The University of Newcastle, Australia

Selected Topic in Number Theory

Closing Date: 12 November 2018

PhD Scholarship

One domestic PhD scholarship is available in Number Theory. A possible project concerns Ducci sequences, which are sequences of n-tuples of integers formed by taking cyclic absolute differences, and is described in the next paragraph. Other topics proposed by the candidate will also be considered.


A Ducci sequence is a sequence of integer n-tuples where each n-tuple is formed from the previous n-tuple by forming absolute differences between adjacent entries (and where the first and last entries are also considered adjacent), for example: (1,4,5) -> (3,1,4) -> (2,3,1) -> (1,2,1) -> (1,1,0) -> (0,1,1) -> (1,0,1) -> (1,1,0) -> ... Such a sequence is eventually periodic, and for each n one may study the distribution of periods and the lengths of the preperiodic portions. A number of open problems remain. Ducci sequences may also be generalised in a number of different directions. This topic has links to many areas of Mathematics, such as cyclotomic fields, polynomials over finite fields, arithmetic dynamics, spectral graph theory, cellular automata and more. Alternatively, candidates may also propose topics of their own choice.

PhD Scholarship details

Funding: $27,082 per annum (2018 rate) indexed annually. The living allowance scholarship is for 3.5 years and the tuition fee scholarship is for four years. Scholarships also include up to $1,500 relocation allowance if applicable.

Supervisor: Professor Florian Breuer

Available to: Domestic students


Eligibility Criteria

In addition to the minimum eligibility criteria detailed on the Eligibility webpage, the successful candidate must be able to commence by 31 March 2019.

Application Procedure

Interested applicants should send an email expressing their interest along with scanned copies of their academic transcripts, CV, a brief statement of their research interests and a proposal that specifically links them to the research project.

Please send the email expressing interest to by 5pm on 12 November 2018.

Applications Close 12 November 2018

Contact Professor Florian Breuer
Phone +61 2 4033 9609

PhD and Research MastersFind out more