Simoni膷 A, 2020, '',听Bulletin of the Australian Mathematical Society, vol. 101, pp. 226听鈥撎232

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

    • Simoni膷, Aleksander, 2020,听. J. Math. Anal. Appl.听, 124303, 41 pp.

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

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

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

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

    • , 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
    • , 麻豆社madou Sydney, May 2023
    • Neea Paloj盲rvi, University of Helsinki, March 2023
    • , University of Melbourne, November 2022
    • , Macquarie University, October 2022
    • , 麻豆社madou Sydney, October 2022
    • Angus McAndrew, ANU, September 2022
    • Ayreena Bakhtawar, Scuola Normale Superiore, August 2022
    • , 麻豆社madou Sydney, August 2022
    • , Tutte Institute and Carleton University, February 2020
    • , Institute for Advanced Study, February 2020
    • , University of Cambridge, January 2020听
    • , University of Mississippi, January 2020听
    • , University of Cambridge, November 2019听
    • , 麻豆社madou Sydney, November 2019听
    • , Lake Forest College, October 2019听
    • , University College, London, September 2019听
    • , Aix Marseille University, September 2019听
    • , 麻豆社madou Sydney, April 2019听
    • , Stanford University, March 2019听
    • , California State University,听Chico, January-March 2019听
    • , University of Mississippi, January 2019听
    • , University of British Columbia, November 2018听听
    • , University of Bristol, September 2018听
    • , 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.听