Research

Broadly speaking, I am interested in discrete mathematics, especially analytic number theory, combinatorics, and finite fields. For my PhD project, I work on arithmetic statistics of multivariate Diophantine equations (related to algebraic groups), using techniques from analytic number theory. During my bachelor and master studies, I did a total of two final projects over finite fields. However, I am open for learning other topics.

Publications

• Aleams Barra and Muhammad Afifurrahman. The total vertex irregularity strength for cubic graphs with a perfect matching, Discrete Math., 348 5 (2025), 114402.
• Muhammad Afifurrahman and Chandler C. Corrigan. Solutions to multiplicative Diophantine equations in orthotopes, submitted. arXiV:2501.15372.
• Muhammad Afifurrahman. A uniform formula on the number of integer matrices with given determinant and height, submitted. arXiV:2407.08191.
• Muhammad Afifurrahman, Vivian Kuperberg, Alina Ostafe, and Igor E. Shparlinski. Statistics of ranks, determinants and characteristic polynomials of rational matrices, Forum Math., to appear. arXiV:2401.10086.
• Muhammad Afifurrahman. Some counting questions for matrix products, Bull. Aust. Math. Soc. 110 1 (2024), 32-43. arXiV:2306.04885.
• Muhammad Afifurrahman and Aleams 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.

Other projects coming soon.

Research Talks

Slides supplied when available.

• 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. Slides
• 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.
• 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.
• UNSW Number Theory Seminar, May 2024. Arithmetic statistics of rational matrices of bounded height. Slides
• 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.

What I can do right now… is to keep composing songs[papers]… - Kanade Yoisaki

Education

PhD in Mathematics, University of New South Wales, Sydney, Australia (2022-2026 (expected))

• Current thesis topic: Arithmetic statistics of multivariable Diophantine equations
• 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