My current mathematical interests lie at the interface of theoretical mathematics and mathematical modelling, with a focus on developing mathematically rigorous frameworks for analysing structured and biological data. Acentral theme of my work - particularly algebraic and geometric structure- can be used to represent complex systems in a principled and interpretable way.
During my Bachelor's degree, I mainly focused on commutative algebra and module theory. Under the supervision of Prof. Indah Emilia Wijayanti, I wrote a Bachelor thesis on some properties of certain maps between a collection of submodules of a module and a collection of ideals of a commutative ring. In particular, I studied some sufficient conditions for these maps to be lattice homomorphism or anti-homomorphism.
During my Master's degree, I studied some algebraic aspects of geometric objects. Under the supervision of Dr. Bram Petri, I wrote a Master thesis that mainly discusses hyperbolic manifolds. In particular, I studied the number of complete hyperbolic manifolds of certain dimension with volume less than a given positive number.
During my doctoral studies at Aalto University, I worked on mathematical approaches to phylogenetics. My research focused on the study of phylogenetic invariants, group-based models, and stochastic processes on discrete structures. This work contributed to understanding how mathematical structure governs evolutionary models and how it can be used to distinguish between different phylogenetic scenarios.
A key aspect of my doctoral work was the use of algebraic tools to analyse identifiability and structural properties of statistical models arising in biology. This experience shaped my broader research perspective: rather than treating biological data purely as a statistical object, I approach it as a structured mathematical entity, where algebraic, geometric, and combinatorial properties play a fundamental role.
In my current postdoctoral position at the University of Jyväskylä, I have expanded my research toward algorithmic and probabilistic modelling of biological sequence data. In particular, I have been developing new modelling frameworks based on partial order alignments and stochastic representations of sequence data. These models aim to capture complex dependencies that are not well represented by classical alignment methods. This work integrates discrete mathematics, probability, and computational implementation, and has strengthened my ability to connect theoretical ideas with data-driven applications.
Overall, my research to date has developed along two complementary directions: (i) the use of mathematical methods to study the structure of complex models, and (ii) the development of computational and probabilistic frameworks that translate these structures into practical modelling tools.
Publications and Preprints
Puguh Wahyu Prasetyo and Muhammad Ardiyansyah, Gardner problem revisited: further properties of IndaH radical., BAREKENG: Journal of Mathematics and Its Application, Vol 20 No 3 (2026), https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/21435.
Puguh Wahyu Prasetyo, Adhy Kurnia Triatmaja, Fariz Setyawan, Muhammad Ardiyansyah, Angger Hafid Prabawa, Shafa Violeta Chaila Putri, Ayoudya Titan Widyasmara, Hafizh Naufal Azmi, and Samsul Arifin, ADEBOT1: revolutionizing educational robotics with Arduino and Lie algebra simulation. Submitted to a journal.
Puguh Wahyu Prasetyo, Adhy Kurnia Triatmaja, Fariz Setyawan, Angger Hafid Prabawa, Hafiz Naufal Azmi, Muhammad Ardiyansyah, and Samsul Arifin, Optimization of robotic movement: applying Lie algebra to improve the performance of mbot2, International Journal on Advanced Science, Engineering, and Information Technology, vol. 15, no. 2, pp. 376–386, Apr. 2025. https://doi.org/10.18517/ijaseit.15.2.20501
Puguh Wahyu Prasetyo, Joe Repka, and Muhammad Ardiyansyah. A note on the n-array unit graphs. Submitted to a journal.
Muhammad Ardiyansyah and Luca Sodomaco, Dimensions of Higher Order Factor Analysis Models, Algebraic Statistics 14-1 (2023), 91-108. DOI: 10.2140/astat.2023.14.91.
Muhammad Ardiyansyah, Dimitra Kosta, and Jordi Roca-Lacostena, Embeddability of centrosymmetric matrices capturing the double-helix structure in natural and synthetic DNA, J. Math. Biol. 86, 69 (2023). https://doi.org/10.1007/s00285-023-01895-8.
Muhammad Ardiyansyah, Distinguishing level-2 phylogenetic networks using phylogenetic invariants, Preprint arXiv:2104.12479. (Revision submitted to a journal)
Muhammad Ardiyansyah, Indah Emilia Wijayanti, and Puguh Wahyu Prasetyo, On a class of λ -modules, Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 3, Mar. 2021, pp. 329 -34. doi:10.37863/umzh.v73i3.513.
Muhammad Ardiyansyah, Kaie Kubjas, and Dimitra Kosta, The model-specific Markov embedding problem for symmetric group-based models, J. Math. Biol. 83, 33 (2021). https://doi.org/10.1007/s00285-021-01656-5.
Books and Dissertations
Burhanudin A Nugroho, Uswatun Khasanah, Puguh Wahyu Prasetyo, Muhammad Ardiyansyah. Permodelan Matematika (Bahasa Indonesia). UAD Press.
Muhammad Ardiyansyah. Doctoral thesis: algebraic aspects of hidden variable models (2023).
Puguh Wahyu Prasetyo and Muhammad Ardiyansyah. Pengantar Teori Ring (Bahasa Indonesia). UAD Press.
Others
Industrial design certificate for "Robot Mobil ADEBOT1" configuration. Puguh Wahyu Prasetyo, Adhy Kurnia Triatmaja, Fariz Setyawan, Angger Hafid Prabawa, Hafiz Naufal Azmi, Muhammad Ardiyansyah, and Samsul Arifin.
In preparation
Ardiyansyah et al. POAnoise: A Denoising Pipeline for High-Throughput DNA Sequencing Accuracy.