Research
Broadly speaking, I am interested in various aspects of discrete mathematics, especially analytic number theory, arithmetic statistics, additive combinatorics and finite fields. My PhD project is centered on arithmetic statistics of algebraic groups. Problems arising from this field often lead to studying distributions of integer or rational solutions to some system of Diophantine equations, with particular focus on analysing the growth of the number of such solutions as their ‘height’ goes to infinity. In particular, I have worked on problems in arithmetic statistics of matrix groups and algebraic groups defined by multiplicative equations. The problems are attacked with various techniques, mostly stemming from analytic number theory.
I have also worked on several problems in graph theory and finite fields, as can be seen from my publications below.
Publications
- Muhammad Afifurrahman, V. Iverson and G. C. Sanjaya. Multiplicatively dependent integer vectors on a hyperplane, submitted. arXiV:2510.10855.
- Muhammad Afifurrahman and F. F. Hadiputra. Upper bounds on the odd graceful chromatic number of graphs , submitted. arXiV:2508.17799.
- Muhammad Afifurrahman and C. C. Corrigan. Moments of restricted divisor functions, Mathematika, 72 (2026), e70060. arXiV:2501.15372.
- Muhammad Afifurrahman. A uniform formula on the number of integer matrices with given determinant and height, J. Number Theory, 281 (2026), 741-770. arXiV:2407.08191.
- Muhammad Afifurrahman, D. I. D. Primaskun, P. E. Putri, and L. P. Wijaya. On constructing 1-factors of labelled complete graph, Bol. Soc. Mat. Mex., 31 82 (2025).
- Muhammad Afifurrahman, V. Kuperberg, A. Ostafe, and I. E. Shparlinski. Statistics of ranks, determinants and characteristic polynomials of rational matrices, Forum Math., 37 4 (2025), 1259-1289. arXiV:2401.10086.
- A. Barra and Muhammad Afifurrahman. The total vertex irregularity strength for cubic graphs with a perfect matching, Discrete Math., 348 5 (2025), 114402.
- Muhammad Afifurrahman. Some counting questions for matrix products, Bull. Aust. Math. Soc. 110 1 (2024), 32-43. arXiV:2306.04885.
- Muhammad Afifurrahman and A. Barra. Determining Sidon polynomials on Sidon sets over finite fields, J. Algebra Comb. Discrete Struct. Appl., 11 3 (2024), 175-187. arXiV:2111.08886.
- Muhammad Afifurrahman. On the number of different entries in involutory MDS matrices over finite fields of characteristic two, AIP Conference Proceedings 2423 060002 (2021). arXiV:2111.08352.
What I can do right now… is to keep composing songs[papers]… - Kanade Yoisaki
Talks
Slides supplied when available.
List of invited talks
Invited Talks
- UNSW Canberra Number Theory Seminar, UNSW ADFA, Canberra, Australia, November 2025. Multiplicatively dependent integer vectors on a hyperplane.
- University of Waterloo Number Theory Seminar (online), October 2025. Multiplicatively dependent integer vectors on a hyperplane. Slides
- UNSW Number Theory Seminar, UNSW, Sydney, Australia, October 2025. Multiplicatively dependent integer vectors on a hyperplane.
- Visiting Talk, Universitas Indonesia, Depok, Indonesia, February 2025. Counting rational matrices with bounded height.
- Visiting Talk, Universitas Gadjah Mada, Yogyakarta, Indonesia, February 2025. A uniform formula on the number of integer matrices with given determinant and height.
- Visiting Talk, Universitas Diponegoro, Semarang, Indonesia, January 2025. Counting rational matrices with bounded height.
- Visiting Talk, Institut Teknologi Bandung, Bandung, Indonesia, December 2024. Counting rational matrices with bounded height.
- UNSW Number Theory Seminar, UNSW, Sydney, Australia, May 2024. Arithmetic statistics of rational matrices with bounded height. Slides
List of contributed talks
Contributed Talks
- The 67th Annual Meeting of the Australian Mathematical Society (AustMS 2025), La Trobe University, Melbourne, Australia, December 2025. Multiplicatively dependent integer vectors on a hyperplane.
- 13rd Number Theory Down Under Conference, University of Canterbury, Christchurch, New Zealand, August 2025. Moments of restricted divisor functions: an introduction.
- UNSW Number Theory Days, UNSW Sydney, Australia, August 2025. Multiplicatively dependent integer vectors on a hyperplane.
- UNSW School of Mathematics and Statistics 12th Postgraduate Seminar, August 2025. Multiplicatively dependent integer vectors on a hyperplane.
- 33èmes Journées Arithmétiques, University of Luxembourg, Luxembourg, July 2025. A uniform formula on the number of integer matrices with given determinant and height.
- Combinatorial Number Theory And Connected Topics (CONTACT - IV) (online), March 2025. A uniform formula on the number of integer matrices with given determinant and height.
- Joint AustMS-NZMS-AMS Conference, University of Auckland, Auckland, New Zealand, December 2024. A uniform formula on the number of integer matrices with given determinant and height.
- 7th Australian Mathematical Sciences Students Conference 2024, Western Sydney University, Sydney, Australia, December 2024. Counting rational matrices with bounded height.
- 12th Number Theory Down Under Conference, La Trobe University, Bendigo, Australia, September 2024. A uniform formula on the number of integer matrices with given determinant and height.
- UNSW School of Mathematics and Statistics 11th Postgraduate Seminar, August 2024. Arithmetic statistics of rational matrices of bounded height.
- Combinatorial Number Theory And Connected Topics (CONTACT - III) (online), March 2024. Counting products of integer matrices with bounded height.
- First Joint IIIMT – Algebra Forum Conference 2023, Universitas Mataram, Mataram, Indonesia (online), December 2023. Arithmetic statistics of rational matrices of bounded height.
- The 67th Annual Meeting of the Australian Mathematical Society (AustMS 2023), University of Queensland, Brisbane, Australia, December 2023. Arithmetic statistics of rational matrices of bounded height Slides
- 11th Number Theory Down Under Conference, Mathematical Science Institute, Australian National University Canberra, Australia, September 2023. Counting products of integer matrices with bounded height. Slides
- MathTech 2020 , Universiti Sains Malaysia, Penang, Malaysia (online), November 2020. On the number of different entries in involutory MDS matrices over finite fields of characteristic two.
Lies are the purest form of love! - Ai Hoshino
Education
PhD in Mathematics, University of New South Wales, Sydney, Australia (2022-2026 (expected))
- Thesis: Arithmetic statistics of algebraic groups
- Advisors: Alina Ostafe & Igor E. Shparlinski
MSc (M.Si.) in Mathematics, Institut Teknologi Bandung, Bandung, Indonesia (2020-2021)
- Thesis: Polynomial parametrization for some classes of maximum Sidon sets over finite fields
- Advisor: Aleams Barra (also well-known for his YouTube channel. He might be the most-subscribed Indonesian lecturer in Youtube.)
BSc (S.Si.) in Mathematics, Institut Teknologi Bandung, Bandung, Indonesia (2016-2020)
- Thesis: On the mumber of different entries in involutory MDS matrices over finite fields of characteristic two
- Advisor: Aleams Barra
Our everyday lives, may, in fact, be a series of miracles. - Mio Naganohara